Organization: Pearson
Product Name: enVisionmath2.0 Grade 1 2017
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Curriculum Standards:


Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. - 4.1.2.6
Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. - 4.1.2.5
Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. - 4.1.2.3
Create a line plot to represent a given or generated data set, and analyze the data to answer questions and solve problems, recognizing the outliers and generating the median. - 5.DS.A.2
Create a line graph to represent a data set, and analyze the data to answer questions and solve problems. - 5.DS.A.1
Understand two-digit numbers are composed of ten(s) and one(s). - 1.NBT.A.2
Compare two two-digit numbers using the symbols >, = or <. - 1.NBT.A.3
Recognize that the volume of rectangular prisms can be determined by the number of cubes (n) and by the product of the dimensions of the prism (a × b × c = n). Know that rectangular prisms of different dimensions (p, q, and r) can have the same volume if a × b × c = p × q × r = n. - 5.GM.2.1
Understand that 10 can be thought of as a bundle of 10 ones – called a “ten”. - 1.NBT.A.1
Count by 10s to 120 starting at any number. - 1.NBT.A.4
Use patterns to add numbers together. - K.OA.9
Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones. - NC.2.NBT.1
Count within 1000; skip-count by 5s, 10s, and 100s. - NC.2.NBT.2
Read and write numbers, within 1000, using base-ten numerals, number names, and expanded form. - NC.2.NBT.3
Compare two three-digit numbers based on the value of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. - NC.2.NBT.4
Add up to three two-digit numbers using strategies based on place value and properties of operations. - NC.2.NBT.6
Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900. - NC.2.NBT.8
Define a first quadrant Cartesian coordinate system. - 5.GM.C.6
Plot and interpret points in the first quadrant of the Cartesian coordinate plane. - 5.GM.C.7
Show numbers in many ways. - K.OA.1
Represent addition as adding to a number. - K.OA.2
Determine if a set of objects has an odd or even number of members. - 2.RA.B.2
Find the total number of objects arranged in a rectangular array with up to 5 rows and 5 columns, and write an equation to represent the total as a sum of equal addends. - 2.RA.B.3
Solve addition problems. - K.OA.7
Tell time to the hour and half-hour (analog and digital). - 1.GM.3.1
Building and drawing triangles, rectangles, squares, hexagons, circles. - NC.K.G.5.a
Building cubes, cones, spheres, and cylinders. - NC.K.G.5.b
Represent problems using equations with a letter standing for the unknown quantity. - NC.4.OA.3.c
Interpret remainders in word problems. - NC.4.OA.3.b
Use estimation strategies to assess reasonableness of answers. - NC.4.OA.3.a
Create simple patterns using objects, pictures, numbers and rules. Identify possible rules to complete or extend patterns. Patterns may be repeating, growing or shrinking. Calculators can be used to create and explore patterns. - 1.2.1.1
Add, subtract, multiply, or divide to solve one-step word problems involving whole number measurements of length, weight, and capacity in the same customary units. - NC.3.MD.2.c
Use math to explain what you know about counting. - K.NCC.11
Estimate and measure lengths in customary units to the quarter-inch and half-inch, and feet and yards to the whole unit. - NC.3.MD.2.a
Estimate and measure capacity and weight in customary units to a whole number: cups, pints, quarts, gallons, ounces, and pounds. - NC.3.MD.2.b
Compare groups by counting. - K.NCC.15
Count to the numbers 6 and 7. - K.NCC.18
Read and write the numbers 6 and 7. - K.NCC.19
Compare two decimals to thousandths based on the value of the digits in each place, using >, =, and < symbols to record the results of comparisons. - NC.5.NBT.3.b
Write decimals using base-ten numerals, number names, and expanded form. - NC.5.NBT.3.a
Identify, create, complete, and extend repeating, growing, and shrinking patterns with quantity, numbers, or shapes in a variety of real-world and mathematical contexts. - 1.A.1.1
Use doubles to solve problems. - 1.OA.11
Add by counting on from a number. - 1.OA.10
Count on to add using a number line. - 1.OA.19
Use structure and identify patterns in order to solve problems. - 1.OA.18
Solve word problems by drawing pictures and writing equations. - 1.OA.17
Use addition facts to 10 to solve subtraction problems. - 1.OA.16
Count back to solve subtraction problems. - 1.OA.15
Use the same addends to write two different equations with the same sum. - 1.OA.14
Use a ten-frame to solve addition facts with 5 and 10. - 1.OA.13
Solve problems using near doubles facts. - 1.OA.12
Recognize, represent and apply the number properties (commutative, identity, and associative properties of addition and multiplication) using models and manipulatives to solve problems. - 3.A.2.2
Find unknowns represented by symbols in arithmetic problems by solving one-step open sentences (equations) and other problems involving addition, subtraction, and multiplication. Generate real-world situations to represent number sentences. - 3.A.2.1
Construct viable arguments and critique the reasoning of others. - K.MP.3
Generate two numerical patterns using two given rules. - NC.5.OA.3
Write, explain, and evaluate numerical expressions involving the four operations to solve up to two-step problems. Include expressions involving: - NC.5.OA.2
Use doubles facts to solve doubles-plus-one facts. - 1.OA.22
Memorize doubles facts. - 1.OA.21
Count on to add using an open number line. - 1.OA.20
Make subtraction easier by making 10 to subtract. - 1.OA.29
Use a number line to subtract by counting on or counting back. - 1.OA.28
Critique the reasoning of others by using known information about addition and subtraction. - 1.OA.27
Solve different types of addition word problems. - 1.OA.26
Solve addition problems using different strategies. - 1.OA.25
Make 10 to add numbers to 20. - 1.OA.24
Use doubles facts to solve doubles-plus-2 facts. - 1.OA.23
Explain strategies used to solve subtraction problems. - 1.OA.33
Use addition facts to find subtraction facts. - 1.OA.32
Make addition and subtraction facts using the same three numbers. - 1.OA.31
Count on to subtract using 10 as a landmark. - 1.OA.30
Use words to compare objects according to length, size, weight and position. - K.3.2.1
Decompose a rectangle into smaller rectangles to find the area of the original rectangle. - 3.GM.C.14
Find rectangular arrangements that can be formed for a given area. - 3.GM.C.13
Making a two-dimensional composite shape using rectangles, squares, trapezoids, triangles, and half-circles naming the components of the new shape. - NC.1.G.2.a
Multiply whole-number side lengths to solve problems involving the area of rectangles. - 3.GM.C.12
Making a three-dimensional composite shape using cubes, rectangular prisms, cones, and cylinders, naming the components of the new shape. - NC.1.G.2.b
Demonstrate that tiling a rectangle to find the area and multiplying the side lengths result in the same value. - 3.GM.C.11
Label area measurements with squared units. - 3.GM.C.10
Construct equal-sized portions through fair sharing including length, set, and area models for halves, thirds, and fourths. - 2.N.3.2
Identify the parts of a set and area that represent fractions for halves, thirds, and fourths. - 2.N.3.1
Order 2 or 3 objects using measurable attributes, such as length and weight. - K.3.2.2
Properties of operations - NC.1.NBT.6.d
The relationship between addition and subtraction - NC.1.NBT.6.e
Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. - M.4.13
Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. - M.4.12
Concrete models and drawings - NC.1.NBT.6.a
Number lines - NC.1.NBT.6.b
Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. - M.4.11
Strategies based on place value - NC.1.NBT.6.c
Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. - M.4.10
Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). - M.4.17
Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100 (e.g., express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100). Instructional Note: Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade. - M.4.16
Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...) - M.4.19
Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, = or <, and justify the conclusions by using a visual model. - M.4.18
Generate measurement data to the nearest whole unit, and display the data in a line plot. - 2.DS.A.2
Draw a picture graph or a bar graph to represent a data set with up to four categories. - 2.DS.A.3
Create a line plot to represent a set of numeric data, given a horizontal scale marked in whole numbers. - 2.DS.A.1
Solve problems using information presented in line plots, picture graphs and bar graphs. - 2.DS.A.4
Draw conclusions from line plots, picture graphs and bar graphs. - 2.DS.A.5
Generate two numeric patterns given two rules. - 5.RA.A.1a
Graph numeric patterns on the Cartesian coordinate plane. - 5.RA.A.1c
Translate two numeric patterns into two sets of ordered pairs. - 5.RA.A.1b
Identify the relationship between two numeric patterns. - 5.RA.A.1d
Measure angles in whole-number degrees using a protractor and sketch angles of specified measure. - M.4.24
Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: - M.4.23
Draw points, lines, line segments, rays, angles (right, acute, obtuse) and perpendicular and parallel lines. Identify these in two-dimensional figures. - M.4.26
Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems (e.g., by using an equation with a symbol for the unknown angle measure). - M.4.25
Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. - M.4.20
Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). - M.4.22
Apply the area and perimeter formulas for rectangles in real world and mathematical problems by viewing the area formula as a multiplication equation with an unknown factor. (e.g., find the width of a rectangular room given the area of the flooring and the length.) - M.4.21
Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. - M.4.28
Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. - M.4.27
Use the relationship between addition and subtraction to solve problems. - 2.NBT.B.9
Add or subtract within 1000, and justify the solution. - 2.NBT.B.8
Add up to four two-digit numbers. - 2.NBT.B.7
Demonstrate fluency with addition and subtraction within 100. - 2.NBT.B.6
Use addition and subtraction within 100 to solve problems involving lengths that are given in the same units. - 2.GM.C.8
Represent whole numbers as lengths on a number line, and represent whole-number sums and differences within 100 on a number line. - 2.GM.C.9
Compose simple shapes to form larger shapes using manipulatives. - K.GM.C.10
Interpret quotients of whole numbers. - 3.RA.A.2
Interpret products of whole numbers. - 3.RA.A.1
Use multiplication and division within 100 to solve problems. - 3.RA.A.4
Describe in words or drawings a problem that illustrates a multiplication or division situation. - 3.RA.A.3
Determine the unknown number in a multiplication or division equation relating three whole numbers. - 3.RA.A.5
The student will tell time and write time to the nearest five minutes, using analog and digital clocks. - 2.9
Explain the relationship between the size of the unit of measurement and the number of units needed to measure the length of an object. - 2.GM.2.1
Explain the relationship between length and the numbers on a ruler by using a ruler to measure lengths to the nearest whole unit. - 2.GM.2.2
Multiply decimals with a product to thousandths using models, drawings, or strategies based on place value. - NC.5.NBT.7.b
Add and subtract decimals to thousandths using models, drawings or strategies based on place value. - NC.5.NBT.7.a
Use estimation strategies to assess reasonableness of answers. - NC.5.NBT.7.d
Divide a whole number by a decimal and divide a decimal by a whole number, using repeated subtraction or area models. Decimals should be limited to hundredths. - NC.5.NBT.7.c
Understand that the volume of a right rectangular prism can be found by stacking multiple layers of the base. - 5.GM.B.4b
Describe a cube with edge length 1 unit as a “unit cube” and is said to have “one cubic unit” of volume and can be used to measure volume. - 5.GM.B.4a
Graph points in the first quadrant of a coordinate plane, and identify and interpret the x and y coordinates to solve problems. - NC.5.G.1
Classify quadrilaterals into categories based on their properties. - NC.5.G.3
Parentheses, using the order of operations. - NC.5.OA.2.a
Commutative, associative and distributive properties. - NC.5.OA.2.b
The student will create equations to represent equivalent mathematical relationships. - 3.17
The student will round whole numbers, 9,999 or less, to the nearest ten, hundred, and thousand. - 3.1b
Find the measure of an angle that turns through a fraction of a circle. - 4.MD.13
Add to/Take from- Change Unknown - NC.2.OA.1.b.1
Recognize and draw lines, rays, and angles with different measures. - 4.MD.12
Add to/Take from- Change Unknown - NC.2.OA.1.b.2
Find the unknown length or width of a rectangle using the known area or perimeter. - 4.MD.10
Measure the length of an object in standard units by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. - NC.2.MD.1
Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. - NC.2.MD.7
Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points and represent whole-number sums and differences, within 100, on a number line. - NC.2.MD.6
Estimate lengths in using standard units of inches, feet, yards, centimeters, and meters. - NC.2.MD.3
Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. - NC.2.MD.2
Use addition and subtraction, within 100, to solve word problems involving lengths that are given in the same units, using equations with a symbol for the unknown number to represent the problem. - NC.2.MD.5
Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. - NC.2.MD.4
Unitize by making a ten from a collection of ten ones. - NC.1.NBT.2.a
One-Step problems: - NC.2.OA.1.a
Model the numbers from 11 to 19 as composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones. - NC.1.NBT.2.b
Two-Step problems involving single digits: - NC.2.OA.1.b
Demonstrate that the numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens, with 0 ones. - NC.1.NBT.2.c
The student will compare fractions having like and unlike denominators, using words and symbols (>, <, =, or ≠), with models. - 3.2c
The student will represent fractions and mixed numbers with models and symbols. - 3.2b
The student will name and write fractions and mixed numbers represented by a model. - 3.2a
Solve problems involving addition and subtraction of minutes. - 3.GM.B.6
Estimate time intervals in minutes. - 3.GM.B.5
Use the four operations to solve problems involving lengths, liquid volumes or weights given in the same units. - 3.GM.B.8
Measure or estimate length, liquid volume and weight of objects. - 3.GM.B.7
Tell and write time to the nearest minute. - 3.GM.B.4
The student will create and solve single-step and multistep practical problems involving sums or differences of two whole numbers, each 9,999 or less. - 3.3b
Use addition and subtraction to solve problems with unknown angle measures. - 4.MD.16
The student will estimate and determine the sum or difference of two whole numbers. - 3.3a
Use a protractor to measure and draw angles. - 4.MD.15
Use known angle measures to measure unknown angles. - 4.MD.14
Compare and order fractions and decimals, including mixed numbers and fractions less than one, and locate on a number line. - 5.N.2.3
Recognize and generate equivalent decimals, fractions, mixed numbers, and fractions less than one in various contexts. - 5.N.2.4
Represent decimal fractions (e.g.,1/10, 1/100) using a variety of models (e.g., 10 by 10 grids, rational number wheel, base-ten blocks, meter stick) and make connections between fractions and decimals. - 5.N.2.1
Represent, read and write decimals using place value to describe decimal numbers including fractional numbers as small as thousandths and whole numbers as large as millions. - 5.N.2.2
The student will solve single-step practical problems involving multiplication of whole numbers, where one factor is 99 or less and the second factor is 5 or less. - 3.4d
Model and explain how fractions can be represented by multiplying a whole number by a unit fraction, using this understanding to multiply a whole number by any fraction less than one. - NC.4.NF.4.a
Solve word problems involving multiplication of a fraction by a whole number. - NC.4.NF.4.b
The student will demonstrate fluency with multiplication facts of 0, 1, 2, 5, and 10. - 3.4c
The student will create and solve single-step practical problems that involve multiplication and division through 10 x 10. - 3.4b
The student will represent multiplication and division through 10 × 10, using a variety of approaches and models. - 3.4a
Demonstrate fluency with addition and subtraction within 10. - 1.RA.C.8
Recognize area as an attribute of plane figures and understand concepts of area measurement. A square with side length 1 unit, called “a unit square,” is said to have “one square unit” of area and can be used to measure area. - M.3.20a
Add and subtract within 20. - 1.RA.C.7
Recognize area as an attribute of plane figures and understand concepts of area measurement. A plane figure which can be covered without gaps or overlaps by b unit squares is said to have an area of b square units. - M.3.20b
Compose and decompose numbers up to 10 with objects and pictures. - K.1.2.2
Use objects and draw pictures to find the sums and differences of numbers between 0 and 10. - K.1.2.1
Evaluate expressions and solve equations involving variables when values for the variables are given. - 5.2.3.3
Make sense of problems and persevere in solving them. - MP.1
Reason abstractly and quantitatively. - MP.2
Look for and make use of structure. - MP.7
Look for and express regularity in repeated reasoning. - MP.8
Construct viable arguments and critique the reasoning of others. - MP.3
Model with mathematics. - MP.4
Use appropriate tools strategically. - MP.5
Attend to precision. - MP.6
Describe the numerator as representing the number of pieces being considered. - 3.NF.A.2a
Add and subtract fractions, including mixed numbers, with unlike denominators using related fractions: halves, fourths and eighths; thirds, sixths, and twelfths; fifths, tenths, and hundredths. - NC.5.NF.1
Use fractions to model and solve division problems. - NC.5.NF.3
Describe the denominator as the number of pieces that make the whole. - 3.NF.A.2b
The student will estimate and use U.S. Customary and metric units to measure liquid volume in cups, pints, quarts, gallons, and liters. - 3.7b
The student will estimate and use U.S. Customary and metric units to measure length to the nearest ½ inch, inch, foot, yard, centimeter, and meter. - 3.7a
Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction, including mixed numbers. - NC.5.NF.4
Use words or mathematical symbols to express a rule for a given pattern. - 4.RA.C.7
Generate a number pattern that follows a given rule. - 4.RA.C.6
Relate volume to the operations of multiplication and addition and solve real-world and mathematical problems involving volume. Recognize volume as additive and find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real-world problems. - M.5.22c
Solve one-step word problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions using area and length models, and equations to represent the problem. - NC.5.NF.7
Relate volume to the operations of multiplication and addition and solve real-world and mathematical problems involving volume. Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole number edge lengths in the context of solving real-world and mathematical problems. - M.5.22b
Relate volume to the operations of multiplication and addition and solve real-world and mathematical problems involving volume. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes (e.g., to represent the associative property of multiplication). - M.5.22a
The student will estimate and count the number of square units needed to cover a given surface in order to determine its area. - 3.8b
The student will estimate and measure the distance around a polygon in order to determine its perimeter using U.S. Customary and metric units. - 3.8a
Reason with two-dimensional shapes and their attributes. - NC.3.G.1
Use strategies and algorithms based on knowledge of place value, equality and properties of addition and multiplication to multiply a two-digit number by a one-digit number. - 3.N.2.8
Recognize the relationship between multiplication and division to represent and solve real-world problems. - 3.N.2.7
Recognize when to round numbers and apply understanding to round numbers to the nearest ten thousand, thousand, hundred, and ten and use compatible numbers to estimate sums and differences. - 3.N.2.4
Use strategies and algorithms based on knowledge of place value and equality to fluently add and subtract multi-digit numbers. - 3.N.2.3
Represent division facts by using a variety of approaches, such as repeated subtraction, equal sharing and forming equal groups. - 3.N.2.6
Use addition and subtraction to solve real-world and mathematical problems involving whole numbers. Use various strategies, including the relationship between addition and subtraction, the use of technology, and the context of the problem to assess the reasonableness of results. - 3.N.2.5
Identify and name basic two- and three-dimensional shapes, such as squares, circles, triangles, rectangles, trapezoids, hexagons, cubes, rectangular prisms, cones, cylinders and spheres. - 2.3.1.2
Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. - 4.3.3.2
Demonstrate fluency of multiplication facts with factors up to 10. - 3.N.2.2
Represent multiplication facts by using a variety of approaches, such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line and skip counting. - 3.N.2.1
The student will solve practical problems related to elapsed time in one-hour increments within a 12-hour period. - 3.9b
The student will tell time to the nearest minute, using analog and digital clocks. - 3.9a
Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. - 4.4.1.1
Skip count by tens to 100. - K.NCC.41
Count by tens and ones from any number up to 100. - K.NCC.44
Explain that the length of a bar in a bar graph or the number of objects in a picture graph represents the number of data points for a given category. - 2.D.1.1
Organize a collection of data with up to four categories using pictographs and bar graphs with intervals of 1s, 2s, 5s or 10s. - 2.D.1.2
Write and solve one-step word problems involving addition or subtraction using data represented within pictographs and bar graphs with intervals of one. - 2.D.1.3
Draw conclusions and make predictions from information in a graph. - 2.D.1.4
Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. - 4.GM.A.1
Classify two-dimensional shapes by their sides and/or angles. - 4.GM.A.2
Ask and answer questions about the total number of data points. - NC.1.MD.4.a
Ask and answer questions about how many in each category. - NC.1.MD.4.b
Ask and answer questions about how many more or less are in one category than in another. - NC.1.MD.4.c
Construct lines of symmetry for a two-dimensional figure. - 4.GM.A.3
Tell time to the half hour. - 1.MD.13
Use reasoning to tell and write time. - 1.MD.14
Choose an appropriate tool and use it to measure a given object. - 1.MD.10
Tell time to the hour. - 1.MD.11
Tell time to the hour using analog and digital clocks. - 1.MD.12
Read and write numerals and represent a number of objects with a written numeral. - 1.NS.A.2
Understand the whole is partitioned into equal parts. - 3.NF.A.3b
Count to 120, starting at any number less than 120. - 1.NS.A.1
Count to the numbers 8 and 9. - K.NCC.20
Understand the whole is the interval from 0 to 1. - 3.NF.A.3a
Count by 5s to 100 starting at any multiple of five. - 1.NS.A.4
Count backward from a given number between 20 and 1. - 1.NS.A.3
Show how to make a group of ten. - K.NCC.24
Compare groups of numbers using numerals to 10. - K.NCC.27
Compare two numbers. - K.NCC.29
Understand a fraction represents the endpoint of the length a given number of partitions from 0. - 3.NF.A.3c
Read and write fractions with words and symbols. Recognize that fractions can be used to represent parts of a whole, parts of a set, points on a number line, or distances on a number line. - 3.1.3.1
Understand that the size of a fractional part is relative to the size of the whole. - 3.1.3.2
Count and write numbers 11 and 12. - K.NCC.32
Count and write numbers 13, 14, and 15. - K.NCC.33
Count forward from any number to a number within 20. - K.NCC.36
Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. - 4.NF.B.6
Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. - 4.NF.B.7
Use patterns to count to 30. - K.NCC.39
Understand addition and subtraction of fractions as joining or composing and separating or decomposing parts referring to the same whole. - 4.NF.B.4
Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. - 4.NF.B.5
Interpret organized data. - 1.MD.3
Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. - 5.1.1.4
Estimate solutions to arithmetic problems in order to assess the reasonableness of results. - 5.1.1.3
Collect and organize information using a picture graph. - 1.MD.2
Use perseverance to solve problems about sets of data. - 1.MD.5
Use a picture graph to interpret data. - 1.MD.4
Indirectly compare objects by length. - 1.MD.7
Order objects by length. - 1.MD.6
Solve problems involving multiplication of a fraction by a whole number. - 4.NF.B.8
Use cubes and other units to compare lengths and heights of objects. - 1.MD.9
Use objects to measure length. - 1.MD.8
Organize data into categories. - 1.MD.1
Compare and order whole numbers up to 1000. - 2.1.1.5
Use place value to describe whole numbers between 10 and 1000 in terms of hundreds, tens and ones. Know that 100 is 10 tens, and 1000 is 10 hundreds. - 2.1.1.2
Find 10 more or 10 less than a given three-digit number. Find 100 more or 100 less than a given three-digit number. - 2.1.1.3
Read, write and represent whole numbers up to 1000. Representations may include numerals, addition, subtraction, multiplication, words, pictures, tally marks, number lines and manipulatives, such as bundles of sticks and base 10 blocks. - 2.1.1.1
Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. - 5.1.1.2
Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. - 5.1.1.1
Write numerals to show how many objects are in a group. - 1.NC.6
Find better and faster ways to solve problems. - 1.NC.7
Find number patterns on a number chart. - 1.NC.4
Count to 120 using an open number line. - 1.NC.5
Represent and identify unit fractions using area and length models. - NC.3.NF.1.b
Explain that a unit fraction is one of those parts. - NC.3.NF.1.a
Read and write numbers 11 to 19. - 1.NC.8
Show groups of 10 with connecting cubes. - 1.NC.9
Solve multi-step problems that require measurement conversions. - 5.GM.D.9
Count by 1s to 120. - 1.NC.2
Count on a number chart to 120 - 1.NC.3
Count by 10s to 120. - 1.NC.1
Solve one- and two-step problems using categorical data represented with a frequency table, pictograph, or bar graph with scaled intervals. - 3.D.1.2
Order and compare unit fractions and fractions with like denominators by using models and an understanding of the concept of numerator and denominator. - 3.1.3.3
Relate area to the operations of multiplication and addition. Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c. Use area models to represent the distributive property in mathematical reasoning. - M.3.22c
Relate area to the operations of multiplication and addition. Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning. - M.3.22b
Relate area to the operations of multiplication and addition. Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths. - M.3.22a
Convert measurements of capacity, length and weight within a given measurement system. - 5.GM.D.8
Create and use input-output rules involving addition, subtraction, multiplication and division to solve problems in various contexts. Record the inputs and outputs in a chart or table. - 4.2.1.1
Relate area to the operations of multiplication and addition. Recognize area as additive and find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems. - M.3.22d
Partition circles and rectangles into two and four equal shares. - NC.1.G.3
Write, evaluate and interpret numeric expressions using the order of operations. - 5.RA.B.3
Translate written expressions into algebraic expressions. - 5.RA.B.4
Summarize and construct a data set with multiple categories using a frequency table, line plot, pictograph, and/or bar graph with scaled intervals. - 3.D.1.1
Use parentheses, brackets or braces in numerical expressions and evaluate expressions with these symbols. - M.5.1
Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. - M.5.4
Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. - M.5.5
Write simple expressions that record calculations with numbers and interpret numerical expressions without evaluating them. (e.g., Express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.) - M.5.2
Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. (e.g., Given the rule “Add 3” and the starting number 0 and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.) - M.5.3
Fluently multiply multi-digit whole numbers using the standard algorithm. - M.5.8
Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. - M.5.9
Use place value understanding to round decimals to any place. - M.5.7
Create and analyze line and double-bar graphs with whole numbers, fractions, and decimals increments. - 5.D.1.2
Look for and make use of structure. - 1.MP.7
Attend to precision. - 1.MP.6
Look for and express regularity in repeated reasoning. - 1.MP.8
Multiply a whole number by a fraction. - 5.NC.61
Make sense of problems and persevere in solving them. - 1.MP.1
Construct viable arguments and critique the reasoning of others. - 1.MP.3
Multiply two fractions. - 5.NC.65
Reason abstractly and quantitatively. - 1.MP.2
Use models to multiply two fractions. - 5.NC.64
Use appropriate tools strategically. - 1.MP.5
Multiply fractions and whole numbers. - 5.NC.63
Model with mathematics. - 1.MP.4
Multiply a fraction by a whole number. - 5.NC.62
Locate points on a coordinate grid. - 5.G.1
Graph points on a coordinate grid. - 5.G.2
Solve real-world problems by graphing points. - 5.G.3
Classify triangles by their angles and sides. - 5.G.5
Classify quadrilaterals by their properties. - 5.G.6
Add and subtract mixed numbers using equivalent fractions and a common denominator. - 5.NC.59
Classify quadrilaterals using a hierarchy. - 5.G.7
Counting on - NC.1.OA.6.a
Using a number line - NC.1.OA.6.e
Using the relationship between addition and subtraction - NC.1.OA.6.d
Decomposing a number leading to a ten - NC.1.OA.6.c
Making ten - NC.1.OA.6.b
Use multiplication to divide a whole number by a unit fraction. - 5.NC.72
Implement division of fractions to show quotients as fractions and mixed numbers. - 5.NC.71
Understand how fractions are related to division. - 5.NC.70
Creating equivalent but simpler or known sums - NC.1.OA.6.f
Solve multi-step problems involving division with unit fractions. - 5.NC.76
Use models to divide whole numbers and unit fractions. Check your answer using multiplication. - 5.NC.75
Use models to divide unit fractions by non-zero whole numbers. - 5.NC.74
Use models such as pictorial models or a number line to show dividing a whole number by a unit fraction. - 5.NC.73
Compare the size of the product to the size of one factor without multiplying to consider multiplication as scaling. - 5.NC.68
Use models, equations, and previously learned strategies to multiply mixed numbers. - 5.NC.67
Find the area of a rectangle using fractions and diagrams. - 5.NC.66
Create or extend a number sequence based on a rule. Identify features of the pattern in the sequence that are not described by the rule. - 4.OA.11
Use a rule to extend a number pattern and solve a problem. Identify features of the pattern. - 4.OA.12
Use multiplication to find multiples of a given number. - 4.OA.10
Generate a shape pattern that follows a given rule and predict a shape in the pattern. - 4.OA.13
Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each (e.g., describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8). - M.3.2
Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays and measurement quantities (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). - M.3.3
Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each (e.g., describe context in which a total number of objects can be expressed as 5 × 7). - M.3.1
Understand division as an unknown-factor problem (e.g., find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8). - M.3.6
Learn multiplication tables (facts) with speed and memory in order to fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows that 40 ÷ 5 = 8) or properties of operations by the end of Grade 3. - M.3.7
Determine the unknown whole number in a multiplication or division equation relating three whole numbers (e.g., determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = ? ÷ 3, 6 × 6 =?). - M.3.4
Apply properties of operations as strategies to multiply and divide (e.g., If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known: Commutative Property of Multiplication. 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30: Associative Property of Multiplication. Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56: Distributive Property. Instructional Note: Students need not use formal terms for these properties. - M.3.5
Solve two-step word problems using the four operations, represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Instructional Note: This standard is limited to problems posed with whole numbers and having whole number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations). - M.3.8
Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain those using properties of operations (e.g., observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addends). - M.3.9
The student will collect, organize, and represent data in pictographs or bar graphs. - 3.15a
The student will read and interpret data represented in pictographs and bar graphs. - 3.15b
Draw conclusions from object graphs, picture graphs, T-charts and tallies. - 1.DS.A.2
Collect, organize and represent data with up to three categories. - 1.DS.A.1
Recognize the relative size of customary units of length and convert from a larger unit to a smaller unit. - 4.MD.5
Recognize the relative size of customary units of capacity and convert from a larger unit to a smaller unit. - 4.MD.6
Recognize the relative size of customary units of weight and convert from a larger unit to a smaller unit. - 4.MD.7
Recognize the relative size of metric units of length and convert from a larger unit to a smaller unit. - 4.MD.8
Use an understanding of place value to multiply or divide a number by 10, 100 and 1,000. - 4.N.1.2
Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors. (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). - 4.N.1.6
Read and interpret data using line plots. - 4.MD.1
Represent data using line plots and interpret data in line plots to solve problems. - 4.MD.2
Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. - 4.N.1.5
Recognize and use the relationship between millimeters, centimeters, and meters to measure and compare objects. - 5.GM.3.4
Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. - 4.N.1.4
Solve problems involving line plots and fractions. - 4.MD.3
Recognize and use the relationship between inches, feet, and yards to measure and compare objects. - 5.GM.3.3
Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms. - 4.N.1.3
Use models and strategies to solve word problems. - 5.NC.20
Add and subtract decimals. - 5.NC.13
Subtract decimals to the hundredths using the standard algorithm. - 5.NC.12
Add decimals to the hundredths using the standard algorithm. - 5.NC.11
Use knowledge about place value and multiplying with 2-digit and 3-digit numbers to multiply with zeros. - 5.NC.18
Multiply 3-digit by 2-digit numbers by combining equal groups and adding partial products. - 5.NC.17
Use rounding and compatible numbers to estimate products. - 5.NC.16
Use place-value understandings and patterns to mentally multiply whole numbers and powers of 10. - 5.NC.15
Use properties and the standard algorithm for multiplication to find the product of multi-digit numbers. - 5.NC.19
Create an input/output chart or table to represent or extend a numerical pattern. - 4.A.1.1
Create growth patterns involving geometric shapes and define the single operation rule of the pattern. - 4.A.1.3
Use place-value patterns and mental math to find quotients. - 5.NC.32
Multiply decimals using the standard algorithm for multiplication and multiplication strategies. - 5.NC.30
Use place-value understanding and the standard multiplication algorithm to multiply a decimal by a whole number. - 5.NC.25
Use models to represent multiplying a decimal and a whole number. - 5.NC.24
Use rounding and compatible numbers to estimate the product of a decimal and a whole number. - 5.NC.23
Use knowledge about place value and patterns to find the product of a decimal number and a power of 10. - 5.NC.22
Use number sense and reasoning to place the decimal point in a product. - 5.NC.29
Use properties to multiply decimals. - 5.NC.28
Multiply decimals using partial products and models. - 5.NC.27
Use grids to model decimals and find the product of a decimal and a decimal. - 5.NC.26
Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. - M.3.12
Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. - M.3.11
Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. Instructional Note: Fractions in this standard are limited to denominators of 2, 3, 4, 6, and 8. - M.3.13
Sketch polygons with a given number of sides or vertices (corners), such as pentagons, hexagons and octagons. - 3.3.1.2
Use place value understanding to round whole numbers to the nearest 10 or 100. - M.3.10
Identify parallel and perpendicular lines in various contexts, and use them to describe and create geometric shapes, such as right triangles, rectangles, parallelograms and trapezoids. - 3.3.1.1
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units—whole numbers, halves or quarters. - M.3.19
Find the perimeter of different polygons. - 3.MD.21
Tell and write time to the nearest minute, measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes (e.g., by representing the problem on a number line diagram). - M.3.16
Use the given sides of a polygon and the known perimeter to find the unknown side length. - 3.MD.23
Find the perimeter of different polygons with common shapes. - 3.MD.22
Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs (e.g., draw a bar graph in which each square in the bar graph might represent 5 pets). - M.3.18
Understand the relationship of shapes with the same area and different perimeters. - 3.MD.25
Understand the relationship of shapes with the same perimeter and different areas. - 3.MD.24
Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg) and liters (l). Add, subtract, multiply or divide to solve one-step word problems involving masses or volumes that are given in the same units (e.g., by using drawings, such as a beaker with a measurement scale) to represent the problem. Instructional Note: Exclude compound units such as cm3 and finding the geometric volume of a container. - M.3.17
Use concrete models and structured arrangements, such as repeated addition, arrays and ten frames to develop understanding of multiplication. - 2.N.2.6
Solve real-world and mathematical addition and subtraction problems involving whole numbers up to 2 digits. - 2.N.2.5
Use strategies and algorithms based on knowledge of place value and equality to add and subtract two-digit numbers. - 2.N.2.4
Use the standard algorithm for division to divide decimals by a whole number. - 5.NC.43
Demonstrate fluency with basic addition facts and related subtraction facts up to 20. - 2.N.2.2
Use models to help find quotients in problems involving decimals. - 5.NC.42
Use the relationship between addition and subtraction to generate basic facts up to 20. - 2.N.2.1
Use reason and strategies such as rounding and compatible numbers to estimate quotients in problems with decimals. - 5.NC.41
Use mental math and place-value patterns to divide a decimal by a power of 10. - 5.NC.40
Find the quotient when the divisor is a multiple of 10. - 5.NC.36
Round greater whole numbers to estimate sums and differences. - 4.NC.7
Solve division problems using partial quotients. - 5.NC.35
Add numbers to one million with and without regrouping using the standard algorithm. - 4.NC.8
Use place value and an algorithm to subtract whole numbers. - 4.NC.9
Use models to find quotients. - 5.NC.34
Use compatible numbers and place-value patterns to estimate quotients. - 5.NC.33
Use estimation to decide whether a quotient is reasonable when dividing by 2-digit divisors. - 5.NC.38
Decide where to place the first digit of the quotient when dividing whole numbers. - 5.NC.37
Use number sense and models of addition and subtraction, such as objects and number lines, to identify the missing number in an equation such as: 2 + 4 = ⧠; 3 + ⧠ = 7; 5 = ⧠ – 3. - 1.2.2.3
Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. - M.3.23
Use standard units to estimate liquid volume. - 3.MD.16
Use addition or subtraction basic facts to represent a given problem situation using a number sentence. - 1.2.2.4
Solve word problems involving addition and subtraction to measure quantities of time. - 3.MD.15
Represent real-world situations involving addition and subtraction basic facts, using objects and number sentences. - 1.2.2.1
Read and write numbers in expanded form, with numerals, and using number names. - 4.NC.1
Use a pan balance with metric weights to measure the mass of objects in grams and kilograms. - 3.MD.18
Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as ¼ or the area of the shape. - M.3.25
Determine if equations involving addition and subtraction are true. - 1.2.2.2
Recognize the relationship between adjacent digits in a multi-digit number. - 4.NC.2
Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), that the shared attributes can define a larger category (e.g. quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. - M.3.24
Use standard units to estimate the masses of solid objects. - 3.MD.17
Use place value to compare multi-digit numbers. - 4.NC.3
Use pictures to help solve problems about mass and volume. - 3.MD.19
Use place value to round multi-digit numbers. - 4.NC.4
Measure areas by counting unit squares (square cm, square m, square in, square ft. and improvised units). - M.3.21
Add and subtract whole numbers mentally using a variety of methods. - 4.NC.6
Use scaled bar graphs to represent data sets. - 3.MD.10
Use graphs to solve problems. - 3.MD.11
Tell and write time to the nearest minute and measure time intervals in minutes. - 3.MD.14
Show and tell time to the nearest minute using analog and digital clocks. - 3.MD.13
Find common denominators for fractions with unlike denominators. - 5.NC.50
Estimate sums and differences of fractions and mixed numbers. - 5.NC.54
Write equivalent fractions to add and subtract fractions with unlike denominators. - 5.NC.53
Subtract fractions with unlike denominators. - 5.NC.52
Add fractions with unlike denominators using equivalent fractions with a common denominator. - 5.NC.51
Construct math arguments in order to solve addition and subtraction problems. - 1.OA.9
Use the standard algorithm to divide decimals, annexing zeros as needed. - 5.NC.47
Use the standard algorithm and place-value patterns to divide a decimal by another decimal. - 5.NC.46
Solve addition problems by finding a missing addend. - 1.OA.7
Use number sense and reasoning to place the decimal point in the quotient when dividing two decimals. - 5.NC.45
Solve problems involving putting together or taking apart. - 1.OA.8
Use models to visualize the relationship between division and multiplication to divide decimals by a 2-digit whole number. - 5.NC.44
Estimate sums and differences of fractions by using the nearest half or whole number. - 5.NC.49
Solve addition problems involving situations of adding one part to another part. - 1.OA.1
Solve addition problems involving situations of putting two parts together. - 1.OA.2
Solve subtraction problems that involve comparing to find how many more objects are in one group than another group. - 1.OA.5
Solve subtraction problems that involve comparing to find how many fewer objects are in one group than another group. - 1.OA.6
Solve addition word problems by breaking apart a total number of objects. - 1.OA.3
Solve subtraction problems involving taking from a group. - 1.OA.4
The student will investigate and describe the concept of variable. - 5.19a
The student will write an equation to represent a given mathematical relationship, using a variable. - 5.19b
Create, describe, and extend patterns involving addition, subtraction, or multiplication to solve problems in a variety of contexts. - 3.A.1.1
Recognize the relationship between multiplying fractions and finding the areas of rectangles with fractional side lengths. - 5.NF.B.7a
Calculate and interpret the product of two fractions less than one. - 5.NF.B.7c
Calculate and interpret the product of a fraction by a whole number and a whole number by a fraction. - 5.NF.B.7b
Count by 2s to 100 starting with any even number. - 2.RA.B.2a
Express even numbers as pairings or groups of 2, and write an expression to represent the number using addends of 2. - 2.RA.B.2b
Determine if equations involving addition and subtraction are true. - 1.N.2.2
Represent and solve real-world and mathematical problems using addition and subtraction up to ten. - 1.N.2.1
Demonstrate fluency with basic addition facts and related subtraction facts up to 10. - 1.N.2.3
Describe the whole as two of, or four of the shares. - NC.1.G.3.b
Use rounding or compatible numbers to estimate sums and differences. - 5.NC.9
Explain that decomposing into more equal shares creates smaller shares. - NC.1.G.3.c
Use properties of addition and strategies to solve problems mentally. - 5.NC.8
Describe the shares as halves and fourths, as half of and fourth of. - NC.1.G.3.a
Given a conversion chart, use multiplicative reasoning to solve one-step conversion problems within a given measurement system. - NC.5.MD.1
Use place value to compare decimals through thousandths. - 5.NC.5
Represent and interpret data. - NC.5.MD.2
Read and write decimals through thousandths in different ways. - 5.NC.4
Recognize volume as an attribute of solid figures and measure volume by counting unit cubes, using cubic centimeters, cubic inches, cubic feet, and improvised units. - NC.5.MD.4
Round decimals to different places. - 5.NC.6
Use exponents to write powers of 10 and calculate products. - 5.NC.1
Represent decimals to thousandths as fractions and fractions with denominators of 1,000 as decimals. - 5.NC.3
Read and write whole numbers using standard form, expanded form, and number names. - 5.NC.2
Estimate the size of the product based on the size of the two factors. - 5.NF.B.5a
Relate volume to the operations of multiplication and addition. - NC.5.MD.5
Explain why multiplying a given number by a fraction less than 1 results in a product smaller than the given number. - 5.NF.B.5c
Explain why multiplying a given number by a fraction greater than 1 results in a product larger than the given number. - 5.NF.B.5b
Explain why multiplying the numerator and denominator by the same number is equivalent to multiplying the fraction by 1. - 5.NF.B.5d
Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems. - NC.4.MD.6.c
Measure and sketch angles in whole-number degrees using a protractor. - NC.4.MD.6.b
Make a representation of data and interpret data in a frequency table, scaled picture graph, and/or scaled bar graph with axes provided. - NC.3.MD.3.b
Understand angles as geometric shapes that are formed wherever two rays share a common endpoint, and are measured in degrees. - NC.4.MD.6.a
Solve one and two-step “how many more” and “how many less” problems using information from these graphs. - NC.3.MD.3.c
Express even numbers as being composed of equal groups and write an expression to represent the number with 2 equal addends. - 2.RA.B.2c
Collect data by asking a question that yields data in up to four categories. - NC.3.MD.3.a
Identify arithmetic patterns and explain the patterns using properties of operations. - 3.RA.E.11
Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. - NC.5.NF.1.a
Solve one- and two-step word problems in context using area and length models to develop the algorithm. Represent the word problem in an equation. - NC.5.NF.1.b
Apply properties of operations as strategies to multiply and divide. - 3.RA.B.6
Read and write time to the quarter-hour on an analog and digital clock. Distinguish between a.m. and p.m. - 2.GM.3.1
The student will identify, trace, describe, and sort plane figures (triangles, squares, rectangles, and circles) according to number of sides, vertices, and angles. - 1.11a
The student will identify and describe representations of circles, squares, rectangles, and triangles in different environments, regardless of orientation, and explain reasoning. - 1.11b
Recognize two- and three-dimensional shapes from different perspectives and orientations. - 1.GM.A.3
Classify quadrilaterals in a hierarchy based on properties. - NC.5.G.3.b
Compose and decompose two- and three-dimensional shapes to build an understanding of part-whole relationships and the properties of the original and composite shapes. - 1.GM.A.2
Distinguish between defining attributes versus non-defining attributes; build and draw shapes that possess defining attributes. - 1.GM.A.1
The student will collect, organize, and represent various forms of data using tables, picture graphs, and object graphs. - 1.12a
Explain that attributes belonging to a category of quadrilaterals also belong to all subcategories of that category. - NC.5.G.3.a
The student will read and interpret data displayed in tables, picture graphs, and object graphs, using the vocabulary more, less, fewer, greater than, less than, and equal to. - 1.12b
Partition circles and rectangles into two or four equal shares, and describe the shares and the wholes verbally. - 1.GM.A.4
Group tens to solve problems. - 1.NC.10
The student will identify, describe, compare, and contrast plane and solid figures according to their characteristics (number of angles, vertices, edges, and the number and shape of faces) using concrete models and pictorial representations. - 4.11
The student will classify quadrilaterals as a parallelograms, rectangles, squares, rhombi, and/or trapezoids. - 4.12
Use tens and ones to make numbers in different ways. - 1.NC.13
Find numbers that are more or less than a given number. - 1.NC.14
Count tens and ones to find a two-digit number. - 1.NC.11
The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. - 4.15
Use drawings to solve problems with tens and ones. - 1.NC.12
The student will recognize and demonstrate the meaning of equality in an equation. - 4.16
Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. - NC.4.NF.3.a
Decompose a fraction into a sum of unit fractions and a sum of fractions with the same denominator in more than one way using area models, length models, and equations. - NC.4.NF.3.b
Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. - NC.4.NF.3.c
Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem. - NC.4.NF.3.d
Find the area of two-dimensional figures by counting total number of same size unit squares that fill the shape without gaps or overlaps. - 3.GM.2.8
Develop and use formulas to determine the area of rectangles. Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns. - 3.GM.2.2
Find perimeter of polygon, given whole number lengths of the sides, in real-world and mathematical situations. - 3.GM.2.1
Choose an appropriate measurement instrument and measure the length of objects to the nearest whole yard, whole foot, or half inch. - 3.GM.2.4
Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. - 5.2.2.1
The student will classify triangles as right, acute, or obtuse and equilateral, scalene, or isosceles. - 5.13a
Draw diagrams and write equations to solve two-step problems involving addition and subtraction of whole numbers. - 3.OA.37
The student will read, write, and identify the place and value of each digit in a nine-digit whole number. - 4.1a
Draw diagrams and write equations to solve two-step problems involving multiplication and division of whole numbers. - 3.OA.38
Examine relationships between quantities in a two-step word problem by writing equations. Choose and apply the operations needed to find the answer. - 3.OA.39
The student will compare and order whole numbers expressed through millions. - 4.1b
Use strategies such as skip counting and properties of operations to multiply. - 3.OA.32
The student will round whole numbers expressed through millions to the nearest thousand, ten thousand, and hundred thousand. - 4.1c
Solve multiplication and division problems that involve different strategies and representations. - 3.OA.33
Use multiplication to write and solve real-world problems involving equal groups. - 3.OA.34
Use division to write and solve real-world problems involving equal groups. - 3.OA.35
Identify, create, complete, and extend simple patterns using shape, color, size, number, sounds and movements. Patterns may be repeating, growing or shrinking such as ABB, ABB, ABB or ●, ●●, ●●●. - K.2.1.1
Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths. - NC.3.MD.7.a
Determine the unknown whole number in a multiplication or division equation relating three whole numbers. - NC.3.OA.7.c
Know from memory all products with factors up to and including 10. - NC.3.OA.7.a
Illustrate and explain using the relationship between multiplication and division. - NC.3.OA.7.b
Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving problems, and represent whole-number products as rectangular areas in mathematical reasoning. - NC.3.MD.7.b
Use tiles and/or arrays to illustrate and explain that the area of a rectangle can be found by partitioning it into two smaller rectangles, and that the area of the large rectangle is the sum of the two smaller rectangles. - NC.3.MD.7.c
Solve and justify multi-step problems involving variables, whole numbers, fractions and decimals. - 5.RA.C.5
The student will represent equivalent fractions. - 4.2b
Use the Associative Property of Multiplication to group 3 factors and multiply. - 3.OA.20
Use benchmarks, area models, and number lines to compare fractions. - 4.NC.46
Use division to find equivalent fractions. - 4.NC.45
Use models or rename fractions to compare. - 4.NC.47
Solve problems involving separating parts of the same whole by subtracting fractions. - 4.NC.53
Use the Distributive Property to solve problems involving multiplication within 100. - 3.OA.14
The student will read, write, represent, and identify decimals expressed through thousandths. - 4.3a
Use tools such as fraction strips, area models, and number lines to subtract fractions. - 4.NC.52
Use appropriate tools and the Distributive Property to break apart unknown facts with 3 as a factor. - 3.OA.15
Use the Distributive Property to break apart unknown facts with 4 as a factor. - 3.OA.16
Use number lines and benchmark fractions to estimate fraction sums and differences. - 4.NC.55
The student will compare and order decimals. - 4.3c
Use the Distributive Property to break apart unknown facts with 6 or 7 as a factor. - 3.OA.17
The student will given a model, write the decimal and fraction equivalents. - 4.3d
Count forward or backward on a number line to add or subtract. - 4.NC.54
Gain fluency in multiplication when multiplying by 0 or 1. - 3.OA.10
Gain fluency in multiplication when multiplying by 10. - 3.OA.11
Students will use number relationships and patterns to develop reasoning strategies to support their recall of the basic multiplication facts. - 3.OA.12
Solve problems involving joining parts of the same whole by adding fractions. - 4.NC.51
Describe the relative positions of objects in space. - K.GM.C.7
Decompose a fraction or mixed number into a sum of fractions in more than one way. - 4.NC.50
Identify shapes and describe objects in the environment using names of shapes, recognizing the name stays the same regardless of orientation or size. - K.GM.C.6
Draw or model simple two-dimensional shapes. - K.GM.C.9
Identify and describe the attribute of shapes, and use the attributes to sort a collection of shapes - K.GM.C.8
Use the Distributive Property and known facts to break apart unknown facts with 8 as a factor. - 3.OA.18
Generate equivalent numerical expressions and solve problems involving whole numbers by applying the commutative, associative, and distributive properties and order of operations (no exponents). - 5.A.2.1
Use strategies such as bar diagrams and arrays with known facts to solve multiplication problems. - 3.OA.19
Use words to compare objects according to length, size, weight, position, and location. - K.GM.2.1
The student, given a practical problem, will represent data in line plots and stem-and-leaf plots. - 5.16a
The student, given a practical problem, will interpret data represented in line plots and stem-and-leaf plots. - 5.16b
Add to/Take From-Result Unknown - NC.K.OA.2.a
Use partial quotients and place-value understandings to divide with greater dividends. - 4.NC.39
Use partial quotients to divide. - 4.NC.38
Use a multiplication table to find the missing factor in a division problem. - 3.OA.30
Use number sense and reasoning while practicing multiplication and division basic facts. - 3.OA.31
Use objects and number lines to represent number sentences. - 2.A.2.1
Use place-value patterns and division facts to estimate quotients for 4-digit dividends. - 4.NC.35
Generate real-world situations to represent number sentences and vice versa. - 2.A.2.2
Use compatible numbers to estimate quotients. - 4.NC.34
Apply commutative and identity properties and number sense to find values for unknowns that make number sentences involving addition and subtraction true or false. - 2.A.2.3
Use place-value and drawings to divide 2- and 3-digit numbers by 1-digit numbers. - 4.NC.37
Solve division problems and interpret remainders. - 4.NC.36
The student will estimate and determine sums, differences, and products of whole numbers. - 4.4b
Use properties to understand division involving 0 and 1. - 3.OA.25
Use area models to recognize and generate equivalent fractions. - 4.NC.42
The student will estimate and determine quotients of whole numbers, with and without remainders. - 4.4c
Use patterns and known facts to find unknown multiplication facts. Use multiplication facts to find related division facts. - 3.OA.26
Divide 4-digit numbers by 1-digit numbers using the standard division algorithm. - 4.NC.41
Use number sentences involving addition, subtraction, and unknowns to represent given problem situations. Use number sense and properties of addition and subtraction to find values for the unknowns that make the number sentences true. - 2.2.2.2
The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. - 4.4d
Use multiplication and division facts to find unknown values in equations. - 3.OA.27
Use multiplication to find equivalent fractions. - 4.NC.44
Use a number line to locate and identify equivalent fractions. - 4.NC.43
Use multiplication facts to divide. - 3.OA.22
Divide 2- and 3-digit numbers by 1-digit numbers using the standard division algorithm. - 4.NC.40
Use multiplication facts to find related division facts. - 3.OA.23
Use knowledge of even and odd numbers to identify multiplication patterns. - 3.OA.24
Use the multiplication table and the Distributive Property to find patterns in factors and products. - 3.OA.29
The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. - 4.4a
Sort and group up to 10 objects into a set based upon characteristics such as color, size, and shape. Explain verbally what the objects have in common. - K.A.1.1
Use fractions or decimals to solve word problems involving money. - 4.NC.68
Add fractions with denominators of 10 and 100 by using equivalent fractions. - 4.NC.67
The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. - 4.5c
Calculate area by using unit squares to cover a plane figure with no gaps or overlaps. - 3.GM.C.9
The student will add and subtract fractions and mixed numbers having like and unlike denominators. - 4.5b
Recognize numbers to 20 without counting (subitize) the quantity of structured arrangements. - 1.N.1.1
Read, write, discuss, and represent whole numbers up to 100. Representations may include numerals, addition and subtraction, pictures, tally marks, number lines and manipulatives, such as bundles of sticks and base 10 blocks. - 1.N.1.3
Use concrete representations to describe whole numbers between 10 and 100 in terms of tens and ones. - 1.N.1.2
Find a number that is 10 more or 10 less than a given number up to 100. - 1.N.1.5
Count forward, with and without objects, from any given number up to 100 by 1s, 2s, 5s and 10s. - 1.N.1.4
Use knowledge of number relationships to locate the position of a given whole number on an open number line up to 20. - 1.N.1.7
Compare and order whole numbers from 0 to 100. - 1.N.1.6
Use a model to understand a fraction as a multiple of a unit fraction. - 4.NC.59
Use objects to represent and use words to describe the relative size of numbers, such as more than, less than, and equal to. - 1.N.1.8
Relate fractions and decimals with denominators of 10 to 100. - 4.NC.64
Use the four operations to solve problems involving time. - 4.NC.63
Calculate and interpret the quotient of a whole number by a unit fraction. - 5.NF.B.8b
Compare decimals by reasoning about their size. - 4.NC.66
Locate and describe fractions and decimals on number lines. - 4.NC.65
Calculate and interpret the quotient of a unit fraction by a non-zero whole number. - 5.NF.B.8a
Use models to multiply fractions by whole numbers. - 4.NC.60
Compare two decimals to the hundredths place using the symbols >, = or <, and justify the solution. - 4.NF.C.12
Use drawings and equations to represent and solve problems involving multiplying a whole number and a mixed number. - 4.NC.62
Use symbols and equations to multiply a fraction by a whole number. - 4.NC.61
Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form. - 4.NF.C.11
Understand that fractions and decimals are equivalent representations of the same quantity. - 4.NF.C.10
The student will add and subtract with decimals. - 4.6a
The student will solve single-step and multistep practical problems involving addition and subtraction with decimals. - 4.6b
Use different strategies to solve word problems with 3 addends. - 1.OA.39
Find the missing numbers in equations to make them true. - 1.OA.38
Determine if addition and subtraction equations are true or false. - 1.OA.37
Find the unknown number in an equation. - 1.OA.36
Use reasoning to write and solve number stories. - 1.OA.35
Count to 100 by ones and tens. - K.NS.A.1
Construct math arguments using fractions. - 3.NC.36
Count forward beginning from a given number between 1 and 20. - K.NS.A.2
Solve different types of addition and subtraction problems with unknowns in different positions. - 1.OA.34
Use fraction names to represent whole numbers. - 3.NC.35
Understand how to interpret number sentences involving multiplication and division basic facts and unknowns. Create real-world situations to represent number sentences. - 3.2.2.1
Use multiplication and division basic facts to represent a given problem situation using a number sentence. Use number sense and multiplication and division basic facts to find values for the unknowns that make the number sentences true. - 3.2.2.2
Use number sense and regrouping to subtract across zeros. - 4.NC.10
Use precision to determine the missing number or symbol in an equation. - 1.OA.42
Solve word problems involving comparisons. - 1.OA.41
Put together/Take Apart-Addend Unknown - NC.1.OA.1.b
Use different strategies to add three numbers. - 1.OA.40
Add to/Take from-Change Unknown - NC.1.OA.1.a
Compose larger shapes from simple shapes. - NC.K.G.6
Identify squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres as two-dimensional or three-dimensional. - NC.K.G.3
Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, attributes and other properties. - NC.K.G.4
Identify points, lines, line segments, rays, angles, endpoints, and parallel and perpendicular lines in various contexts. - 4.GM.1.1
Describe, classify, and sketch quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms, and kites. Recognize quadrilaterals in various contexts. - 4.GM.1.2
Count backward from a given number between 10 and 1. - K.NS.A.3
Read and write numerals and represent a number of objects from 0 to 20. - K.NS.A.4
Describe objects in the environment using names of shapes, and describe the relative positions of objects using positional terms. - NC.K.G.1
Correctly name squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres regardless of their orientations or overall size. - NC.K.G.2
The student will given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. - 4.8c
The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. - 4.8d
Use an open number line to add 3-digit numbers. - 2.NC.47
Use different strategies to find products when one factor is a multiple of 10. - 3.NC.19
Add 3-digit numbers using mental math strategies. - 2.NC.48
Use properties of multiplication to find products when one factor is a multiple of 10. - 3.NC.18
Add 3-digit numbers using partial sums. - 2.NC.49
Use an open number line to find products when one factor is a multiple of 10. - 3.NC.17
Subtract a 3-digit number from another 3-digit number with one or more zeros by using the standard algorithm. - 3.NC.15
Subtract 3-digit numbers using the standard algorithm. - 3.NC.14
Subtract multi-digit numbers using the expanded algorithm. - 3.NC.13
Use place value and partial products to calculate products of 2-digit by 2-digit multiplication problems. - 4.NC.28
Use the Distributive Property and an area model to multiply two 2-digit numbers. - 4.NC.27
Use area models and place-value strategies to multiply 2-digit numbers by multiples of 10. - 4.NC.29
Estimate products for 2-digit by 2-digit multiplication problems by rounding the factors to multiples of ten. - 4.NC.24
Use models and properties of operations to multiply 2-digit numbers by multiples of ten. - 4.NC.23
Use arrays, place value, partial products, and properties of operations to multiply two 2-digit numbers. - 4.NC.26
Use compatible numbers to estimate products of 2-digit by 2-digit multiplication problems. - 4.NC.25
Use models and algorithms to solve 2-digit by 2-digit multiplication problems. - 4.NC.31
Use the expanded and the standard algorithm to multiply 2-digit by 2-digit numbers. Estimate to check if products are reasonable. - 4.NC.30
Use mental-math and place-value strategies to divide multiples of 10 and 100 by 1-digit divisors. - 4.NC.33
Make the numbers 14, 15, and 16. - K.NC.2
Make the numbers 17, 18, and 19. - K.NC.3
Find parts of the numbers 14, 15, and 16. - K.NC.5
Use models to add 3-digit numbers. - 2.NC.50
Determine and draw the whole (unit) given one part (unit fraction). - 3.NC.23
Use different addition strategies and explain why they work. - 2.NC.51
Use a fraction to represent multiple copies of a unit fraction. - 3.NC.22
Understand how to read and write unit fractions for equal-size parts of a region. - 3.NC.21
Subtract 10 or 100 mentally using place-value strategies. - 2.NC.53
Use an open number line to count back to subtract 3-digit numbers. - 2.NC.54
Use an open number line to add up to subtract 3-digit numbers. - 2.NC.55
Use models to subtract 3-digit numbers. - 2.NC.57
Understand place value and count by hundreds to 1,000. - 2.NC.36
Use place-value blocks and drawings to model and write 3-digit numbers. - 2.NC.37
Compare two or more sets of objects and identify which set is equal to, more than or less than the other. - K.NS.C.10
Tell the value of a digit by where it is placed in a number. - 2.NC.38
Find equivalent fractions that name the same part of the whole. - 3.NC.29
Compare-Difference Unknown - NC.1.OA.1.c
Compare two numerals, between 1 and 10, and determine which is more than or less than the other. - K.NS.C.11
Read and write 3-digit numbers in expanded form, standard form, and word form. - 2.NC.39
Decompose numbers less than or equal to 10 in more than one way. - K.RA.A.3
Measure length to the nearest half inch and show the data on a line plot. - 3.NC.27
Make 10 for any number from 1 to 9. - K.RA.A.4
Measure length to the nearest fourth inch and show the data on a line plot. - 3.NC.26
Represent addition and subtraction within 10. - K.RA.A.1
Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. - 4.2.2.1
Represent fractions greater than 1 on a number line. - 3.NC.25
Demonstrate fluency for addition and subtraction within 5. - K.RA.A.2
Represent fractions on a number line. - 3.NC.24
Use place value and partial products to multiply 3- and 4-digit numbers by 1-digit numbers. - 4.NC.17
Use arrays and partial products to multiply 3- and 4-digit numbers by 1-digit numbers. - 4.NC.16
Use the standard algorithm to multiply 4-digit numbers by 1-digit numbers. - 4.NC.19
Use place value and the standard algorithm to multiply 2-and 3-digit numbers by 1-digit numbers. - 4.NC.18
Quarters, dimes, nickels, and pennies within 99¢, using ¢ symbols appropriately. - NC.2.MD.8.a
Write and solve problems involving addition and subtraction within 100. - 2.NBT.C.11
Model sums and differences of decimals. - 5.NC.10
Use rounding to estimate products and check if answers are reasonable. - 4.NC.13
Multiply multiples of 10, 100, and 1,000 using mental math and place-value strategies - 4.NC.12
Use place value and properties of operations to multiply mentally. - 4.NC.15
Whole dollar amounts, using the $ symbol appropriately. - NC.2.MD.8.b
Use the Distributive Property to multiply larger numbers. - 4.NC.14
Use the standard algorithm to multiply 2-, 3-, and 4-digit numbers by 1-digit numbers. Estimate to check if answers are reasonable. - 4.NC.20
Use mental-math strategies to multiply 2-digit by 2-digit multiples of ten. - 4.NC.22
Use a number line to compare fractions. - 3.NC.34
Make and name a number in different ways to show the same value. - 2.NC.40
Use benchmark numbers to compare fractions. - 3.NC.33
Use place-value patterns to mentally count by 1s and 10s from a given number. - 2.NC.41
Use models such as fraction strips to compare fractions that refer to the same whole and have the same numerator. - 3.NC.32
Skip count by 5s, 10s, and 100s using a number line. - 2.NC.42
Use models such as fraction strips to compare fractions that refer to the same whole and have the same denominator. - 3.NC.31
Solve simple put-together, take-apart, and compare problems using information presented in a picture and a bar graph. - NC.2.MD.10.b
Compare numbers using place value. - 2.NC.43
Represent equivalent fractions on a number line. - 3.NC.30
Draw a picture graph and a bar graph with a single-unit scale to represent a data set. - NC.2.MD.10.a
Add 10 or 100 mentally using place value. - 2.NC.46
Solve one- and two-step problems using addition or subtraction. - 2.NC.25
Exchange 1 ten for 10 ones. - 2.NC.27
Use place value and models to subtract 2-digit and 1-digit numbers. - 2.NC.28
Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations. - M.4.1
Use place value and regrouping to subtract. - 2.NC.29
Multiply or divide to solve word problems involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem) and distinguish multiplicative comparison from additive comparison. - M.4.2
Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) - M.4.5
Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (e.g., recognize that 700 ÷ 70 = 10 by applying concepts of place value and division). - M.4.6
Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. - M.4.3
Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. - M.4.4
Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. - NC.2.OA.4
Fluently add and subtract multi-digit whole numbers using the standard algorithm. - M.4.9
Demonstrate fluency with addition and subtraction, within 20, using mental strategies. - NC.2.OA.2
Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. - M.4.7
Use place value understanding to round multi-digit whole numbers to any place. - M.4.8
Estimate solutions to division problems in order to assess the reasonableness of results. - 5.N.1.1
Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number (e.g., use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. In general, n × (a/b) = (n × a)/b). - M.4.15b
Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, (e.g., use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)). - M.4.15a
Solve real-world and mathematical problems requiring addition, subtraction, multiplication, and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. - 5.N.1.4
Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problem (e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?). - M.4.15c
Divide multi-digit numbers, by one- and two-digit divisors, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. - 5.N.1.2
Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal and consider the context in which a problem is situated to select and interpret the most useful form of the quotient for the solution. - 5.N.1.3
Solve multiplication word problems with factors up to and including 10. Represent the problem using arrays, pictures, and/or equations with a symbol for the unknown number to represent the problem. - NC.3.OA.3.a
Demonstrate fluency with addition and subtraction of whole numbers. - 4.NBT.A.5
Solve division word problems with a divisor and quotient up to and including 10. Represent the problem using arrays, pictures, repeated subtraction and/or equations with a symbol for the unknown number to represent the problem. - NC.3.OA.3.b
Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. - 4.2.2.2
Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. - 4.NBT.A.6
Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. - 4.NBT.A.7
Use place value and models to subtract 2-digit numbers. - 2.NC.30
Use place value to subtract 2-digit numbers. - 2.NC.31
Add to check subtraction. - 2.NC.32
Subtract 2-digit numbers and decide when to regroup and when not to regroup. - 2.NC.33
Use models and equations to solve word problems. - 2.NC.34
Add three or four 2-digit numbers. - 2.NC.14
Use mental math strategies and models to add more than two numbers. - 2.NC.15
Use drawings, models, and equations to solve one- and two-step problems. - 2.NC.16
Make models to help solve math problems. - 2.NC.17
Use a hundred chart to subtract tens and ones. - 2.NC.18
Use an open number line to subtract tens. - 2.NC.19
Add, subtract, multiply, and divide to solve one-step word problems involving whole-number measurements of length, mass, and capacity that are given in metric units. - NC.4.MD.1.b
Measure to solve problems involving metric units: centimeter, meter, gram, kilogram, Liter, milliliter. - NC.4.MD.1.a
Compare two fractions using the symbols >, = or <, and justify the solution. - 4.NF.A.3
Explain and/or illustrate why two fractions are equivalent. - 4.NF.A.1
Recognize and generate equivalent fractions. - 4.NF.A.2
Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. - M.4.14a
Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation and justify decompositions by using a visual fraction model (e.g., 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8). - M.4.14b
Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem. - M.4.14d
Add three or more numbers using the standard algorithm. - 3.NC.12
Add 3-digit numbers using the standard algorithm. - 3.NC.11
Add two 3-digit numbers by breaking apart problems into simpler problems. - 3.NC.10
Use an open number line to subtract tens and ones. - 2.NC.20
Add up to subtract using an open number line. - 2.NC.21
Break apart 1-digit numbers to make it easier to subtract mentally. - 2.NC.22
Break apart 2-digit numbers to make it easier to subtract. - 2.NC.23
Make numbers that are easier to subtract, and use mental math to find the difference. - 2.NC.24
Use an open number line to solve subtraction problems. - 1.NC.31
Use addition to subtract tens. - 1.NC.32
Use a hundred chart to subtract a multiple of 10 from another multiple of 10. - 1.NC.30
Use attributes to describe different objects. - K.MD.8
Model thinking to solve problems. - 1.NC.35
Use mental math to subtract ten from a two-digit number. - 1.NC.33
Compare objects by length and height. - K.MD.5
Use different strategies to subtract. - 1.NC.34
Model and solve problems by drawing a picture and writing an equation. - 1.NC.28
Use models to subtract tens. - 1.NC.29
Add 2 two-digit numbers. - 1.NC.26
Solve addition problems using different strategies. - 1.NC.27
Add using place value and partial sums. - 2.NC.10
Add numbers using partial sums. - 2.NC.11
Use models to add 2-digit numbers and then explain the work. - 2.NC.12
Add 2-digit numbers and then explain the work. - 2.NC.13
Add 2 multiples of 10. - 1.NC.20
Use mental math to add tens to two-digit numbers. - 1.NC.21
Solve addition problems by using blocks or drawings. - 1.NC.24
Round multi-digit whole numbers to any place. - 4.NBT.A.1
Make a ten to help solve addition problems. - 1.NC.25
Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. - 4.NBT.A.2
Use a hundred chart to add tens and ones. - 1.NC.22
Interpret comparisons as multiplication or addition equations. - 4.OA.1
Compare two multi-digit numbers using the symbols >, = or <, and justify the solution. - 4.NBT.A.3
Use a number line to solve addition problems. - 1.NC.23
Understand that in a multi-digit whole number, a digit represent 10 times what it would represents in the place to its right. - 4.NBT.A.4
Identify and estimate angles and their measure. - 4.GM.B.4
Draw and measure angles in whole-number degrees using a protractor. - 4.GM.B.5
Solve two-step problems by finding and solving the hidden question first. - 4.OA.3
Compare two numbers using a greater than, a less than, or an equal to sign. - 1.NC.17
Compare and write two-digit numbers that are greater than or less than other two-digit numbers. - 1.NC.18
Count how many objects are in different categories. - K.MD.2
Use multiplication and division to compare two quantities. - 4.OA.2
Use a hundred chart to find 1 more, 1 less, and 10 more, 10 less. - 1.NC.15
Classify objects into categories and tell why they are in each category. - K.MD.1
Solve multi-step problems by finding and solving hidden questions first. - 4.OA.4
Use place-value blocks to compare 2 two-digit numbers. - 1.NC.16
Use multiplication to find all the factor pairs for a whole number. - 4.OA.7
Use arrays to find the factors of a given whole number. - 4.OA.6
Make sense of a problem and find the best way to solve it. - 1.NC.19
Use factors to determine whether a whole number greater than 1 is prime or composite. - 4.OA.9
Compare benchmark fractions (¼, ⅓, ½, ⅔, ¾) an
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