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Product Name: Investigations 3 Grade 4 2017
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Curriculum Standards:


Solving multiplication problems - 3.8.1.4
Representing a multiplication problem with pictures, diagrams, arrays, or models - 3.8.1.3
Developing strategies for multiplying that involve breaking apart numbers - 3.8.1.2
Multiplying 2-digit by 1-digit numbers - 3.8.1.1
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. - M.2.4
Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions (e.g. by using drawings and equations with a symbol for the unknown number to represent the problem). - M.2.1
Finding the areas of partially covered rectangles - 3.4.2.9
Fluently add and subtract within 20 using mental strategies and by end of Grade 2, know from memory all sums of two one-digit numbers. - M.2.2
Read and write numbers to 1000 using base-ten numerals, number names and expanded form. - M.2.7
Understanding that rectangles can have the same perimeter and different areas or the same area and different perimeters - 3.4.2.8
Compare two three-digit numbers based on meanings of the hundreds, tens and ones digits, using >, = and < symbols to record the results of comparisons. - M.2.8
Finding the area and perimeter of a rectangle - 3.4.2.7
Understand that the three digits of a three-digit number represent amounts of hundreds, tens and ones (e.g., 706 equals 7 hundreds, 0 tens and 6 ones). Understand the following as special cases: - M.2.5
Examining the relationship between areas of rectangles and triangles - 3.4.2.6
Determining area, using square units and half-units - 3.4.2.5
Count within 1000 and skip-count by 5s, 10s and 100s. - M.2.6
Understanding that different shapes can have the same area - 3.4.2.4
Understanding that when measuring area, the space being measured must be completely covered with no gaps or overlaps - 3.4.2.3
Understanding that area is measured in square units - 3.4.2.2
Fluently add and subtract within 100 using strategies based on place value, properties of operations and/or the relationship between addition and subtraction. - M.2.9
Covering a shape with no gaps or overlaps - 3.4.2.1
Identifying how data are sorted into different categories based on similar attributes - 3.2.TMM.1
Benchmark 3: Interpret and use multiplication and division notation. - 3.1.AB.3
Using contexts to understand multiplication involving 1 and 0 - 3.1.1.9
Benchmark 4: Demonstrate fluency with multiplication facts x1, x2, x5, and x10. - 3.1.AB.4
Benchmark 1: Demonstrate an understanding of multiplication and division as involving equal groups. - 3.1.AB.1
Benchmark 2: Solve multiplication and related division problems by using skip counting or known multiplication facts. - 3.1.AB.2
Using and understanding multiplication notation - 3.1.1.5
Finding the multiples of the numbers 2, 3, 4, 5, 6, and 10 - 3.1.1.6
Describing and comparing characteristics of sets of multiples - 3.1.1.7
Understanding that doubling (or halving) one factor in a multiplication expression doubles (or halves) the product - 3.1.1.8
Understanding perimeter as the distance around the outside edges of a 2-D figure - 3.4.1.1
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
Comparing the properties of squares, rectangles, and rhombuses - 3.4.3.7
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
Categorizing quadrilaterals based on their attributes - 3.4.3.6
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
Identifying the attributes of squares, rectangles, and rhombuses - 3.4.3.5
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
Identifying the attributes of quadrilaterals: four sides, four vertices, and four angles - 3.4.3.4
Identifying the attributes of triangles: three sides, three vertices, and three angles - 3.4.3.3
Benchmark 4: Partition 2-D shapes into halves, thirds, and fourths and name the regions. - 2.2.AB.4
Identifying a right angle - 3.4.3.2
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
Benchmark 1: Identify defining attributes of 2-D and 3-D shapes (number and shape of faces, number and length of sides, number of angles and vertices) and draw shapes with those attributes. - 2.2.AB.1
Constructing triangles and quadrilaterals with given attributes - 3.4.3.1
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
Benchmark 2: Make a rectangle out of same size squares and specify the number of rows and the number of squares in each row. - 2.2.AB.2
Using strategies based on the distributive property - 3.5.1.6
Finding the area of arrays by multiplying the dimensions - 3.5.1.5
Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones and sometimes it is necessary to compose or decompose tens or hundreds. - M.2.11
Developing strategies for multiplying that involve breaking apart numbers - 3.5.1.7
Interpreting division as how many equal groups - 3.5.1.2
Recognizing multiples and non-multiples of 3, 4, or 6 - 3.5.1.1
Understanding that doubling one factor in a multiplication expression doubles the product - 3.5.1.4
Understanding and articulating the relationship between multiplication and division - 3.5.1.3
Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units (e.g., by using drawings, such as drawings of rulers), and equations with a symbol for the unknown number to represent the problem. - M.2.18
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
Understanding that area is additive through finding the areas of rectilinear shapes - 3.4.2.13
Estimate lengths using units of inches, feet, centimeters, and meters. - M.2.16
Finding the area of an irregular shape - 3.4.2.10
Finding areas of rectangles in square units - 3.4.2.11
Applying the properties of multiplication to find missing factors - 3.1.TMM.6
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
Using multiplication patterns to determine a sequence of multiples - 3.1.TMM.5
Benchmark 1: Partition a quantity into equal parts, and name those parts as fractions. - 3.6.AB.1
Benchmark 1: Use knowledge of place value to read, write, sequence, and round numbers up to 1,000. - 3.3.AB.1
Benchmark 2: Solve addition problems with 3-digit numbers (up to 400) by using strategies that involve breaking each number apart by place, or by adding on one number in parts. - 3.3.AB.2
Benchmark 3: Solve subtraction problems with 2- and 3-digit numbers (up to 300) by using strategies that involve either subtracting one number in parts, adding up, or subtracting back. - 3.3.AB.3
Benchmark 4: Tell time to the nearest minute. - 3.3.AB.4
Generate measurement data by measuring lengths of several objects to the nearest whole unit or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. - M.2.22
Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces (sizes are compared directly or visually, not compared by measuring). Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. - M.2.24
Benchmark 5: Measure to the nearest fourth inch and represent measurement data to the nearest fourth inch on a line plot. - 3.6.AB.5
Benchmark 4: Identify equivalent fractions. - 3.6.AB.4
Benchmark 3: Compare fractions with the same numerator or same denominator by reasoning about their size. - 3.6.AB.3
Benchmark 2: Represent fractions as numbers on a number line. - 3.6.AB.2
Finding the difference between 2- and 3-digit numbers and 100 - 3.3.2.3
Solving addition problems with 2- and 3-digit numbers (up to 400) by using strategies that involve breaking each number apart by place or adding on one number in parts - 3.3.2.2
Using known division facts and related multiplication facts to determine quotients of more difficult facts - 3.8.3.2
Developing fluency with division facts - 3.8.3.1
Finding pairs of numbers that add to 100 - 3.3.2.5
Representing a subtraction problem on a number line - 3.3.2.4
Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. - M.2.25
Estimating the sums of 2- and 3-digit numbers using knowledge of place value and known combinations - 3.3.2.7
Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. - M.2.26
Using known pairs of 2-digit numbers that add to 100 to find related pairs that add to 100 or a number close to 100 (e.g., 20 + 80 = 100, so 22 + 78 = 100) - 3.3.2.6
Using multiples of 100 as landmarks to solve subtraction problems - 3.3.2.9
Developing strategies for solving addition problems by focusing on how each strategy starts - 3.3.2.8
Benchmark 1: Solve a 2-step story problem that involves finding the difference between a 2-digit number and 100 - 2.5.AB.1
Benchmark 3: Read, write, count, and compare numbers to 1,000 - 2.5.AB.3
Benchmark 2: Understand that 3-digit numbers represent - 2.5.AB.2
Benchmark 5: Add fluently within 100 - 2.5.AB.5
Benchmark 7: Count by 5s, 10s, and 100s within 1,000 - 2.5.AB.7
Benchmark 6: Solve comparison story problems with a bigger unknown - 2.5.AB.6
Benchmark 4: Estimate and measure liquid volume and mass using standard units. - 3.7.AB.4
Benchmark 3: Solve 3-digit subtraction problems fluently. - 3.7.AB.3
Using equations to represent how fractions relate to each other and to a whole - 3.6.4.5
Benchmark 2: Solve 3-digit addition problems using at least one strategy fluently. - 3.7.AB.2
Understanding and using notation for fractions greater than 1 (e.g., 3/2, 7/4) - 3.6.4.4
Benchmark 1: Solve addition and subtraction problems involving masses or volumes. - 3.7.AB.1
Understanding and using notation for fractions equivalent to 1 (e.g., 2/2, 3/3) - 3.6.4.3
Understanding and using notation for fractions with numerators greater than 1 (e.g., 3/4, 2/3) - 3.6.4.2
Understanding and using notation for unit fractions (1/2, 1/3, 1/4, 1/6, 1/8) - 3.6.4.1
Finding the difference between two numbers by either adding up or subtracting - 3.3.2.10
Solving addition problems with more than 2 addends - 3.7.2.7
Estimating and solving addition problems with sums greater than 1,000 - 3.7.2.6
Solving subtraction problems with 2- and 3-digit numbers (up to 300) using strategies that involve subtracting one number in parts, adding up, or subtracting back - 3.3.2.12
Subtracting from multiples of 100 - 3.7.2.9
Reasoning about how increasing or decreasing one of the numbers in a subtraction problem affects the difference - 3.3.2.11
Determining combinations of addends for a given sum - 3.7.2.8
Representing addition strategies - 3.3.2.13
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
Benchmark 4: Understand that 100 can be seen as 1 hundred, as 10 tens, and as 100 ones. - 2.3.AB.4
Benchmark 3: Solve two-step story problems about money. - 2.3.AB.3
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
Naming, notating, and telling time to the nearest minute on a digital or analog clock - 3.3.TMM.3
Benchmark 1: Solve a put together/take apart story problem with both addends unknown, and find all the possible combinations. - 2.3.AB.1
Determining intervals of time to the nearest minute - 3.3.TMM.4
Solving multi-step word problems - 3.7.2.3
Solving addition and subtraction problems in the context of distance traveled - 3.7.2.2
Reading, writing, and sequencing numbers to 1,000 - 3.3.1.2
Use place value understanding to round whole numbers to the nearest 10 or 100. - M.3.10
Solving addition problems with 3-digit numbers - 3.7.2.5
Constructing 1,000 from 10 groups of 100 - 3.3.1.1
Combining hundreds to numbers above 1,000 - 3.7.2.4
Making sense of remainders in terms of the problem context - 3.8.2.4
Solving add to, take from, put together/take apart, and compare story problems - 3.3.3.2
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
Visualizing and representing add to, take from, put together/take apart, and compare problems - 3.3.3.1
Solving related division problems - 3.8.2.3
Using and interpreting division notation - 3.8.2.2
Using the relationship between multiplication and division to solve division problems - 3.8.2.1
Using number lines to represent solutions to comparison problems - 3.3.3.3
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
Benchmark 1: Solve multiplication and division problems within 100. - 3.8.AB.1
Benchmark 8: Fluently add and subtract within 20. - 2.3.AB.8
Benchmark 2: Demonstrate fluency with the division facts. - 3.8.AB.2
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
Benchmark 7: Solve story problems with an unknown start. - 2.3.AB.7
Benchmark 3: Solve multi-step problems involving more than one operation. - 3.8.AB.3
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
Benchmark 1: Organize, represent, and describe categorical data, choosing categories that help make sense of the data. - 3.2.AB.1
Using U.S. standard and metric units to accurately measure length - 3.4.1.9
Benchmark 4: Find the area of a rectangular array by breaking it apart (using the distributive property). - 3.8.AB.4
Benchmark 5: Solve multiplication and division problems involving masses or volumes. - 3.8.AB.5
Establishing measurement benchmarks - 3.4.1.8
Reviewing the length of units of measure (inch, foot, yard, centimeter, and meter) - 3.4.1.7
Finding the unknown side lengths when given the perimeter and some side lengths - 3.4.1.6
Benchmark 5: Generate measurement data by measuring lengths to the half inch. - 3.2.AB.5
Finding the perimeter of an irregular shape - 3.4.1.5
Benchmark 4: Describe and summarize a set of data, describing concentrations of data and what those concentrations mean in terms of the situation the data represent. - 3.2.AB.4
Generating measurement data by measuring to the nearest half inch - 3.2.3.1
Solving division problems - 3.8.2.6
Benchmark 3: Make a line plot for a set of measurement data, with a scale that includes inches and half inches. - 3.2.AB.3
Creating different shapes with the same perimeter - 3.4.1.3
Benchmark 2: Make and interpret a bar graph and a pictograph, including use of scales greater than 1. - 3.2.AB.2
Finding perimeter using standard units - 3.4.1.2
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
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
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
Measure areas by counting unit squares (square cm, square m, square in, square ft. and improvised units). - M.3.21
Benchmark 2: Create, describe, and interpret a variety of data representations, including picture graphs and bar graphs. - 2.4.AB.2
Identifying addition strategies by focusing on how each strategy starts - 3.7.3.1
Adding and subtracting multiples of 10 and 100 - 3.3.2.1
Subtracting 3-digit numbers by using strategies that involve subtracting one number in parts, adding up, or subtracting back - 3.7.3.4
Estimating solutions to 3-digit addition and subtraction problems - 3.5.TMM.3
Explain equivalence of fractions in special cases and compare fractions by reasoning about their size. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. (e.g., Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram.) Instructional Note: Fractions in this standard are limited to denominators of 2, 3, 4, 6, and 8. - M.3.15c
Explain equivalence of fractions in special cases and compare fractions by reasoning about their size. Recognize and generate simple equivalent fractions (e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent (e.g., by using a visual fraction model). Instructional Note: Fractions in this standard are limited to denominators of 2, 3, 4, 6, and 8. - M.3.15b
Explain equivalence of fractions in special cases and compare fractions by reasoning about their size. Understand two fractions as equivalent (equal) if they are the same size or the same point on a number line. Instructional Note: Fractions in this standard are limited to denominators of 2, 3, 4, 6, and 8. - M.3.15a
Breaking apart, reordering, rounding, or changing numbers mentally to determine a reasonable estimate - 3.5.TMM.4
Explain equivalence of fractions in special cases and compare fractions by reasoning about their size. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, = or < and justify the conclusions (e.g., by using a visual fraction model). Instructional Note: Fractions in this standard are limited to denominators of 2, 3, 4, 6, and 8. - M.3.15d
Developing classifications to organize categorical data - 3.2.2.1
Organizing categorical data in different ways to answer different questions - 3.2.2.2
100 can be thought of as a bundle of ten tens – called a “hundred.” - M.2.5a
Finding different combinations of 100s, 10s, and 1s for a given number, and recognizing their equivalence (e.g., 137 equals 1 hundred, 3 tens, and 7 ones, or 1 hundred, 2 tens, and 17 ones, or 13 tens and 7 ones) - 3.3.1.10
Identifying and learning multiplication facts not yet known - 3.5.4.3
Finding a product by using an array or story context to represent breaking it into parts - 3.5.4.2
Understanding division as the splitting of a quantity into equal groups - 3.1.4.1
Learning multiplication facts to 10 x 10 - 3.5.4.4
Benchmark 4: Solve put together/take apart story problems with the total unknown, and add to and take from story problems with the result unknown. - 2.1.AB.4
Using known multiplication facts to determine the product of more difficult facts - 3.5.4.1
Understand a fraction as a number on the number line and represent fractions on a number line diagram. Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line. (e.g., Given that a/b represents 3/4 or 6/4, students partition the number line into fourths and represent these fractions accurately on the same number line; students extend the number line to include the number of wholes required for the given fractions.) Instructional Note: Fractions in this standard are limited to denominators of 2, 3, 4, 6, and 8. - M.3.14b
Understand a fraction as a number on the number line and represent fractions on a number line diagram. Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line. (e.g., Given that b parts is 4 parts, then 1/b represents 1/4. Students partition the number line into fourths and locate 1/4 on the number line.) Instructional Note: Fractions in this standard are limited to denominators of 2, 3, 4, 6, and 8. - M.3.14a
Understanding a unit fraction as a number represented on a number line - 3.6.2.2
Representing fractions on a number line - 3.6.2.1
Representing measurement data to the nearest fourth inch on a line plot - 3.6.2.5
Measuring length to the nearest fourth inch - 3.6.2.4
Understanding fractions with numerators greater than 1 as iterations of a unit fraction on the number line - 3.6.2.3
Using correct notation to write a measurement in feet and inches - 3.2.3.5
Combining feet and inches to get a total measurement - 3.2.3.4
Understanding the relationship between feet and inches - 3.2.3.3
Generating measurement data by measuring lengths longer than the measuring tool - 3.2.3.2
Representing multi-step problems involving more than one operation - 3.8.4.2
Recognizing and demonstrating the equivalence of one 100 to ten 10s and of one 10 to ten 1s - 3.3.1.4
Solving multi-step problems involving more than one operation - 3.8.4.1
Representing the structure of 3-digit numbers as the composition of 100s, 10s, and 1s - 3.3.1.3
Determining the number of hundreds in the sum of 3-digit numbers (e.g., there are 6 hundreds in 329 + 287) - 3.3.1.6
Using place value to determine the size of any number to 1,000 - 3.3.1.5
Using place-value understanding to round whole numbers to the nearest ten or hundred - 3.3.1.8
Recognizing and representing the groups of 10 in 3-digit numbers (e.g., there are 27 tens in 276) - 3.3.1.7
Recognizing and representing the place value of each digit in 2-and 3-digit numbers - 3.3.1.9
Using letters to stand for unknown quantities - 3.8.4.7
Representing multi-step problems with equations - 3.8.4.6
Using summaries such as almost all, very few, half, or more/less than half - 3.2.1.2
Connecting the steps of a general method or rule to the parts of the situation they represent - 3.8.4.5
Using one-half as a benchmark - 3.2.1.3
Using tables to identify and interpret arithmetic patterns - 3.8.4.4
Identifying and explaining arithmetic patterns - 3.8.4.3
Describing and interpreting categorical data - 3.2.1.1
Benchmark 5: Represent and solve addition and subtraction problems with 3-digit numbers. - 2.8.AB.5
Benchmark 3: Fluently subtract two 2-digit numbers. - 2.8.AB.3
Learning multiplication facts using arrays - 3.1.3.1
Using known multiplication facts to determine the product of more difficult facts - 3.1.3.2
Using multiples of 100 to solve subtraction problems - 3.7.2.13
Writing, representing, and solving division problems in context - 3.1.4.2
Using the inverse relationship between multiplication and division to solve problems - 3.1.4.3
Writing a story problem to represent a subtraction equation - 3.7.2.14
Solving add to, take from, put together/take apart, and compare story problems - 3.7.2.15
Using multiplication facts to solve division problems - 3.1.4.4
Using and understanding division notation - 3.1.4.5
Generating and identifying equivalent fractions - 3.6.3.1
Comparing fractions by reasoning about their size - 3.6.3.4
Ordering unit fractions by reasoning about their size - 3.6.3.3
Understanding and explaining why fractions are equivalent - 3.6.3.2
Representing data with bar graphs and pictographs - 3.2.2.5
Using and interpreting a scale on a bar graph or pictograph with intervals larger than 1 - 3.2.2.6
Representing categorical data - 3.2.2.3
Considering how well a data representation communicates to an audience - 3.2.2.4
Interpreting what the numbers and symbols on a line plot mean - 3.2.2.9
Using a line plot to represent ordered, numerical data - 3.2.2.7
Using a line plot to represent measurement data that includes fractions - 3.2.2.8
Adding multiples of 10 and 100 to, and subtracting them from, 3-digit numbers - 3.7.2.10
Estimating and measuring liquid volume and mass - 3.7.1.2
Estimating answers to subtraction problems with 3-digit numbers - 3.7.2.11
Understanding measures of liquid volume and mass - 3.7.1.1
Solving related subtraction problems involving multiples of 100 - 3.7.2.12
Solving addition and subtraction problems involving liquid volume and mass - 3.7.1.3
Benchmark 3: Solve division problems (2-digit number divided by single-digit number). - 3.5.AB.3
Benchmark 4: Demonstrate fluency with multiplication facts to 10 x 10 - 3.5.AB.4
Benchmark 1: Represent and explain the relationship between multiplication and division. - 3.5.AB.1
Benchmark 2: Solve multiplication and division word problems and write equations to represent the problems. - 3.5.AB.2
Benchmark 5: Multiply a single-digit number by a multiple of 10, up to 90. - 3.5.AB.5
Benchmark 6: Solve multi-step problems involving multiplication and addition. - 3.5.AB.6
Writing equations with two operations - 3.5.2.9
Writing equations to show how a number is a multiple or non-multiple of 3, 4, or 6 - 3.5.2.8
Solving multi-step problems involving multiplication and addition - 3.5.2.5
Representing and comparing multiplication problems with pictures, diagrams, or models - 3.5.2.4
Modeling multiplication situations with arrays - 3.1.2.1
Solving problems with multiple solutions - 3.5.2.7
Finding factors of 2-digit numbers up to 30 using arrays - 3.1.2.2
Writing an equation with a letter to represent the unknown - 3.5.2.6
Identifying characteristics of numbers, including prime and square numbers, using arrays - 3.1.2.3
Using multiplication or division to solve word problems - 3.5.2.1
Using the inverse relationship between multiplication and division to solve problems - 3.5.2.3
Using multiplication facts to solve division problems - 3.5.2.2
Identifying and learning multiplication facts not yet known - 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
Benchmark 1: Measure and find the perimeter of 2-D figures using U.S. standard and metric units. - 3.4.AB.1
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
Learning multiplication facts to 10 x 10 - 3.1.3.4
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
Benchmark 3: Categorize quadrilaterals, including squares, rhombuses and rectangles, based on their attributes. - 3.4.AB.3
Benchmark 2: Find the area of 2-D figures using U.S. standard and metric units. - 3.4.AB.2
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
Describing the shape of ordered, numerical data - 3.2.1.6
Summarizing what is typical about the data as a whole - 3.2.1.7
Using data to compare groups - 3.2.1.4
Solving one- and two-step "how many more" and "how many less"  problems based on data presented in bar graphs - 3.2.1.5
Reading and interpreting bar graphs and pictographs - 3.2.1.8
Developing and revising a survey question - 3.2.1.9
Benchmark 2: Estimate and measure lengths in inches, feet, centimeters, and meters. - 2.6.AB.2
Benchmark 1: Recognize that, when measuring the same length, larger units yield smaller counts (and vice versa). - 2.6.AB.1
Benchmark 4: Solve comparison and other story problems about lengths. - 2.6.AB.4
Benchmark 3: Represent measurement data on a line plot. Quiz 1 (Resource Masters, A48–A49) in Session 2.5 - 2.6.AB.3
Writing and interpreting related multiplication and division equations - 3.5.2.10
Understanding multiplication as combining equal groups - 3.1.1.1
Writing, representing, and solving multiplication problems in context - 3.1.1.2
Identifying the number of groups and the number in each group (the factors), and the total number (the product) - 3.1.1.3
Understanding the role of parentheses in equation notation - 3.5.2.12
Understanding the relationship among skip counting, repeated addition, and multiplication - 3.1.1.4
Using and understanding multiplication and division notation - 3.5.2.11
Understanding the effect of multiplying a single-digit number by a multiple of 10 - 3.5.3.2
Multiplying one-digit numbers by multiples of 10 - 3.5.3.1
Benchmark 4: Write an addition equation to express the total number of objects in a rectangular array. - 2.7.AB.4
Benchmark 2: Use known combinations to add several numbers in any order. - 2.1.AB.2
Benchmark 3: Solve problems that involve equal groups. Quiz 1 (Resource Masters, A55) in Session 2.5 - 2.7.AB.3
Finding the product represented by an array by breaking it into parts - 3.1.2.4
Finding the area of a rectangle by covering it with square tiles - 3.1.2.5
Developing an understanding that the area of a rectangle can be found by multiplying its dimensions - 3.1.2.6
Understanding one of the equal parts of a whole as a unit fraction - 3.6.1.2
Representing fractional parts of an area - 3.6.1.1
Using representations to visualize how fractions relate to each other and are parts of a whole. - 3.6.1.7
Demonstrating that different-shaped pieces are the same fraction of a whole - 3.6.1.6
Understanding that the size of a fraction is determined by the whole - 3.6.1.5
Finding fractions of different-sized wholes - 3.6.1.4




List of all Files Validated:


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