Core Content Connectors by Common Core State Standards: Mathematics 3rd Grade

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Grade 3 Overview

Operations and Algebraic Thinking

• Represent and solve problems involving multiplication and division.
• Understand properties of multiplication and the relationship between multiplication and division.
• Multiply and divide within 100.
• Solve problems involving the four operations, and identify and explain patterns in arithmetic.

Number and Operations in Base Ten

• Use place value understanding and properties of operations to perform multi-digit arithmetic.

Numbers and Operations—Fractions

• Develop understanding of fractions as numbers.

Measurement and Data

• Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.
• Represent and interpret data.
• Geometric measurement: understand concepts of area and relate area to multiplication and to addition.
• Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.

Geometry

• Reason with shapes and their attributes.

Operations and Algebraic Thinking	3.OA
Represent and solve problems involving multiplication and division.
1. Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.
CCCs linked to 3.OA.A.1	3.NO.2d1 Find the total number of objects when given the number of identical groups and the number of objects in each group, neither number larger than 5.
	3.NO.2d2 Find the total number inside an array with neither number in the columns or rows larger than 5.
	3.NO.2d3 Solve multiplication problems with neither number greater than 5.
	3.PRF.1d1 Use objects to model multiplication and division situations involving up to 5 groups with up to 5 objects in each group and interpret the results.
	4.NO.2d6 Find total number inside an array with neither number in the columns or rows larger than 10.
	4.NO.2d8 Match an accurate addition and multiplication equation to a representation.
	4.PRF.1d2 Use objects to model multiplication and division situations involving up to 10 groups with up to 5 objects in each group and interpret the results.
2. 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. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.
CCCs linked to 3.OA.A.2	3.NO.2d4 Determine how many objects go into each group when given the total number of objects and the number of groups where the number in each group or number of groups is not greater than 5.
	3.NO.2d5 Determine the number of groups given the total number of objects and the number of objects in each group where the number in each group and the number of groups is not greater than 5.
	3.PRF.1d1 Use objects to model multiplication and division situations involving up to 5 groups with up to 5 objects in each group and interpret the results.
3. 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.
CCCs linked to 3.0A.A.3	3.NO.2e1 Solve or solve and check one- or two-step word problems requiring addition, subtraction or multiplication with answers up to 100.
4. Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = _ ÷ 3, 6 × 6 = ?.
CCCs linked to 3.0A.A.4	4.NO.2d7 Determine how many objects go into each group when given the total number of objects and the number of groups where the number in each group or number of groups is not greater than 10.
Understand properties of multiplication and the relationship between multiplication and division.
5. Apply properties of operations as strategies to multiply and divide. Examples: 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).
CCCs linked to 3.OA.B.5	3.PRF.2d2 Apply properties of operations as strategies to multiply and divide.
6. Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.
CCCs linked to 3.OA.B.6	3.NO.2d4 Determine how many objects go into each group when given the total number of objects and the number of groups where the number in each group or number of groups is not greater than 5.
	3.NO.2d5 Determine the number of groups given the total number of objects and the number of objects in each group where the number in each group and the number of groups is not greater than 5.
Multiply and divide within 100.
7. 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 40 ÷ 5 = 8) or properties of operations. By the end of grade 3, know from memory all products of two one-digit numbers.
CCCs linked to 3.OA.C.7	None
Solve problems involving the four operations, and identify and explain problems in arithmetic.
8. 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.
CCCs linked to 3.OA.D.8	3.NO.2e1 Solve or solve and check one or two step word problems requiring addition, subtraction or multiplication with answers up to 100.
9. Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that four times a number is always even, and explain why four times a number can be decomposed into two equal addends.
CCCs linked to 3.OA.D.9	3.PRF.1e1 Describe the rule for a numerical pattern (e.g., increase by 2, 5 or 10).
	3.PRF.1e2 Select or name the three next terms in a numerical pattern where numbers increase by 2, 5 or 10.
	3.PRF.2d1 Identify multiplication patterns in a real word setting.

Numbers and Operations in Base Ten	3.NBT
Use place value understanding and properties of operations to perform multi-digit arithmetic.
1. Use place value understanding to round whole numbers to the nearest 10 or 100.
CCCs linked to 3.NBT.A.1	3.NO.1j3 Use place value to round to the nearest 10 or 100.
	3.NO.1j4 Use rounding to solve word problems.
2. 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.
CCCs linked to 3.NBT.A.2	3.NO.2c1 Solve multi-step addition and subtraction problems up to 100.
	3.NO.2b1 Use the relationships between addition and subtraction to solve problems.
	4.NO.2c2 Solve multi-digit addition and subtraction problems up to 1000.
3. 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.
CCCs linked to 3.NBT.A.3	4.NO.2f2 Solve multiplication problems up to two digits by one digit.

Numbers and Operations – Fractions	3.NF
Develop an understanding of fractions as numbers.
1. 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.
CCCs linked to 3.NF.A.1	3.NO.1l1 Identify the number of highlighted parts (numerator) of a given representation (rectangles and circles).
	3.NO.1l2 Identify the total number of parts (denominator) of a given representation (rectangles and circles).
	3.NO.1l3 Identify the fraction that matches the representation (rectangles and circles; halves, fourths, thirds, eighths).
	4.NO.1n1 Select a model of a given fraction (halves, thirds, fourths, sixths, eighths).
	4.NO.2g1 Using a representation, decompose a fraction into multiple copies of a unit fraction (e.g., ¾ = ¼ + ¼ + ¼ ).
2. Understand a fraction as a number on the number line; represent fractions on a number line diagram.
a. 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.
b. 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.
CCCs linked to 3.NF.A.2	3.NO.1l4 Identify that a part of a rectangle can be represented as a fraction that has a value between 0 and 1.
	3.NO.1l5 Locate given common unit fractions (i.e., ½, ¼, 1/8,) on a number line or ruler.
	4.NO.1l6 Locate fractions on a number line.
	4.NO.1l7 Order fractions on a number line.
3. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
4. Understand two fractions as equivalent (equal) if they are the same size or the same point on a number line.
5. 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.
6. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: 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.
7. 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.
CCCs linked to 3.NF.A.3	3.SE.1g1 Use =, <, or > to compare two fractions with the same numerator or denominator.
	4.SE.1h1 Express whole numbers as fractions.
	4.NO.1m1 Determine equivalent fractions.
	4.NO.2h3 Solve word problems involving addition and subtraction of fractions with like denominators (2, 3, 4, or 8).

Measurement and Data	3.MD
Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.
1. Tell and write time to the nearest minute and 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.
CCCs linked to 3.MD.A.1	3.ME.1a2 Solve word problems involving the addition and subtraction of time intervals of whole hours or within an hour (whole hours: 5:00 to 8:00, within hours: 7:15 to 7:45).
	3.PRF.1f1 Determine the equivalence between number of minutes and the fraction of the hour (e.g., 30 minutes = ½ hour).
	3.PRF.1f 2 Determine the equivalence between the number of minutes and the number of hours (e.g., 60 minutes = 1 hour).
2. 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.
CCCs linked to 3.MD.A.2	3.ME.1f1 Select appropriate units for measurement (liquid volume, area, time, money).
	3.ME.1f2 Add to solve one-step word problems.
	3.ME.2e1 Select appropriate tool for measurement: liquid volume, area, time, money.
	3.ME.2i1 Estimate liquid volume.
	4.ME.2g1 Determine whether a situation calls for a precise measurement or an estimation (distance, volume, mass, time, money).
Represent and interpret data.
3. 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. For example, draw a bar graph in which each square in the bar graph might represent five pets.
CCCs linked to 3.MD.B.3	3.DPS.1g1 Collect data, organize into picture or bar graph.
	3.DPS.1i1 Select the appropriate statement that describes the data representations based on a given graph (picture, bar, line plots).
	4.DPS.1g3 Collect data, organize in graph (e.g. picture graph, line plot, bar graph).
	4.DPS.1i1 Select the appropriate statement that describes the data representations based on a given graph (picture, bar, line plots).
	4.DPS.1j1 Select an appropriate statement that describes the most frequent or the least frequent data point using a line plot, picture graph, or bar graph.
	5.DPS.1c1 Collect and graph data: bar graph, line plots, picture graph (e.g., average height among three classrooms, # of boys and girls).
4. 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.
CCCs linked to 3.MD.B.4	3.ME.2e2 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch.
	3.ME.2e3 Measure to solve problems using number lines and ruler to 1 inch, ½ inch, or ¼ of an inch.
	3.DPS.1g2 Organize measurement data into a line plot.
	4.DPS.1k2 Apply results of data to a real world situation.
Geometric measurement: understand concepts of area and relate area to multiplication and to addition.
5. Recognize area as an attribute of plane figures and understand concepts of area measurement.
a. 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.
b. A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.
CCCs linked to 3.MD.C.5	3.ME.1d1 Use tiling and multiplication to determine area.
6. Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).
CCCs linked to 3.MD.C.6	3.ME1d2 Measure area of rectangles by counting squares.
7. Relate area to the operations of multiplication and addition.
a. 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.
b. 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.
c. 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.
d. Recognize area as additive. 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.
CCCs linked to 3.MD.C.7	3.ME.1d1 Use tiling and addition to determine area.
	4.ME.1d3 Use tiling and multiplication to determine area.
	4.ME.2h1 Apply the formulas for area and perimeter to solve real world problems.
	4.PRF.1f3 Apply the distributive property to solve problems with models.
Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.
8. 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.
CCCs linked to 3.MD.D.8	3.ME.1g1 Identify a figure as getting larger or smaller when the dimensions of the figure change.
	3.ME.2h1 Use addition to find the perimeter of a rectangle.
	4.ME.2h1 Apply the formulas for area and perimeter to solve real world problems.

Geometry	3.G
Reason with shapes and their attributes.
1. Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and 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.
CCCs linked to 3.G.A.1	3.GM.1h1 Identify shared attributes of shapes.
2. 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 four parts with equal area, and describe the area of each part as 1/4 of the area of the shape.
CCCs linked to 3.G.A.2	3.GM.1i1 Partition rectangles into equal parts with equal area.