Grade 3 | Mathematics

Action steps

1. Use place value understanding to round whole numbers to the nearest 10 or 100.

2. Add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

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.

Action steps

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.

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.

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.

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 = ?

5. Apply properties of operations as strategies to multiply and divide. Example: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known.

6. Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.

7. 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.

8. Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity.

9. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

10. Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.

Action steps

1. Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts.

2. Understand a fraction a/b as the quantity formed by a parts of size 1/b.

3. Understand a fraction as a number on the number line.

4. Represent fractions on a number line diagram.

5. Explain and represent equivalence of fractions using models and number lines.

6. Compare fractions by reasoning about their size.

Action steps

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).

2. Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.

3. 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 1/4 of the area of the shape.

Action steps

1. Tell and write time to the nearest minute and measure time intervals in minutes.

2. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram.

3. Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l).

4. 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.

5. Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories.

6. 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 5 pets.

7. Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch.

8. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units— whole numbers, halves, or quarters.

9. Recognize area as an attribute of plane figures and understand concepts of area measurement.

10. Measure areas by counting unit squares (square cm, square m, square in, square ft., and improvised units).

11. Relate area to the operations of multiplication and addition.

12. Solve real world and mathematical problems involving perimeters of polygons.Include 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.