In Grade 3, instructional time should focus on four critical areas: (1) developing understanding of multiplication and division and strategies for multiplication and division within 100; (2) developing understanding of fractions, especially unit fractions (fractions with numerator 1); (3) developing understanding of the structure of rectangular arrays and of area; and (4) describing and analyzing two-dimensional shapes.
Represent and solve problems involving multiplication and division.
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.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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2 - Interpret (products of whole numbers)
2 - Interpret (5x7 as total number of objects in 5 groups of 7 objects each)
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2 - I can interpret (products of whole numbers)
2 - I can interpret (5x7 as total number of objects in 5 groups of 7 objects each)
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A. Multiplication is a way of representing repeated addition of the same number.
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A.1 Is there a faster way to add if the numbers in the problem are all the same?
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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.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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2 - Interpret (quotients of whole numbers)
2 - Interpret (56/8 as number of objects in each share when 56 objects are partitioned into equal shares)
2 - Interpret (56/8 as the number of shares when 56 is partitioned into into equal shares of 8 objects each)
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2 - I can interpret (quotients of whole numbers)
2 - I can interpret (56/8 as number of objects in each share when 56 objects are partitioned into equal shares)
2 - I can interpret (56/8 as the number of shares when 56 is partitioned into into equal shares of 8 objects each)
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A. Division is a way of representing repeated subtraction with the same number.
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A.1 Is there a faster way to subtract if the numbers in the problem are all the same?
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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.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Multiplication and division
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3 - Use (multiplication and division within 100 to solve word problems)
2 - Solve (word problems involving equal groups)
2 - Solve (word problems involving arrays)
2 - Solve (word problems involving measurement quantities)
3 - Use (drawings and equations with a symbol for the unknown number)
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3 - I can use multiplication and division within 100 to solve word problems.
2 - I can solve word problems involving equal groups.
2 - I can solve word problems involving arrays.
2 - I can solve word problems involving measurement quantities.
3 - I can use drawings and equations with a symbol for the unknown number.
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A. Multiplication and division is used to solve real world problems.
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A.1 How can I work a multiplication or division problem if I am having trouble with it?
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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 = ?.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Multiplication and division
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2 - Determine (the unknown whole number in a multiplication equation relating 3 whole numbers)
2 - Determine (the unknown whole number in a division equation relating 3 whole numbers)
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2 - I can determine the unknown whole number in a multiplication equation relating 3 whole numbers.
2 - I can determine the unknown whole number in a division equation relating 3 whole numbers.
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A. Determining the unknown number in a multiplication or division equation is a basic skill in mathematics.
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A.1 Why do I need to know how to find the unknown number in a multiplication or division equation?
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Understand properties of multiplication and the relationship between multiplication and division.
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.)
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Properties
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3 - Apply (properties of operations to multiply and divide)
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3 - I can apply properties of operations to multiply and divide.
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A. Knowing the properties of operations makes problem solving easier.
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A.1 Why should I understand the properties of operations?
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Understand division as an unknown-factor problem.
For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Division
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2 - Understand (division as an unknown-factor problem)
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2 - I can understand division as an unknown-factor problem.
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A. One can solve simple division problems by using multiplication facts.
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A.1 Can I use multiplication to do division problems?
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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.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Multiplication
Division
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2 - Multiply (within 100 with fluency)
2 - Divide (within 100 with fluency)
3 - Use (strategies such as relationship between multiplication and division or properties of operations)
1 - Memorize (all products of two one-digit numbers)
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2 - I can multiply within 100 with fluency.
2 - I can divide within 100 with fluency.
3 - I can use strategies such as relationship between multiplication and division or properties of operations.
1 - I can memorize all products of two one-digit numbers.
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A. Multiplying and dividing quickly makes problem solving faster and easier.
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A.1 Why do I need to memorize multiplication facts?
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Solve problems involving the four operations, and identify and explain patterns in arithmetic.
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.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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2 - Solve (two-step word problems using the four operations)
2 - Represent (problems using equations with letter for unknown quantity)
5 - Assess (reasonableness of answer)
3 - Use (mental computation)
3 - Use (estimation)
3 - Use (rounding)
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2 - I can solve two-step word problems using the four operations.
2 - I can represent problems using equations with letter for unknown quantity.
5 - I can assess reasonableness of answer.
3 - I can use mental computation.
3 - I can use estimation.
3 - I can use rounding.
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A. Many real world problems require more than one step to solve.
B. It is a good idea to determine the reasonableness of the answer.
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A.1 When will I need to write an equation?
B.1 How do i check for reasonableness?
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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.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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2 - Identify (arithmetic patterns)
2 - Explain (arithmetic patterns)
3 - Use (properties of operations)
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2 - I can identify arithmetic patterns.
2 - I can explain arithmetic patterns.
3 - I can use properties of operations.
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A. Seeing patterns in mathematics makes math more fun and easier to do.
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A.1 How can I use patterns in math?
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