In this activity, students will demonstrate their ability to use a variety of strategies to mentally solve division problems. Understanding the way these strategies work helps build students’ number sense, flexibility with numbers, and confidence in manipulating numbers in a variety of ways. Students will learn, review, and practice using four division strategies before showing their strategy skills on a mini quiz.
MP2 | Reason abstractly and quantitatively. |
MP3 | Construct viable arguments and critique the reasoning of others. |
MP7 | Look for and make use of structure. |
MP8 | Look for and express regularity in repeated reasoning. |
CCSS.Math.Content.3.OA.A.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. |
CCSS.Math.Content.3.OA.A.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 = ? |
CCSS.Math.Content.3.OA.B.5 - Apply properties of operations as strategies to multiply and divide.^{2} 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.) |
CCSS.Math.Content.3.OA.B.6 – Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8. |
CCSS.Math.Content.3.OA.C.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. |
CCSS.Math.Content.3.OA.D.9 – 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. |
CCSS.Math.Content.3.NBT.A.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. |
CCSS.Math.Content.4.OA.B.4 - 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. |
CCSS.Math.Content.4.NBT.B.5 - 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. |
CCSS.Math.Content.5.OA.A.2 - Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. |
CCSS.Math.Content.5.NBT.B.6 - 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. |
Students will be able to use a variety of number-sense based strategies to mentally solve division problems.
Students will use writing to reflect on the effectiveness and efficiency of each strategy used.
• Building Blocks of Math series, specifically Division
• Division Strategy Spotlights PowerPoint Presentation
• Division Strategy Spotlights Note-Taking Guide (1 per student)
• Optional Assessment: Division Strategy Spotlights Mini Quiz (1 per student)
• Optional: Manipulatives (counters, beads, tokens, base ten blocks etc.)
For additional support, allow students to use manipulatives to help make the division strategies more concrete and therefore easier to understand. Students can physically move manipulatives to split numbers into equal sized groups.
• Repeated Subtraction
• Number Lines
• Using Multiplication
• Halving
These procedures are general and can be applied to each strategy spotlighted in this activity.
Optional: After students have had exposure to and practice using all four strategies highlighted in this activity, consider using the optional mini quiz as a form of assessment. Here, students are provided four addition problems and asked to solve them using whatever strategies they would like. In addition, students must justify why they chose the strategies they did.