In this activity, students will demonstrate their ability to use a variety of strategies to mentally solve multiplication 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 multiplication 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.2.OA.C.4 - 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 sum of equal addends. |
CCSS.Math.Content.3.OA.A.1 – Interpret products of whole numbers, e.g., interpret 5 x 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 x 7. |
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.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.A.1 - Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. |
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.4 - Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. 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. |
Students will be able to use a variety of number-sense based strategies to mentally solve multiplication problems.
Students will use writing to reflect on the effectiveness and efficiency of each strategy used.
• Building Blocks of Math series, specifically Multiplication
• Multiplication Strategy Spotlights PowerPoint Presentation
• Multiplication Strategy Spotlights Note-Taking Guide (1 per student)
• Optional Assessment: Multiplication 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 multiplication strategies more concrete and therefore easier to understand. Students can physically move manipulatives to show groups of equal size.
• Repeated Addition
• Skip Counting
• Doubles
• Decompose with Place Value
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 multiplication problems and asked to solve them using whatever strategies they would like. In addition, students must justify why they chose the strategies they did.