For Educators

Multiplication Strategy Spotlights

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.

Common Core State Standards

Mathematical Practices:

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.

2nd Grade

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.

3rd Grade

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.

4th Grade

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.

5th Grade

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.

Downloads

Multiplication strategy PowerPoint

Note-taking guide

Optional assessment

Objectives:

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.

Materials:

• 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.)

Differentiation Considerations:

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.

Addition Stratagies Highlights:

• Repeated Addition

• Skip Counting

• Doubles

• Decompose with Place Value

Procedures:

These procedures are general and can be applied to each strategy spotlighted in this activity.

Name and describe the strategy using the slides in the presentation.
Review/model your thinking aloud for both examples, highlighting the strategy and allowing time for students to process and ask relevant questions.
3Transition and provide one note-taking guide to each student. Present the first problem and provide them 1-2 minutes for students think independently and solve the problem in their guide. Next, have students spend another 1-2 minutes sharing their strategy choice and thinking with a neighbor. Finally, allow 2-3 students to share their thinking with the entire class. If possible, determine students to share ahead of time. It can be beneficial to highlight strong uses of a strategy or to address any major misconceptions here. Repeat these steps with the remaining problems on the note-taking guide.
Read the written response question aloud and provide 3-5 minutes for students to reflect and respond independently. Provide time for 2-3 students to share their thinking and encourage students to add anything interesting from their peers to their own written responses.
Summarize the activity by reviewing the strategy and readdressing any major misconceptions.
Repeat steps 1-5 for each strategy. Consider highlighting one strategy at a time (per class period, per week, etc.) and practicing related problems so students have time to practice and develop their strategic thinking.

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.