Tuesday, September 6, 2016

CCSS: 4th Grade Math - The Relationship Between Multiplication and Division

Common Core State Standard: Use place value understanding and properties of operations to perform multi-digit arithmetic.

Specific Objectives: Using base-10 blocks and calculators, students will determine how multiplication and division are interrelated through building, drawing, and explaining.

Vocabulary Terms:
Division (to divide): sharing or grouping a number into equal parts.  
Dividend: The number being divided.
Divisor: A number that will divide the dividend exactly.
Quotient: The result of division. 
Multiplication (to multiply): A mathematical operation where a number is added to itself a number of times. 
Factor: A whole number that multiplies with another number to make a third number.  
Product: The result when two numbers are multiplied.

Materials needed by Teacher: Paper for drawings, base-10 blocks, placemats, colored pencils, mini basketball and net.

Materials needed by Student: Paper for drawings, base-10 blocks, placemats, colored pencils, and calculators.

Plan A
      • Introduce multiplication and division with literature connection (5 min.).
      • Discuss prior knowledge by having students share what they know about multiplication and division. (5 min.)
      • Have students find a partner; pass out base-10 blocks, placemats, and calculators. (5 min.)
      • Use the overhead to model how to build, draw, and solve multiplication and division questions. Explain each step to students. (10 min.)
      • Provide questions for students: 11 × 4, 17 × 22, 23 × 34, 18 ÷ 3, 32 ÷ 4. Have each student draw their own replica of what they built with the base-10 blocks. Have students explain their process after they complete each question. (15 min.)
      • Assess students by observing and collecting their drawings, and asking questions for understanding during the activity. Have them check answers using calculators.
      •  Review this concept by playing “Basketball Math”. Split the class into two teams. Set two desks up with the base-10 blocks and placemats.
      • Call the first two-team members to the desks. Give them a multiplication or division problem and have them build. The first one with the correct answer is invited to the free throw line to take a shot for a point. The team with the most points at the end wins. (20 min.)
      • Encourage students to practice the concept by teaching someone at home.
Plan B
      • To extend to a higher level of thinking, give students division questions where the quotient has a remainder.
      • Have students build, draw, and explain their answers to the question. Have them check their answers with a calculator. (15 min.)
      • Have students create their own definition of a remainder based on their observations. (5 min.)
      • Play “Basketball Math.” (20 min.)
Plan C
      • To simplify, show students how multiplication is actually repeated addition and how division is grouping a number into equal parts. Use graphic organizers on the whiteboard for a visual. (10 min.)
      • Ask multiplication and division questions using single digits. Have students build, draw, and explain their answers to the question. Have them check their answers with a calculator. (15 min.)
      • Play "Basketball Math." (20 min.)

Discussion and Closure with Students: Answer any of the students’ questions. Make sure that they understand the concept. Have them draw a picture of an object that they own being multiplied or divided. (10 min.) 

Published in the December 2014 Edition of the MEA Voice (P. 20)