# Math Teaching Tip: Multiplying and Dividing by Ten

Thanks to its partnership with publisher Eye on Education, EducationWorld is pleased to present this math teaching tip from Math Intervention: Building Number Power with Formative Assessments, Differentiation, and Games (Grades 3-5) by Jennifer Taylor-Cox.

This tip emphasizes four main goals for math instructors: they must help students achieve (1) accuracy, (2) efficiency, (3) flexibility and (4) fluency in solving math problems. Learn how and why to teach the concept of multiplying and dividing by ten, and explore a game intended to help students build on this concept.

Multiplying and dividing by ten builds fluency with number relationships and computation. When students understand the multiplying and dividing by ten concept, they are more apt to use mental math to solve problems and verify answers. Initially, students multiple ten by single-digit numbers and use two-digit dividends to divide by ten. Building on this idea, they can learn to work with numbers having greater than two digits.

Formative Assessment
To find out if a student can multiple and divide by ten, ask the student to solve the following equations: 2 x10, 3 x10, 4 x10, 40 ÷ 10, 60 ÷ 10, 90 ÷ 10
Ask the student to explain how he solved each problem. Analyze the student's level of proficiency through his accuracy, speed and explanations.

Successful Strategies
One of the foundational concepts associated with multiplying and dividing by ten is rational counting by 10s. Encourage students to skip county by tens starting with zero to help them learn the multiples of ten. To further help students understand the multiplying and dividing by ten concepts, use base ten blocks or other manipulatives to model operations.

Math Words to Use
Tens, Multiply, Multiplication, Divide, Division, Times Sign, Division Sign

Questions at Different Levels of Cognitive Demand

Recall:  What is 5 x10?
Comprehension:  How do you multiple a number by ten?
Application:  How would you use 7 x10 to solve 70 ÷ 10?
Analysis:  Which facts are not directly related to multiples of ten?
Evaluation:  How would you recommend that someone learn how to multiply and divide by ten?
Synthesis:  How could you use the multiplying and dividing by ten concepts to multiple and divide by nine?

Turtle Race (Game)

 Materials: Decahedron die (labeled 0-9) or 0-9 spinner Turtle Race Game Board (Multiplication) 2 small plastic turtles (or cubes to represent turtles) Directions: Each player places a turtle on one of the start boxes. The first player rolls the die (or spins the spinner). The number showing is multiplied by ten. The player can move her turtle if the box is in a box that is touching the box that the turtle is currently occupying. Moves can be forward, backward, vertical, horizontal, or diagonal. If the player cannot move, she misses her turn. If a move is possible, the player must move her turtle (even backwards). The next player rolls the die (or spins the spinner) and moves his turtle, if possible. Both turtles can occupy the same box at the same time, if necessary. Players take turns. The winner is the first player to finish line.

Content Differentiation:
Moving Back:  Use a hundred chart as a reference. Model equations with base ten blocks.
Moving Ahead:  Play the divide by ten version of this game by using numeral cards (0, 10, 20, 30, 40, 50, 60, 70, 80, 90) instead of die or spinner with the Turtle Race (Division) game board. Or add zero to each value on the multiplication game board and multiply by 100.

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