Mathematical Emphasis
Investigation 1—Multiplication Tables

• Looking for and using the multiplication patterns of numbers (for example, students identify multiples of 5 by checking that the units digit is either a 5 or a 0)
• Becoming familiar with the multiples of larger numbers (for example, skip counting by double-digit numbers such as 25)
• Identifying factors of larger numbers

Investigation 2—Double-Digit Multiplication

• Using familiar landmark numbers to solve problems (for example, determining whether the solution is greater than 100, 200, 300, and so on)
• Partitioning large numbers to multiply them more easily (for example, 24 x 8 is thought of as [20 x 8] + [4 x 8])
• Solving double-digit multiplication problems (for example, 32 x 21)

Investigation 3—Multiplication and Division Choices

• Understanding how division notation can represent a variety of division situations (including sharing and grouping situations)
• Creating a context that is representative of a division equation
• Using familiar landmark numbers to solve problems
• Using multiplication and division relationships to solve problems
• Exploring factors of large numbers (including triple-digit numbers) and developing conjectures about divisibility
• Finding multiples

Tips For Helping At Home
Questions To Ask:

• What is the problem about? Tell me in your own words.
• What did you do in class to get started?
• Can you solve a simpler version of the problem?
• What have you already tried? What steps did you take?
• Did you show all of your work?
• Does the answer make sense?
• How do you know your answer is correct?

Helping At Home

• Think about when you use multiplication and division in your everyday life and enlist your child’s help in solving these problems. For example, how many people are we expecting for a party? How many cookies do we need if we want to give each person 4 cookies? If you are going on a 3-day trip and need to travel 950 miles, about how many miles will you need to travel each day?
• Continue looking for items around your house that are arranged in arrays (rows and columns), such as tiles on the ceiling or floor. Talk with your child about ways of figuring out the total number.
• Play the Division Bingo game your child brings home for homework.
• Encourage your child to explain his or her strategies for multiplying and dividing numbers. Emphasis during this unit will be on thinking and reasoning carefully to solve mathematical problems. Students will be encouraged to develop more than one way to solve a problem and to use methods that are based on understanding numbers and their relationships. Some methods may not be the ones you are familiar with. Have your child teach you the strategies that are unfamiliar to you.

Vocabulary Terms

Arrays

Rectangular shape of rows and columns whose dimensions equal the factors of a multiplication problem and whose area equals the answer to that multiplication problem

Cluster Problems

A set of problems related to a larger division problem

Factors

Numbers in a multiplication problem that are multiplied to get the product

Multiple

Counting up by a specific number (3, 6, 9, 12, 15…)

Multiplication Table

A 12 x 12 table with multiplication factors from 1-12 across the top and down the left side. Answers to the multiplication problems are written at the intersections of the rows and columns

Partitioning

Breaking apart numbers into place value digits, example: 28 is 20 and 8

Remainder

Amount left over after dividing a number

Mathematics Vocabulary Web site

Mathematics Strategy—The Relationship Between Division and Multiplication

Multiplication and division are related operations: both involve two factors and the multiple created by multiplying those two factors. For example, the following is the set of linked multiplication and division problems:

Mathematics educators call all of these “multiplicative” situations because they all involve the relationships of factors and multiples. Many problems children encounter can be described by either multiplication or division. For example:

I bought a package of 24 treats for my dog. If I give her 3 treats every day, how many days will the package last?

This problem can be solved as division or multiplication: 24 ÷ 3 = 8 or 8 x ___ = 24.

The order of factors doesn’t matter in a multiplication situation. 3 treats for 8 days gives the same answer as 8 days with 3 treats per day.

Many elementary children are more comfortable with multiplication than with division. By recognizing the relationship between multiplication and division, children are able to solve problems more easily. Understanding the relationship between multiplication and division gives students a more solid understanding of number sense and the way our number system works.

Source: Investigations in Number, Data, and Space: Packages and Groups. Dale Seymour, 1998. (Page 35)

Mathematics Game—Division BINGO

Materials

Completed Multiplication Table for each player

One deck of Division BINGO Number Cards

Counters

Players: 1, 2 or 3

Playing the Game

1. Every player has a multiplication table to use as a Bingo card. The goal is to cover five numbers in a row, across, up and down or diagonally.



2. Take turns drawing a number card. Every player covers one number on their board that is a factor of the number card



3. If a wild card is drawn, that player decides on the number to call. (Try to call a number that does not help other players!)



4. The first player with five in a row wins Division Bingo.

Get to Multiplication Table for each player (for printing)

Get to BINGO Number Cards (for printing)