Mathematical Emphasis
Investigation 1—Exploring Distance Between Numbers

• Skip counting by 2-, 3-, and 4-digit numbers between any two 4- or 5-digit number
• Relating repeated addition (or skip counting) to multiplication
• Using skip counting patterns to help solve multiplication and division problems
• Developing, explaining, and comparing strategies for subtracting 4- and 5- digit numbers
• Recording computation strategies using words, numbers, and arithmetic symbols
• Reading, writing, and sequencing 4- and 5-digit numbers

Investigation 2—Multiplication and Division Situations

• Developing, recording, and comparing strategies for solving multiplication and division problems
• Making sense of remainders
• Understanding relationships between multiplication and division
• Understanding how multiplication and division can represent a variety of situations
• Modeling situations with multiplication, division, and other operations

Investigation 3—Ways to Multiply and Divide

• Developing, explaining, and comparing strategies for estimating and finding exact answers to multiplication and division problems
• Recording strategies for solving multiplication and division problems
• Solving multiplication and division problems in more than one way
• Using relationships between multiplication and division to help solve problems

Tips For Helping At Home
Questions To Ask:

• What do you need to find out?
• What did you do in class to get started?
• Have you solved similar problems that would help?
• Can you make a drawing (model) to explain your thinking?
• What would happen if…?
• What do you need to do next?
• How do you know your answer is reasonable?
• Has the question been answered?
• Are there any questions you want to ask your teacher?

Helping At Home

• Notice when you use multiplication and division in your everyday life. Enlist your child’s help. For example, if you are planning a picnic, have your child help figure out what you need to buy. If there are 20 slices of bread in a loaf, how many loaves will be needed if each person eats two sandwiches?
• Play the games your child brings home. In the Digits Game, you’ll be finding the difference between two large numbers.
• Ask your child to tell you how he or she is multiplying and dividing. Show that you are interested in the approaches being learned at school. Because these strategies may be unfamiliar to you, listen carefully to your child’s explanation; you might even try to do a problem or two using the new procedure. Let your child be the teacher!

Vocabulary Terms

Factor

One of two or more numbers that are multiplied to get a product

Multiple

The product of a given whole number and another whole number

Multiplication Clusters

Groups of multiplication problems that will assist in solving a challenging multiplication problem. Multiplication clusters may include landmark numbers, decomposed numbers, or problems with answers close to the answer being sought.

Remainders

The amount left over, or extra, after solving a division problem

Skip Counting

Counting up repeatedly by a number (7, 14, 21, 28, 35…)

Strategy

A method of solving a problem

Mathematics Vocabulary Web site

Mathematics Strategy—Choosing Strategies for Computation

One goal of this unit is for students to explore many different computation strategies. As they come to understand these well, they will develop a deeper sense of computation and have more choices when trying to solve problems. During this unit, fifth graders will be:

• Working with a variety of strategies. They will understand why the strategies work and develop confidence using them.
• Finding similarities among strategies which will highlight the efficiency of different approaches.
• Thinking through different ways to approach problems, allowing students to examine which methods would be the easiest or most efficient to use in different situations.
• Emphasizing strategies over answers which helps children see there are multiple ways to reach one answer.
• Emphasizing the different meaning of operations so students will recognize what problems are asking of them.
• Thinking about why and when certain strategies are easy to use.

The focus of this unit will build the base for students to become accurate, efficient, and flexible in their computation work.

Source: Investigations in Number, Data, and Space: Building on Numbers You Know. Dale Seymour, 1998. (Pages 23, 24, 34, 56, 97 and 98)

Mathematics Game—The Estimating Game

Materials

Estimation Record Sheet

Calculator

Watch or clock

Numeral Cards

Playing the Game

1. Choose a format for the problems. Example: __ __ __ x __ __



2. Players take turns being the leader.



3. The leader deals out one card for each digit of the problem and records them in order without showing the players. Example: 7 4 1 x 0 3



4. The leader uncovers the problem and starts timing the play. Players have exactly 30 seconds to mentally estimate the answer without pencil and paper. (The leader finds the exact answer with a calculator.)



5. Players record their estimates on the record sheets. The leader gives the exact answer and the players find the difference between the exact answer and their estimate. This is the score for the round.



6. The leader deals out new cards for rounds 2 and 3 using the same problem format and same method of play.



7. After three rounds, the scores are totaled and the lowest score wins.

Extensions:

• Times can be less or more
• Vary the number of digits in the numbers
• Change the mathematical operation
• Decide what to do with remainders before rounds of play

Get to Estimation Record Sheet (for printing)

Get to Numeral Cards (for printing)