Mathematical Emphasis
Investigation 1—Everyday Uses of Money

• Exploring number relationships in the context of money
• Developing strategies for combining numbers, particularly money amounts
• Using landmark numbers (multiples of 10 or 0.10 and 100 or 1.00) to compare and find differences between two quantities
• Using standard addition and subtraction notation to record combining and comparing situations
• Using the calculator to solve problems
• Interpreting decimals on the calculator as amounts of money

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

• How do you know your answer is correct?
• When you buy several things, ask your child to help you estimate how much all the items will cost.
• If your family goes to a restaurant, ask your child to estimate how much the meal will cost. See if he or she can figure out the cost without using pencil and paper. Ask your child how he or she figured it out.
• Children need to get first-hand experience with distances like 1/10 of a mile, 1/2 of a mile, or a mile. If you drive, show them the odometer on your car and ask them to help you figure our how far it is to the store. Encourage your child to figure out the answer mentally.
• Another way to get experience with decimals is by walking, running, or riding bikes on routes where you know the distance. Help your child figure out how far it is to different places in your neighborhood. If he/she goes somewhere and back, how far is it?

Vocabulary Terms

Integer

Positive whole numbers, negative whole numbers, and zero

Landmark Number

A familiar number that can be used to solve a problem using less familiar numbers; examples of landmark numbers include 10, 25, 100

Negative Integer

Whole numbers less than zero

Positive Integer

Whole numbers greater than zero

Mathematics Vocabulary Web site

Mathematics Strategy—Three Powerful Addition Strategies

Left to Right Addition—Biggest Quantities First
When students develop their own strategies for addition from an early age, they usually move from left to right, starting with bigger parts of the quantities.

For example, when adding 27 + 27, a student might say, “20 and 20 is 40, then 7 and 7 is 14, so 40 plus 10 more is 50 and then 4 more makes 54.”

One advantage of this approach for students is that when they work with the largest quantities first, it’s easier to maintain a good sense of what the final sum should be. Another advantage is that students keep seeing the quantity of 27 as a whole quantity rather than breaking it into separate digits and losing track of the whole.

This strategy is both efficient and accurate. Some people who are extremely good at computation use this strategy as their basic approach to addition, even with large numbers.

Using Nearby Landmarks
Changing an unfamiliar number to a more familiar one that is easier to compute with is another strategy that students should develop. Multiples of 10 and 100 are especially useful landmarks at this age.

For example, in order to add 199 and 149, a student might think of the problem 200 plus 150, find a total of 350, then subtract 2 to compensate for the 2 added at the beginning and get an answer of 348.

There are other useful landmarks. If adding 22, 26, and 28, a child might use 25 as the landmark: “Three 25’s is 75. I’m under by 3 and over by 4 so my answer is 76.”

There are no rules about which landmarks in the number system are the best to use. It simply depends on whether using nearby landmarks helps a child solve the problem.

Changing the Order of the Numbers
Simply changing the order of the numbers being added is often a great help. For example, when adding 33 + 26 + 7, the problem becomes much simpler as soon as 33 + 7 is recognized as 40. Changing the order of numbers can also involve breaking some numbers into two parts. For example, when adding 108 + 45 + 162, one might add it this way:

160 + 40 is 200, plus another 100 is 300; 2 + 8 is 10 plus 5 more is 15 for a total of 315.

These strategies may be used alone or in combination, whether the problem is being done mentally, on paper, or with a calculator. Children should always be encouraged to look over the whole problem before starting. There are no rules for which strategies are best for which problems. It depends on what works for a particular child and how that child sees a particular problem.

Source: Investigations in Number, Data, and Space: Money, Miles and Large Numbers. Dale Seymour, 1998. (Pages 10 and 11)

Mathematics Game—Get to Zero

Materials

One deck of numeral cards

Score sheet for each player

Players: 1, 2 or 3

Playing the Game

1. Deal out six numeral cards to each player.



2. Players make two numbers with four of the cards. The goal is to make two numbers whose sum is as close to 100 as possible. If a player had a 3, 5, 7, and 9, a player could make 57 + 39 = 96.



3. These addition problems are written on the score sheet for round one.



4. To find your score, find the difference between your total and 100. For 57 + 39 + 96, the score would be 4 because 100 – 96 = 4. Your goal is to get as close to 0 as possible.



5. Put the used cards in a discard pile and deal four new cards to each player.



6. For each round of play, make more numbers whose sum is close to 100. When you run out of cards, mix up the discard pile and use them again.



7. Five rounds make one game. Total your scores for the five rounds. Lowest score wins!

Variation

• For students needing a challenge, work with 2-digit numbers but use a decimal point somewhere in each number. (Caution: Children have been using a decimal point in reference to money; this might be a difficult concept to use out of the familiar context of money.)

Get to Numeral Cards (for printing)

Get to Score Sheet (for printing)