Mathematical Emphasis
Investigation 1—Comparisons with Record Numbers

• Comparing two numbers and developing strategies for determining their difference
• Developing ways of getting close to 100 by combining numbers
• Using landmark numbers (multiples of 10 and 100) to compare two quantities

Investigation 3—Adding with Money, Inches, and Time

• Solving addition problems with multiple addends and keeping track of the steps
• Developing a repertoire of addition strategies that rely on students’ number sense and understanding of number relationships
• Recognizing and using standard addition notation while using approaches based on sound number and operation sense
• Exploring number relationships and using important equivalencies in time, money, and linear measure
• Using estimation to make good approximations

Investigation 4—Working with Hundreds

• Developing and communicating strategies for combining and comparing quantities in the hundreds and thousands
• Using standard addition and subtraction notation to record comparison problems
• Using multiples of 100 as landmarks for adding and subtracting
• Collecting, recording, and graphing data
• Making predictions about data, describing and interpreting data

Investigation 5—Calendar Comparisons

• Exploring mathematical characteristics of the calendar and using them to solve problems

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 make a drawing (model) to help you figure out the problem?
• Can you solve a simpler version of the problem?
• What have you already tried? What steps did you take?
• Does your answer make sense?
• How do you know your answer is correct?
• Did you show all of your work?

Helping At Home

• When your child has an assignment to do at home—such as collecting data about the ages of pets and oldest relatives—offer your help and ask your child about what he or she is doing in class.
• Ask your child to describe any of the homework problems and tell you about the strategy used to solve it. Communication is an important part of mathematics, and students need to describe their strategies through talking, writing, drawing, or using concrete objects. You can be an important audience.
• You can also share your own ideas. At one point the class will work on the mathematics of “party planning.” You might explain how you would figure out how to fit a number of different activities into a two-hour block of time.
• An important emphasis in this unit is for students to recognize when and how to apply addition and subtraction and to develop procedures for adding and subtracting that they understand thoroughly and can use confidently. One of the most important things you can do is to show genuine interest in the ways your child solves problems, even if they are different from your own.

Vocabulary Terms

Landmark Number

Numbers that are familiar and can be used to solve other unfamiliar problems (10, 25, 50, 100)

Line Plot

Graph showing the values of data along a horizontal axis and X’s to mark the frequency of those values

Multiple

A mathematical operation where a number is added to itself a number of times

Strategy

Method used to solve a problem

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.

Rounding to Nearby Landmarks

Changing a 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 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.

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: Combining and Comparing. Dale Seymour, 1998. (Pages 37 and 38)

Mathematics Game—Get to Zero

Materials

One deck of numeral cards 0-9 (four of each, remove Wild Cards)

Score sheet for each player

Playing the Game

1. Deal six numeral cards to each player.



2. Players will use four of their cards to try and make two numbers that, when added, will be a sum of 100 (a 6 and a 5 could create the numbers 56 or 65). The goal is to get as close to 100 as possible. The player’s score is the difference between 100 and his/her sum.



3. Take turns using four cards to try to make 100.



4. To find the score for each turn, write the numbers and the total on the student score sheet. The score for the round is the difference between the total and 100. (43 + 55 = 98 and 100 – 98 = 2 so the score is 2.)



5. Put the used cards in a discard pile and deal out four new cards to each player. If a player runs out of cards before the end of the game, shuffle the discard pile and use them again.



6. After five rounds, total the scores. The player with the lowest score is the winner.

Get to Deck of Numeral Cards (for printing)

Get to Score Sheet (for printing)