Mathematical Emphasis
Investigation 1—Net Change

• Developing the concept of net change
• Developing strategies for computing net change and for using net change to find a missing end point or starting point
• Recognizing that net change is the same regardless of the order in which changes are carried out
• Using a change in the negative direction to cancel a change in the positive direction
• Developing strategies for adding a long sequence of changes, including the use of a calculator
• Constructing different sequences of positive and negative numbers to produce the same net change/li>

Investigation 2—Representing Elevator Trips

• Representing numbers graphically
• Interpreting changes in direction on a graph
• Understanding how the passage of time is represented on graphs showing change over time
• Finding net change on graphs
• Comparing overall shapes of graphs

Investigation 3—Inventing Board Games

• Relating the direction of movement (left or right, up or down) to positive and negative numbers
• Using net change to determine an end point

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

• Sometimes your child will bring home games to teach you. As you play together, talk with your child about his or her strategies for thinking about and keeping track of the changes that happen in the elevator trips. You and your child should feel free to invent your own problems as you play.
• Look at graphs in newspapers and other sources that show things that change over time. These could include temperatures, heights, or populations. Your child may be asked to look for graphs showing change; if you can, help your child find graphs to bring to school.
• Using numbers to describe how something changes is a very important part of mathematics. Talking about the ups and downs of numbers helps children learn how to describe mathematical change.

Vocabulary Terms

Negative direction

Moving down or left on a number line

Negative number

Numbers with a value less than zero and located to the left of zero on a number line, can also indicate a change in the negative direction

Net change

How far and in what direction (positive and negative) an object has moved in all after a series of moves

Positive direction

Moving up or right on a number line

Positive number

Numbers with a value greater than zero and located to the right of the zero on the number line, can also indicate a change in a positive direction

Mathematics Vocabulary Web site

Mathematics Strategy—More Than One Meaning for -3

One use for negative numbers is to show location on the number line. Vertical number lines are marked with positive numbers above zero and negative numbers (indicated with a minus sign) below zero. Horizontal number lines are marked with positive numbers located to the right of zeros and negative numbers located to the left of zero.

We also use plus and minus signs to indicate changes in position along a number line. A change in position upward or to the right is positive (indicated with a plus sign); a change that runs downward or to the left is negative (indicated by a minus sign).

Source: Investigations in Number, Data, and Space: Up and Down the Number Line. Dale Seymour, 1998. (Page 11)

Mathematics Game—The Change Game

Materials

One set of Net Change Cards

Change Cards—a set for each player

Ladder, Game piece (optional, use if necessary to solve problems)

Playing the Game

1. Players turn their sets of Change Cards face down in front of them and draw seven cards from the pile.



2. Net Change Cards are placed face down in a pile in the middle. The top card is turned over to begin the round.



3. Each player tries to use as many of their seven Change Cards as possible to make the net change shown on the middle card. The ladder may be used to help solve the problems.



4. The goal is to use as many of the seven cards as possible. The player who uses the most cards wins that round of play. (If players use the same amount of cards, both count the round as a win.)



5. For each round, players begin with seven new cards. At the end of five rounds, the player winning the most rounds wins the game.

Variation

• Use the same rules but use only five cards.

Get to Net Change Cards (for printing)

Get to Change Cards (for printing)

Get to Changes Ladder (for printing)