IM: 7.4.4: Half as Much Again (Lesson)

By Newsela Staff

Last updated 2 months ago

12 Questions

4.1: Notice and Wonder: Tape Diagrams

What do you notice? What do you wonder?

4.2: Walking Half as Much Again

Complete the table to show the total distance walked in each case.

Jada’s pet turtle walked 10 feet, and then half that length again.
Jada’s baby brother walked 3 feet, and then half that length again.
Jada’s hamster walked 4.5 feet, and then half that length again.
Jada’s robot walked 1 foot, and then half that length again.
A person walked x feet and then half that length again.

Explain how you computed the total distance in each case.

Two students each wrote an equation to represent the relationship between the initial distance walked, x, and the total distance, y.

Mai wrote y = x+\frac{1}{2}x
Kiran wrote y = \frac{3}{2}x
Do you agree with either of them? Explain your reasoning.

Are you ready for more?

Zeno jumped 8 meters. Then he jumped half as far again (4 meters). Then he jumped half as far again (2 meters). So after 3 jumps, he was 8 + 4 + 2 = 14 meters from his starting place.

Zeno kept jumping half as far again. How far would he be after 4 jumps? 5 jumps? 6 jumps?

Before he started jumping, Zeno put a mark on the floor that was exactly 16 meters from his starting place. How close can Zeno get to the mark if he keeps jumping half as far again?

If you enjoyed thinking about this problem, consider researching Zeno's Paradox.

4.3: More and Less

Match each situation with a diagram.

Write a story for one of the diagrams that doesn't have a match.

For Diagram A, write an equation that represents the relationship between x and y.

10.

For Diagram B, write an equation that represents the relationship between x and y.

11.

For Diagram C, write an equation that represents the relationship between x and y.

12.

For Diagram D, write an equation that represents the relationship between x and y.

4.4: Card Sort: Representations of Proportional Relationships

Your teacher will give you a set of cards that have proportional relationships represented three different ways: as descriptions, equations, and tables. Mix up the cards and place them all face-up.

Take turns with a partner to match a description with an equation and a table.
For each match you find, explain to your partner how you know it’s a match.
For each match your partner finds, listen carefully to their explanation, and if you disagree, explain your thinking.

When you agree on all of the matches, check your answers with the answer key. If there are any errors, discuss why and revise your matches.