IM 6.5.2 Lesson: Using Diagrams to Represent Addition and Subtraction

Author:GeoGebra Classroom Activities, IM 6 – 8 Math, IM 6 - 8 Math

Here is a rectangle.

What number does the rectangle represent if each small square represents:

0.1?

0.01?

0.001?

Here is a square.

What number does the square represent if each small rectangle represents:

10?

0.1?

0.00001?

You may be familiar with base-ten blocks that represent ones, tens, and hundreds. Here are some diagrams that we will use to represent digital base-ten units. A large square represents 1 one. A rectangle represents 1 tenth. A small square represents 1 hundredth.

The applet has tools that create each of the base-ten blocks. Select a Block tool, and then click on the screen to place it.

Click on the Move tool when you are done choosing blocks.

Here is the diagram that Priya drew to represent 0.13. Draw a different diagram in the applet below that represents 0.13. Explain why your diagram and Priya’s diagram represent the same number.

Here is the diagram that Han drew to represent 0.25. Draw a different diagram that represents 0.25 in the applet below. Explain why your diagram and Han’s diagram represent the same number.

Draw or describe two different diagrams that represent 0.1.

Draw or describe two different diagrams that represent 0.02.

Draw or describe two different diagrams that represent 0.43.

Use diagrams of base-ten units to represent 0.03 + 0.05 and find the resulting value. Think about how you could use as few units as possible to represent each number.

Use diagrams of base-ten units to represent 0.06 + 0.07 and find the resulting value. Think about how you could use as few units as possible to represent each number.

Use diagrams of base-ten units to represent 0.4 + 0.7 and find the resulting value. Think about how you could use as few units as possible to represent each number.

Here are two ways to calculate the value of 0.26 + 0.07. In the diagram, each rectangle represents 0.1 and each square represents 0.01.

Use what you know about base-ten units and addition of base-ten numbers to explain why ten squares can be “bundled” into a rectangle.

Use what you know about base-ten units and addition of base-ten numbers to explain how this “bundling” is reflected in the computation.

Find the value of by drawing a diagram in the applet below. Can you find the sum without bundling? Would it be useful to bundle some pieces? Explain your reasoning.

Calculate . Check your calculation against your diagram in the previous question.

Find each sum.

The larger square represents 1, the rectangle represents 0.1, and the smaller square represents 0.01.

A distant, magical land uses jewels for their bartering system. The jewels are valued and ranked in order of their rarity. Each jewel is worth 3 times the jewel immediately below it in the ranking. The ranking is red, orange, yellow, green, blue, indigo, and violet. So a red jewel is worth 3 orange jewels, a green jewel is worth 3 blue jewels, and so on. If you had 500 violet jewels and wanted to trade so that you carried as few jewels as possible, which jewels would you have?

Suppose you have 1 orange jewel, 2 yellow jewels, and 1 indigo jewel. If you’re given 2 green jewels and 1 yellow jewels, what is the fewest number of jewels that could represent the value of the jewels you have?

Here are diagrams that represent differences. Removed pieces are marked with Xs. The larger rectangle represents 1 tenth. For each diagram, write a numerical subtraction expression and determine the value of the expression.

Express each subtraction in words.

Find each difference by drawing a diagram and by calculating with numbers. Make sure the answers from both methods match. If not, check your diagram and your numerical calculation.