(c) 2022 George Gadanidis

# ABOUT

**Topics:** *from patterns to algebra; relationships where one quantity varies while another stays constant; linear and non-linear relations*

The Making 10 activity is designed to have a **low floor** and a **high ceiling** and may be used across a number grades.

- We first did this activity in grades 4/5 classrooms.
- Then in grades 6-8 classrooms.
- And also in a grade 9 classrooms.
- We also did part of this activity in grades 1-3 classrooms with concrete materials, as shown in the concept map below.

**MENU**

1. INITIAL TASK

#### 1.a. **Do the following**

- Roll a number cube to get a number 1-6
- Place the number rolled in the first blank of __ + __ = 10
- Calculate and record the missing number for the second blank
- For example, if you rolled a 3, your number sentence would become 3 + 7 = 10

- Repeat this until you exhaust all possibilities
- 3 + 7 = 10
- __ + __ = 10
- __ + __ = 10
- …

- Record the pairs of numbers in a table, and also as ordered pairs

- Plot the ordered pairs on a grid, as shown below for (3, 7): 3 across and 7 up

#### 1.B. REFLECT

- What do you notice about the graph?
- Offer an explanation.

#### 1.C. VIDEO OVERVIEW

View the video below, which summarizes and extends the activity above.

2. IN A STORY

#### 2.A. READ THE STORY

Read The Pleasure of Making 10.

- STOP ON PAGE 7
- What surprise did Molly and Alexander experience?
- What made it surprising?

- STOP ON PAGE 17
- What is the most interesting fact you learned about Rene Descartes?
- Conduct an Internet search to find one more interesting fact about Rene Descartes.

- STOP ON PAGE 21
- What beauty have you experienced in mathematics?

- STOP ON PAGE 26
- What would you do next if you were Molly or Alexander?

#### 2.B. MATH EXTENSIONS

- Complete the math extensions on pages 27-30 of the story.

#### 2.C. A CODING EXTENSION

- Run the RANDOM and the CONSTRAINED code blocks at https://scratch.mit.edu/projects/408092534/editor
- What is the difference in the graphs produced by the 2 code blocks?
- What does the RANDOM code do?
- How does it do it?
- What does the CONSTRAINED code do?
- How does it do it?
- Change x + y = 100 in the CONSTRAINED code as shown below:
- x – y = 100
- x + y < 100
- x + 2y > 100

- Make your own edits and run the code.
- What did you learn?
- What else do you want to know?

3. WITH A SIMULATION

#### 1.A. SIMULATION

Try the simulation at https://researchideas.ca/mathncode/sims-randpairs.html

- Click on the number cube to run the code
- Edit the
**+**and the**10**in x + y = 10 and notice how the graph changes.

#### 2.B. GAME

Try the game at https://researchideas.ca/mathncode/games-randpairs.html

- Select a level.
- Edit the code to try to hit the points with water balloons.

4. WHAT DID YOU DO IN MATH TODAY?

Imagine someone in your family asks you: *What did you do in math today?*

Script a dialogue that would share what you learned in a way that would offer a mathematics surprise.