# MAKING 10

(c) 2022 George Gadanidis

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.

#### 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

1. What do you notice about the graph?
2. 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

• 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

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

#### 2.C. A CODING EXTENSION

1. Run the RANDOM and the CONSTRAINED code blocks at https://scratch.mit.edu/projects/408092534/editor
2. What is the difference in the graphs produced by the 2 code blocks?
3. What does the RANDOM code do?
4. How does it do it?
5. What does the CONSTRAINED code do?
6. How does it do it?
7. Change x + y = 100 in the CONSTRAINED code as shown below:
• x – y = 100
• x + y < 100
• x + 2y > 100
8. Make your own edits and run the code.
9. What did you learn?
10. 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

1. Click on the number cube to run the code
2. 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

1. Select a level.
2. 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.