# 2. MAKING 10

“I know numbers are beautiful. If they aren’t beautiful, nothing is.”
― Paul Erdős

#### IN THE CLASSROOM

###### Ontario Curriculum
• Gr. 1/2
• B2.2 – addition facts up to 10/20
• Gr. 3/4
• B2.1 – use properties of operations to solve problems
• C2.1 – use variables in various contexts
• C.3.2 – read and alter existing code; sequential, concurrent, and repeating & nested events
• Gr.5-8
• C2.2 – evaluate algebraic expressions
• C2.3 – solve equations
• C3.2 – conditional coding structures
• Gr. 6
• C1.1 – growing, shrinking & linear patterns
• C1.2 – various representations of linear growing patterns, algebraic expressions and equations
• Gr. 7/8
• C1.1 – constant rates & initial values)
• C1.2 – various representations of linear growing patterns, algebraic expressions and equations
• Gr. 9
• C1.1 – research an algebraic concept to tell a story
• C3.1 – compare shapes of graphs of linear and non-linear relations, describe their rates of change, make connections to growing and shrinking patterns, and make predictions
• C4.1 – compare characteristics of graphs, tables of values, and equations of linear and non-linear relations
• C2 – apply coding skills to represent mathematical concepts and relationships dynamically, and to solve problems, in algebra and across the other strands
• C4 – demonstrate an understanding of the characteristics of various representations of linear and non-linear relations, using tools, including coding when appropriate
###### Implementation
• Gr. 1-2
• Students use concrete materials to represent possible solutions to __ + __ = 10.
• They notice that bars fit together to form a staircase pattern. As the number of yellow increases, the number of green decreases.
• Gr. 3-9
• Students use a number cube to get the first number in __ + __ = 10. The calculate the second number.
• When they plot the pairs of numbers (ordered pairs) on a grid, they are surprised that they line up!
• Students start with a Scratch code that plots __ + __ = 100.
• They edit the code to solve puzzles of matching different graphs.
• The complexity of the puzzles can vary depending on the grade level.
• This develops the conceptual basis for understanding linear and non-linear relationships.

#### 2.A MAKING 10 – HANDS-ON

Q1. What does this image represent in grades 1/2 classrooms?

#### 2B. PLOTTING RANDOM PAIRS

Q2. 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
• 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

#### 2C. VIDEO OVERVIEW

Q3. View the video below, which summarizes and extends the activity above. What did you learn?

#### 2D. Graphing Puzzle

Q4. Create number sentences that have graphs approximately like the ones shown on the right. Try these as a start:

• __ – __ = 2
• __ x __ = 12
• __2 + __2 = 25

#### 2E. CODING SIMULATION

Q5. Try the simulation at https://imaginethis.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.

#### 2F. CODING PUZZLE – PLOTTING WITH SCRATCH

Q6. Run the code below at this link: https://scratch.mit.edu/projects/1055468823/editor

• What does the code do?
• How does it do it?

Q7. Edit the code to get the following graphs.