1. Visual Algebra for Teachers
Activity Set 2.1
PREP PPTX

2. LINEAR EXPRESSIONS, EQUATIONS AND GRAPHS
Visual Algebra for Teachers
Chapter 2
LINEAR EXPRESSIONS, EQUATIONS AND GRAPHS

3. Visual Algebra for Teachers
Activity Set 2.1
Introduction to
Toothpick Figure
Sequences

4. PURPOSE To learn how to analyze sequences of toothpick figures:
Numerically
In words and
Symbolically
to see and define an underlying algebraic pattern and to use that algebraic pattern to answer questions about the sequence of toothpick figures.

5. MATERIALS
Toothpicks

6. INTRODUCTION

7. Figure Numbers
Figure Numbers, indexed here by the counting numbers; n = 1, 2, indicate the figure positions in a sequence of figures.

8. Counting Using Loops
When counting the number of shapes in a figure, we can use Looping to mark off portions of the figure.
A Loop is simply a shape drawn around a portion of a figure as illustrated here.

9. Counting Using Loops
Notice that the number of picks looped and the shapes of the loops can change; for looping, there are many correct choices.

10. Counting Using Loops
When counting the number of toothpicks in a figure using loops; mark your counts on the figure and write out the complete numerical expression.
Don’t just simplify, for example; “13” is not as helpful for seeing this pattern as the addition expression

11. Describing Looped Diagrams
When describing looping in words, try to use simple phrases.
Words and phrases should be clear and allow another person to see your counting technique.
Common types of phrases you might use while looping include:
1 more (or less) than the figure
Half of 1 more (or less) than the figure
1 more (or less) than twice the figure
Half of 1 more (or less) than twice the figure
Half of the figure
Three times a figure

12. PREP Question #1 (numerically)
Write in your coursepack, Activity Set 2.1 #1 (ONE)
Consider the following sequence of toothpick figures, Triangles. Build the figures with toothpicks if you can.
The FIRST STEP is to look at the figures Numerically
Use looping and count the total number of toothpicks in each figure without simply counting each individual toothpick.
Mark your individual counts by your loops and give each toothpick count as an addition expression (as illustrated in the Introduction).

13. PREP Question #2 (words)
Write in your coursepack, Activity Set 2.1 #2 (ONE)
The SECOND STEP is to describe your previous methods in Words.
Your words should describe the general technique you used for each toothpick figure in the set.
Another person should be able to recreate loops by reading your words.
Use the diagram for #2 ONE to remark loops and write words.

14. PREP Question #3 (use method)
Write in your coursepack, Activity Set 2.1 #3
Use your looping ideas and words to answer:
“How many toothpicks will there be in the 5th Triangles figure?”
Sketch or build the figure to double check your method.

15. PREP Question #4 (symbols)
See your coursepack, Activity Set 2.1 #6 (not #4!)
The THIRD STEP for analyzing the sequence of toothpick figures is to convert your words into Symbols.
Use the symbol n for the toothpick figure number and the symbol T for the total number of toothpicks.
Go back to activity 2, and below your Words, try to write each word expression as a symbolic equation T = an expression involving n and numbers, such as T = 7n (not a valid answer for this sequence).

16. Visual Algebra for Teachers
You are now ready for:
PREP QUIZ 2.1
See Moodle