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C. Algebra · Patterns, Variables, Coding and Modelling

Patterns, Variables, Coding and Modelling: Unit Review

C1.1 C1.2 C1.3 C1.4 C2.1 C2.2 C2.3 C3.1 C3.2 C4 A1.3 A1.4 A1.6About 40 minutes
Learning goals
  • I can describe, create, translate and extend patterns, predict terms and find missing parts.
  • I can use variables, make two sides equal, and find equivalent ways to show numbers to 100.
  • I can write, run, change and debug code, including code for two robots at the same time.
  • I can use the modelling steps to solve a real-life problem.

Words to know

growing pattern
A pattern that gets bigger by the same amount each time.
pattern rule
Tells where a pattern starts and how it changes.
variable
A symbol that stands for a number.
equivalent
Having the same value.
concurrent events
Things that happen at the same time.
model
A drawing, table, pattern or number sentence that shows a real-life problem.

Time to show what you know!

In this unit you were a pattern detective, a mystery-number solver, a balance fixer, a coder and a math modeller. This review has a few questions from every lesson. Try each one, then press Show answer to check.

If a question is tricky, that is okay! Go back to that lesson, look at the examples, and try again.

RepeatingGrowingShrinkingthe core repeatsA B A B A B1, 2, 3, 4add 1 each time4, 3, 2, 1take away 1 each time
The three kinds of patterns from this unit: one repeats a core, one grows by the same amount, and one shrinks by the same amount.
☐ + 410Level, so both sides are equal: ☐ = 6
A level balance means both sides are equal. What plus 4 makes 10? 6, so ☐ = 6.

Patterns in Geometric Designs

1

Repeating, growing or shrinking? 🟦 | 🟦🟦🟦 | 🟦🟦🟦🟦🟦

2

Which two attributes change? big red circle, small yellow circle, big red circle, small yellow circle

3

What is the core? 🔺 🔺 🟩 🔵 🔺 🔺 🟩 🔵

Creating and Translating Patterns with Shapes and Numbers

1

Translate into letters: 🌲 🍁 🍁 🌲 🍁 🍁

2

Translate into numbers: ⚪⚪⚪⚪ | ⚪⚪⚪⚪⚪⚪⚪ | ⚪⚪⚪⚪⚪⚪⚪⚪⚪⚪

3

Create a shrinking pattern that starts at 20 and goes down by 4. Write 4 terms.

Pattern Rules: Extend, Predict and Find What Is Missing

1

Find the rule: 7, 12, 17, 22

2

Find the missing number: 80, 70, ___, 50

3

In 🟥 🟨 🟩 🟥 🟨 🟩 ..., what colour is the 12th term? Justify.

4

Towers have 2, 5, 8 cubes. Predict term 5.

Number Patterns to 100

1

What number is 10 more than 58? 10 less?

2

Count by 25s: 25, ___, ___, 100

3

Continue: 1 + 9 = 10, 11 + 9 = 20, 21 + 9 = 30, ___

Mystery Symbols: Using Variables

1

Find the number: ☐ + 8 = 15

2

Find the number: ⭐ + ⭐ = 20

3

Nia had some crayons. She gave away 4. Now she has 9. Write a number sentence with a variable. What does the variable stand for?

Balancing Act: Making Two Sides Equal

1

What do you add to the left side to make them equal? 7 + 2 ☐ 6 + 6

2

What do you subtract from the right side to make them equal? 10 + 4 ☐ 9 + 9

3

Fill in the box: 30 + 30 + ☐ = 50 + 20

Same Amount, Different Ways: Equivalent Relationships to 100

1

Fill in: 85 = 70 + ___

2

Make it easier: 29 + 6 = 30 + ___

3

Are 3 quarters and 7 dimes plus 1 nickel the same amount?

Coding: Steps in Order and at the Same Time

1

Sequential or concurrent? The snow falls while the children skate.

2

Run the code: START with 35 → ADD 10 → SUBTRACT 5 → SAY the number

3

Beep and Boop start at 0. Each beat, Beep adds 5 and Boop adds 2. After 3 beats, what does each have?

Reading, Changing and Debugging Code

1

Beep is at column 1, row 1. The star is at column 2, row 4. Code: ➡ Move right 1, ⬆ Move up 2. Find the bug.

2

Code: START with 10 → ADD 20 → SAY. If you change ADD 20 to ADD 30, how does the outcome change?

3

Beep (column 2, row 1) and Boop (column 4, row 1) run at the same time. Beat 1: Beep right 1, Boop left 1. What happens?

Math Models: Solving Real-Life Problems

1

What are the four modelling steps?

2

16 children are going to the pool. Each car holds 5 children. How many cars are needed?

3

Your class saves 5 dollars each week. What are you assuming if you say you will have 30 dollars in 6 weeks?

Just for fun

Riddle: What comes next? 🥚 🐣 🐥 ___

A 🐔! It's a growing pattern… a growing chicken!

How to use this review

  • Do two or three sections a day, not the whole review at once.
  • Let your child try each question before pressing Show answer. Ask How do you know? even when the answer is right.
  • Use real objects (blocks, coins, Lego, a hundred chart, a floor grid) whenever you can.
  • Each section is named after a lesson. If a section feels hard, go back to that lesson's examples and More practice questions, then try the review again another day.
Check your understanding

Quiz

1.

What kind of pattern is 30, 25, 20, 15?

2.

Which matches 🔵 🔵 🟥 🔵 🔵 🟥?

3.

What is missing? 14, 18, ___, 26

4.

On a hundred chart, what is directly above 64?

5.

What number is ☐? ☐ − 6 = 14

6.

What do you add to the left side to make them equal? 8 + 3 ☐ 7 + 7

7.

Which is equivalent to 67?

8.

What are concurrent events?

9.

Code: START with 50 → SUBTRACT 10 → SUBTRACT 10. If you remove one SUBTRACT 10, the outcome is...

10.

In mathematical modelling, what is an assumption?

For parents and teachers

Use this review to see which lessons need another look. Each practice section and most quiz questions match one lesson.

What mistakes tell you

  • Patterns in Geometric Designs: notices only one attribute, or calls an uneven list a growing pattern. Revisit the three detective questions and the attribute list.
  • Creating and Translating Patterns: changes the structure while translating (AAB becomes AB) or miscounts terms. Line the two patterns up and touch-count.
  • Pattern Rules, Extend, Predict, Missing: gives a rule without a start, or guesses from only the last term. Make a table and check every jump.
  • Number Patterns to 100: mixes up 10 more and 1 more, or above and below on the hundred chart. Practise on a printed hundred chart and with coins.
  • Mystery Symbols (Variables): adds all the numbers it sees (writes 23 in ☐ + 8 = 15), or gives the same symbol two values. Ask what the symbol stands for in the story.
  • Balancing Act: adds the difference to the bigger side, or works out only one side. Find the value of both sides first, then use a balance or number line.
  • Equivalent Relationships to 100: loses a ten when regrouping (63 = 50 + 3), or forgets to take away what was moved. Use bundles of 10 and coins.
  • Coding (sequential and concurrent): runs one robot's code all the way before the other's. Act it out beat by beat on a floor grid.
  • Reading, Changing and Debugging Code: rewrites everything instead of finding the one wrong step, or cannot say how a change affected the outcome. Run the code slowly and compare old and new outcomes.
  • Math Models: jumps to a number without saying the question or assumption, or forgets leftovers (people without a seat). Revisit the four steps and the picnic table example.

If your child gets most of a section right and can explain how they know, they are ready to move on.