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C. Algebra · Patterns, Equations, Coding and Modelling

Patterns, Equations, Coding and Modelling: Unit Review

A1 C1.1 C1.2 C1.3 C1.4 C2.1 C2.2 C2.3 C3.1 C3.2 C4About 40 minutes
Learning goals
  • I can describe, create, translate and extend patterns, use pattern rules to predict, and find missing elements.
  • I can use variables, compare expressions with = and ≠, and show numbers to 1000 in equivalent ways.
  • I can write, run, change and debug code with loops.
  • I can use the modelling steps to solve a real-life problem.

Words to know

core
The group of elements that repeats in a repeating pattern.
table of values
A two-column table that shows each term number and its value.
variable
A letter or symbol that stands for a number.
equivalent
Having the same value.
loop
Part of the code that repeats.
assumption
Something we treat as true so we can solve a problem.

Let's review!

In this unit you became a pattern detective, used variables, compared expressions, showed numbers to 1000 in many ways, coded with loops and solved real-life problems with math models. This review has a few questions from every lesson. Try each one, then press Show answer to check. If a part feels tricky, go back to that lesson for more practice.

ElementsOperationsMovementscorea group repeats3+47+411+415an operation repeatsquarter turneach timea movement repeats
Three things that can repeat in a pattern: a group of elements, an operation, or a movement.
START with number = 0REPEAT 6 times ADD 3SAY number0+33+36+39+312+315+318The loop adds 3 six times: 6 × 3 = 18
A loop that adds 3 six times makes the jumps 3, 6, 9, 12, 15, 18. That is the same as 6 × 3.

What Repeats? Elements and Operations in Patterns

1

What is the core of 🔺 🔺 🟦 🔺 🔺 🟦?

2

What operation repeats in 9, 18, 27, 36?

3

What repeats in 3, 6, 12, 24?

4

An arrow points left. It turns a quarter turn to the right. Where does it point now?

Creating and Translating Patterns: Shapes, Numbers and Tables

1

Translate ● ● ■ ● ● ■ into letters.

2

Make a table of values: Figure 1 has 5 dots and each figure has 5 more. Show Figures 1 to 4.

3

A table shows 1 → 40, 2 → 36, 3 → 32. What is the value for 4?

Pattern Rules: Extend, Predict and Find Missing Elements

1

Find the missing numbers: 15, □, 35, 45, □

2

In A B C D A B C D …, what is the 10th letter?

3

Rule: Start at 6. Add 4. What is the 5th number? Justify.

Number Patterns to 1000

1

What comes next? 705, 715, 725, …

2

Count back by 100s from 900 to 500.

3

Use 6 + 3 = 9 to find 600 + 300.

4

Fill in: 850 + □ = 1000

Variables: Letters That Stand for Numbers

1

Find n: n + 12 = 30

2

Find b: 5 × b = 35

3

A chair has 4 legs. Write an expression for the legs on c chairs. How many legs on 6 chairs?

Equal or Not Equal? Comparing Expressions

1

Write = or ≠: 4 × 3 □ 2 × 6

2

Write = or ≠: 15 ÷ 3 □ 3 × 3

3

True or false: 7 × 8 = 8 × 7

Same Value, Different Ways: Equivalent Relationships to 1000

1

Write 709 in expanded form.

2

How many tens are in 480?

3

Find □: 300 + 400 = 650 + □

4

How many centimetres are in 2 m and 5 cm?

Coding with Loops: Repeating Events

1

Run: START with number = 0, REPEAT 6 times: ADD 10, SAY number.

2

Rewrite with a loop: Move up 2, Move up 2, Move up 2

3

Write code with a loop that finds 4 × 7.

Reading, Changing and Debugging Code with Loops

1

Code: REPEAT 4 times: Move right 1. Change 4 to 7. How does the outcome change?

2

Beep should move straight up 5 squares. The code is REPEAT 5 times: Move up 1, Move right 1. What is the bug? Fix it.

3

Code A has SAY inside a loop that runs 3 times. Code B has SAY after the loop. How many times does each one say a number?

Just for fun

Why are pattern detectives never bored?

Because something always repeats... something always repeats... something always repeats!

Math Models: Planning with Math in Real Life

1

Each pizza has 8 slices. 20 children each eat 2 slices. How many pizzas should you order? What did you assume?

2

A goal is to read 100 books. The class reads 15 books each week. In which week will they reach the goal?

3

Why is it good to share your assumptions?

How to use this review

  • Do the review over two or three short sittings. Each section matches one lesson.
  • Let your child use tools: counters, blocks, a number line, coins, a measuring tape or paper for tracing code.
  • After each answer, ask "How do you know?" Explaining is as important as the answer.
  • Note which section had mistakes, then revisit that lesson's examples, activity and practice.
Check your understanding

Quiz

1.

What is the core of 🍁 🍂 🍂 🍁 🍂 🍂?

2.

A table of values shows 1 → 7, 2 → 14, 3 → 21. What is the value for 4?

3.

Find the missing number: 64, 56, □, 40

4.

What comes next? 382, 482, 582, …

5.

Find m: m + 25 = 60

6.

Which is equivalent to 4 × 5?

7.

Which is equivalent to $3?

8.

Run: START with number = 0, REPEAT 5 times: ADD 6, SAY number.

9.

A pen robot should draw a square, but it only draws 3 sides. What is the most likely bug?

10.

Each bag holds 10 apples. How many bags do you need for 45 apples?

For parents and teachers

Use mistakes to choose what to revisit. Each review section matches one lesson.

  • Names the wrong core, or says only "it grows" without naming the operation: revisit What Repeats? Elements and Operations in Patterns.
  • Mixes up the columns of a table of values, or gives the same letter to different elements: revisit Creating and Translating Patterns: Shapes, Numbers and Tables.
  • Off by one when predicting (counts 8 jumps to the 8th term), or a rule that works only once: revisit Pattern Rules: Extend, Predict and Find Missing Elements.
  • Changes the wrong digit when adding 10 or 100, or gets stuck crossing a hundred (490 + 10): revisit Number Patterns to 1000.
  • Subtracts in a missing-start problem, or gives the same letter two values: revisit Variables: Letters That Stand for Numbers.
  • Thinks = means "the answer comes next", or switches numbers in subtraction or division: revisit Equal or Not Equal? Comparing Expressions.
  • Says 480 has 8 tens, or mixes up cm and m or cents and dollars: revisit Same Value, Different Ways: Equivalent Relationships to 1000.
  • Runs a loop only once, or loses count of the repeats: revisit Coding with Loops: Repeating Events.
  • Doesn't notice where a line sits (inside or after the loop), or changes the wrong number when debugging: revisit Reading, Changing and Debugging Code with Loops.
  • Gives answers that don't fit real life (like 1 and a bit buses), or forgets to state assumptions: revisit Math Models: Planning with Math in Real Life.

A few mistakes are normal. Praise the strategy your child explains, not only the right answer, and celebrate sticking with a hard problem.