Grade by Grade
C. Algebra · Patterns, Equations, Inequalities, Coding and Modelling

Patterns, Equations, Inequalities, 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, extend and predict repeating and growing patterns, including patterns with decimal tenths.
  • I can show patterns with tables of values and graphs.
  • I can write and solve equations, and solve and graph inequalities.
  • I can write and change code with nested loops.
  • I can use a math model to make predictions.

Words to know

pattern rule
A rule that tells how a pattern starts and how it continues.
table of values
A table with term numbers on one side and term values on the other.
expression
Numbers, variables and operations with no equal sign, like n + 5.
equation
A math sentence with an equal sign, like n + 5 = 12.
inequality
A math sentence with < or >, like n + 5 < 12.
nested loop
A loop inside another loop.
assumption
Something we treat as true so we can solve a problem.

Let's review!

In this unit you described repeating and growing patterns, showed them with tables of values and graphs, used pattern rules to predict, made patterns with decimal tenths, wrote and solved equations, solved and graphed inequalities, wrote and changed code with nested loops, and used math models to make predictions. 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.

Repeating1234525252core 2, 5 repeatsGrowing1234547101316start at 4, add 3Shrinking123452421181512start at 24, subtract 3
Three kinds of patterns on graphs. Repeating points zigzag, growing points climb, and shrinking points go down. The bottom numbers are the term numbers.
1830+ 12− 12742× 6÷ 6
Opposite operations undo each other: subtracting undoes adding, and dividing undoes multiplying. That's how you solve equations.

Repeating and Growing Patterns in Real Life

1

Repeating or growing? Describe it: 9, 14, 19, 24

2

What is the core of ⛸️🏒🏒⛸️🏒🏒⛸️🏒🏒? How many elements?

3

Describe 60, 52, 44, 36.

Showing Patterns with Tables of Values and Graphs

1

Make a table of values for start at 2, add 6 for terms 1 to 4.

2

A graph has points (1, 4), (2, 8), (3, 12). Describe the pattern and find term 4.

3

Translate jump, clap, clap, jump, clap, clap into letters.

Pattern Rules: Predict, Justify and Find Missing Terms

1

Find the missing term: 13, 20, ☐, 34

2

The core is A B C D E. What is the 17th letter?

3

A pattern starts at 6 and adds 4. Predict the 10th term and justify.

Patterns with Whole Numbers and Decimal Tenths

1

Count on by tenths: 2.7, 2.8, 2.9, ?, ?

2

How many tenths are in 5.2?

3

Extend: 0.5, 1.0, 1.5, 2.0, ?

4

What goes with 0.4 to make 1?

Variables in Expressions and Equations

1

Is 5 × q an expression or an equation?

2

Write an expression for 9 less than a number.

3

Find the value of 40 − m when m = 15.

Solving Equations with Adding and Subtracting

1

Solve n + 19 = 46.

2

Solve k − 14 = 22.

3

Solve 50 − w = 35.

Solving Equations with Multiplying and Dividing

1

Solve 7 × n = 35.

2

Solve m ÷ 6 = 8.

3

Boxes hold 4 cupcakes. Write and solve an equation for how many boxes hold 28 cupcakes.

Inequalities: Solving, Checking and Graphing

1

List all whole-number solutions of n + 6 < 10.

2

Solve n − 2 > 15 for whole numbers up to 20 and describe the graph.

3

Is 9 a solution of n + 5 > 14? Verify.

Coding with Nested Loops

1

How many claps?

REPEAT 5 times

    REPEAT 3 times

        CLAP

2

Write nested-loop code for 🌲🌲⛄🌲🌲⛄🌲🌲⛄.

3

What are concurrent events?

Reading and Changing Code with Nested Loops

1

A code has outside REPEAT 2 and inside REPEAT 6, with DRAW a dot inside both loops. Change the outside loop to 4. How does the outcome change?

2

What does this say?

SET n = 0

REPEAT 2 times

    REPEAT 3 times

        ADD 5 to n

    SAY n

3

Code meant to say beep, beep, boop 3 times says beep, boop, beep, boop instead. What is the likely bug?

Math Models: Predicting and Planning in Real Life

1

A plant is 12 cm tall and grows 3 cm a week. Model its height for 4 weeks. State your assumption.

2

A 4 kg bag of birdseed is used at 0.5 kg a day. How many days will it last?

3

Why might a real answer be different from a model's prediction?

Just for fun

Why did the equation look so calm and happy?

It had finally found its balance!

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, toothpicks, paper strips for tenths, graph paper, a 0 to 20 number line, and acting out code.
  • For equations and inequalities, always verify by putting the answer back in.
  • After each answer, ask "How did you know?" Explaining matters as much as the answer.
  • Note which section had mistakes, then revisit that lesson's examples, activity and practice.
Check your understanding

Quiz

1.

Which is a growing pattern?

2.

A table shows 1 → 6, 2 → 11, 3 → 16. What is term 4?

3.

The core is red, red, white. What is the 12th element?

4.

What comes next: 0.7, 0.8, 0.9, ?

5.

Which is an equation?

6.

What is the solution to n − 17 = 25?

7.

What is the solution to 6 × k = 48?

8.

Which numbers are all the whole-number solutions of n + 7 < 10?

9.

CLAP is inside a REPEAT 4 times loop, which is inside a REPEAT 6 times loop. How many claps?

10.

In a modelling problem, what should you do when an assumption changes?

For parents and teachers

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

  • Calls 3, 5, 3, 5 a growing pattern, or names the wrong core: revisit Repeating and Growing Patterns in Real Life.
  • Mixes up the axes or the two columns of a table, or translates with the wrong number of elements: revisit Showing Patterns with Tables of Values and Graphs.
  • Counts 10 jumps instead of 9 to reach term 10, or goes backward with the wrong operation: revisit Pattern Rules: Predict, Justify and Find Missing Terms.
  • Writes 0.10 after 0.9, or can't say a decimal in tenths: revisit Patterns with Whole Numbers and Decimal Tenths with paper strips.
  • Can't tell an expression from an equation, or writes "9 less than n" as 9 − n: revisit Variables in Expressions and Equations.
  • Uses the same operation instead of the opposite (k − 14 = 22 → 22 − 14), or skips checking: revisit Solving Equations with Adding and Subtracting.
  • Mixes up multiplying and dividing to undo, or can't match a story to an equation: revisit Solving Equations with Multiplying and Dividing and practise fact families.
  • Includes the balance point, forgets 0, or mixes up < and >: revisit Inequalities: Solving, Checking and Graphing with a 0 to 20 number line.
  • Adds the loop numbers instead of multiplying, or ignores indents: revisit Coding with Nested Loops and act out the code.
  • Can't predict how a change affects the outcome, or can't find a line in the wrong loop: revisit Reading and Changing Code with Nested Loops.
  • Gives an answer with no assumptions, or doesn't revise when facts change: revisit Math Models: Predicting and Planning in Real Life.

A few mistakes are normal. Praise the strategy your child explains and the checking they do, not only the right answer.