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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 C2.4 C3.1 C3.2 C4About 40 minutes
Learning goals
  • I can describe, extend and predict repeating, growing and shrinking patterns, including with tenths and hundredths.
  • I can translate among words, expressions and pictures, and evaluate expressions.
  • I can solve equations up to 100 and inequalities up to 50, and verify my solutions.
  • I can write, read and change code with conditional statements and loops, and use math models to plan.

Words to know

term-number rule
A rule that gives a term value straight from its term number, like term number × 4 + 1.
hundredth
One of 100 equal parts of a whole: 0.01.
equivalent expressions
Expressions that are always equal, whatever the variable is.
evaluate
Find the value of an expression by substituting numbers.
inequality
A math sentence with < or >. It usually has many solutions.
conditional statement
IF ... THEN ... ELSE code that makes a decision.
assumption
Something we treat as true to make a model.

Let's review!

In this unit you described repeating, growing and shrinking patterns; showed them in tables and graphs; wrote term-number rules to predict far ahead; made patterns with tenths and hundredths; translated among words, expressions and pictures; evaluated expressions; solved equations and inequalities; wrote and changed code with conditional statements; and used math models to plan a class trip.

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.

WordsTableGraphTerm-number rulestart at 3and add 2each time3, 5, 7, 9, ...termvalue1325374905101234term number× 2 + 1term 10:10 × 2 + 1 = 21
One growing pattern shown four ways. The words and table are good for the next term; the term-number rule jumps far ahead. The graph's points climb in a straight line because the pattern adds the same amount each time.

Repeating, Growing and Shrinking Patterns

1

Describe 11, 17, 23, 29, ... and write the next term.

2

Describe 96, 48, 24, 12, ... and write the next two terms.

3

Write the next term: 3, 4, 6, 9, 13, ...

Growing and Shrinking Patterns in Tables and Graphs

1

Make a table with 4 terms for start at 35 and subtract 4 each time.

2

A graph has points at (1, 3), (2, 8), (3, 13). Is the pattern growing or shrinking? What is term 5?

3

Points on a graph go down in a straight line. What does that tell you?

Pattern Rules: Predicting Far Ahead and Finding Missing Elements

1

Write a term-number rule for 6, 11, 16, 21, ... and find term 40.

2

A pattern repeats 🥌⛸️🏒. What is the 25th element?

3

Find the missing terms: 14, ☐, ☐, 41

4

70, 66, 62, ... What is term 11?

Patterns with Whole Numbers, Tenths and Hundredths

1

Continue: 0.96, 0.97, 0.98, ☐, ☐

2

Describe 4, 0.4, 0.04.

3

You know 8 + 2 = 10. What is 0.08 + 0.02?

Words, Expressions and Pictures: Showing Equivalent Relationships

1

Write an expression: 9 less than 5 times a number n.

2

Describe 2 × k + 7 in words.

3

Are 3 × (n + 4) and 3 × n + 12 equivalent? Show one test.

Evaluating Algebraic Expressions

1

Evaluate 9 × n − 8 when n = 7.

2

Evaluate 4 × (m + 6) when m = 9.

3

Evaluate 2 × l + 2 × w when l = 14 and w = 11.

Solving Equations with Whole Numbers up to 100

1

Solve n + 56 = 83.

2

Solve 6 × t = 84.

3

Solve 100 − k = 64.

4

Solve 4 × n + 3 = 47.

4 × n = 28012345678910one solution: n = 74 × n < 28012345678910many solutions: 0 to 67 is the boundary point, not a solution
An equation like 4 × n = 28 has one solution. An inequality like 4 × n < 28 has many: every whole number below the boundary point 7. The ring at 7 shows the boundary is not a solution.

Inequalities with One Operation: Solve, Verify and Graph

1

Solve 5 × n < 30 (whole numbers).

2

Solve n + 14 > 40, up to 50.

3

Solve 35 − n < 20 (whole numbers up to 35).

Coding with Conditional Statements

1

Run IF n > 20 THEN SAY "high" ELSE SAY "low" for n = 20.

2

What is the outcome?

SET n = 1

REPEAT 8 times

    IF n is a multiple of 4 THEN SAY "🔔" ELSE SAY n

    ADD 1 to n

3

What does this SAY?

SET total = 0

REPEAT UNTIL total > 40

    ADD 9 to total

SAY total

Reading and Changing Code with Conditionals and Loops

1

Pattern-maker code (odd → 🍁, even → ❄️) with REPEAT 7 times. What is the outcome?

2

The points code says 32 with n > 6. What does it say with n > 5?

3

Code should say "too many" for more than 30 people: IF people > 31 THEN SAY "too many". Find the bug.

Math Modelling: Planning a Class Trip

1

The bus costs $180 and entry is $4 per student. Write an expression and find the cost for 25 students.

2

Name two assumptions you might make when planning a bake sale.

3

Cookies sell for $0.75. How many cookies make $60?

Just for fun

Why is the equal sign so humble?

Because it knows it isn't greater than or less than anyone else!

How to use this review

  • Do the review over two or three short sittings. Each section matches one lesson.
  • Use tools: grid paper for graphs, coins for decimals, cups and counters for expressions, a 0 to 50 number line for inequalities, and objects to act out code.
  • For equations and inequalities, always verify by substituting your answer.
  • For code, keep a tracking table for each variable.
  • Put a star next to any question you got wrong, and go back to that lesson's practice.
Check your understanding

Quiz

1.

What comes next: 5, 15, 45, ...?

2.

A table shows 1 → 50, 2 → 43, 3 → 36. What is term 4?

3.

Which term-number rule fits 4, 7, 10, 13, ...?

4.

What comes after 0.09 when counting by hundredths?

5.

Which is equivalent to 2 × (n + 7)?

6.

What is 6 × n + 4 when n = 8?

7.

Solve n ÷ 6 = 12.

8.

What are the solutions of 3 × n > 36, up to 50?

9.

IF n < 10 THEN SAY "A" ELSE SAY "B". What does it say when n = 10?

10.

In a math model, why do we write down our assumptions?

For parents and teachers

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

  • Checks only the first jump, or can't describe a pattern that doubles or halves: revisit Repeating, Growing and Shrinking Patterns.
  • Plots points up-then-across, or starts a shrinking table at the wrong number: revisit Growing and Shrinking Patterns in Tables and Graphs.
  • Counts one jump too many (10 jumps to term 10), or forgets the fix-up number in a term-number rule: revisit Pattern Rules: Predicting Far Ahead and Finding Missing Elements.
  • Thinks 0.10 comes after 0.9, or that 0.25 > 0.3: revisit Patterns with Whole Numbers, Tenths and Hundredths with coins and a metre stick.
  • Writes 7 − n for "7 less than n", or ignores brackets when comparing expressions: revisit Words, Expressions and Pictures: Showing Equivalent Relationships with cups and counters.
  • Adds before multiplying (8 + 3 × 4 = 44): revisit Evaluating Algebraic Expressions.
  • Uses the same operation instead of the opposite one, or skips verifying: revisit Solving Equations with Whole Numbers up to 100.
  • Includes the boundary point, or follows the sign's direction when the variable is subtracted: revisit Inequalities with One Operation: Solve, Verify and Graph.
  • Runs both THEN and ELSE, or forgets to change the counter in a loop: revisit Coding with Conditional Statements.
  • Misreads indents or misses boundary bugs (> 50 when 50 should count): revisit Reading and Changing Code with Conditionals and Loops.
  • Gives a number with no assumptions or units, or doesn't revise when facts change: revisit Math Modelling: Planning a Class Trip.

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