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Geometric patterns and direct proportion

Patterns of growing shapes: count, make a table and find the rule. Ratios compare amounts of the same kind; rates compare different units. Read one part at a time and tap “I know this”. Then test yourself in the quiz.

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Geometric patterns

In a geometric pattern shapes grow, like matchsticks or blocks. Count the parts in each picture and make a table.

Picture123410
Matchsticks47101331
Rule

Each new square adds 3 matchsticks: matchsticks = 3 × picture number + 1.

Tap when you could tell someone without looking.

Patterns in designs

Look for repetition, symmetry and turning in beadwork, tiles and mats: which part repeats?

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Ratio

A ratio compares two amounts of the same kind: 2 red to 3 blue = 2 : 3. The order matters.

  • Simplify like a fraction: 6 : 9 = 2 : 3.
  • Share R50 in the ratio 2 : 3: 2 + 3 = 5 parts; 1 part = R10 → R20 and R30.
Tap when you could tell someone without looking.

Rate

A rate compares two different units: 60 km per hour, R12 per kg.

Rule

Which is cheaper? 6 apples for R18 (R3 each) or 4 for R10 (R2,50 each)? The second.

Direct proportion: when one amount doubles, the other doubles too (2 loaves = R30, 4 loaves = R60).

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Remember this and test yourself

Remember this: your summary
  • Count the parts in each picture.
  • Ratio 2 : 3 compares the same kind of things; order matters.
  • Make a table of picture number and amount.
  • Simplify ratios like fractions.
  • Find the rule to predict far pictures.
  • Sharing in a ratio: add the parts, find one part.

Write these points in your book. Read them again the night before the test.

Memory trick

Draw, count, table, rule.

Flash cards · Tap to turn over

Important words

First say the answer yourself, then turn the card over.

Test yourself · Part 2

True or false?

Read the question and the answer. Is the answer right? Tap True or False.

    Now the real quiz!

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