Primary 6 Patterns Study Guide

Primary 6 patterns in five short steps: three for figures that grow and two for patterns that repeat. Each step has a figure to build or step through, and worked examples follow.

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What is a pattern in Primary 6 maths?

A pattern either repeats the same unit or grows by the same amount each time.

In a repeating pattern, your child finds the unit that begins again, then divides to see how many whole units fit and what is left over. In a growing pattern, your child puts the counts in a table, checks that the change is the same twice, then counts gaps to reach a figure too far along to draw.

In this chapter, your child learns to:

  • find the rule of a growing pattern from a table, checking the change twice;
  • work out the count in a figure too far along to draw;
  • work backwards from a count to the figure number;
  • find the repeating unit, then the whole units and the leftover;
  • count the gaps between beads on a string and on a closed loop.
1

Step 1

How to find the rule of a growing pattern

Put the counts in a table, then check the change twice. Draw the first few figures and write each count beside its figure number. Find the change from one figure to the next. Only when the change is the same at least twice can your child say the count goes up by that amount each time.

Identical matchsticks make a row of squares.

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Try it

Figures 1, 2 and 3 use 3, 5 and 8 tiles. Can you name a rule that goes up by the same amount each time?

Growing figuresGrowing figures
2

Step 2

Finding the count in a far figure

Count the gaps after figure 1, and add the change once for each. Figure 1 is the starting count, with nothing added yet. Every step to the next figure crosses one gap and adds the same change. Figure 12 is 11 gaps after figure 1, so the number of gaps is always one less than the figure number.

Figure 1 uses 4 matchsticks, and each figure adds 3.

    Try it

    Figure 1 uses 4 matchsticks and each figure adds 3. How many matchsticks does figure 30 use?

    Growing figuresGrowing figures
    3

    Step 3

    Which figure has a given count?

    Read the table the other way: from a count back to a figure. First find how many were added after figure 1 by subtracting figure 1's count. Divide by the change to get the number of gaps, then add 1, because figure 1 comes before the first gap.

    Tap Next step

      Try it

      Figure 1 uses 4 matchsticks and each figure adds 3. Which figure uses 46 matchsticks?

      Growing figuresGrowing figures
      4

      Step 4

      How to solve repeating pattern questions

      Mark where the pattern begins again, then divide by the unit. The repeating unit is the stretch that starts over. Divide the total by the size of one unit to get whole units and a leftover, never a decimal. Read the leftover from the start of the unit, one item at a time.

      90 shapes repeat: 4 circles, then 3 squares. How many squares?

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        Try it

        A row of 50 beads repeats: red, red, blue, red, red, blue, and so on. How many blue beads are there?

        A repeating unitA repeating unit
        5

        Step 5

        Gaps between beads on a string and a loop

        A string has one gap fewer than black beads; a loop has as many. When white beads sit between black ones, each group of white beads fills one gap. A string has two ends, so its gaps are one fewer than its black beads. Close it into a loop and the last gap joins back to the first black bead.

        Black beads: 4

        3 white beads between every 2 black beads.

        Try it

        A string begins and ends with a black bead, with 7 white beads between every 2 black beads. It has 91 white beads. How many beads are there altogether?

        A repeating unitA repeating unit

        Primary 6 patterns questions, worked step by stepHave a go at each pattern first. Reveal a hint, or the working a line at a time.

        Repeating unitBasic

        Beads are threaded in the order yellow, green, green, blue, then yellow, green, green, blue, and so on. What colour is the 42nd bead?

        Find the repeating unit, divide 42 by its size, and read the leftover from the start.
        1. one unit = yellow, green, green, blue = 4 beads
        2. 42 ÷ 4 = 10 units, 2 left
        3. the 2 left are yellow, green
        The 42nd bead is green.
        Growing figuresBasic

        Identical sticks make a row of hexagons. Figure 1 is 1 hexagon and uses 6 sticks. Figure 2 uses 11 sticks and figure 3 uses 16. How many sticks does figure 15 use?

        Check the change twice, then count the gaps after figure 1.
        1. 11 − 6 = 5 and 16 − 11 = 5, so the count goes up by 5
        2. gaps after figure 1 = 15 − 1 = 14
        3. added = 14 × 5 = 70
        4. figure 15 = 6 + 70 = 76
        76 sticks
        Growing figuresIntermediate

        Square tables are pushed together in a row. 1 table seats 4 children, 2 tables seat 6 and 3 tables seat 8. How many tables are needed to seat 50 children?

        1 table is the first figure. Find how many seats were added after it.
        1. 6 − 4 = 2 and 8 − 6 = 2, so each table adds 2 seats
        2. seats added after 1 table = 50 − 4 = 46
        3. 46 ÷ 2 = 23 gaps
        4. tables = 23 + 1 = 24
        24 tables
        Repeating unitIntermediate

        A path is laid with 3 grey tiles, then 2 white tiles, then 3 grey tiles, then 2 white tiles, and so on. 64 tiles are laid. How many white tiles are used?

        One unit is 5 tiles. Work out what the leftover tiles are before counting.
        1. one unit = 3 grey + 2 white = 5 tiles
        2. 64 ÷ 5 = 12 units, 4 left
        3. the 4 left are grey, grey, grey, white
        4. white tiles = 12 × 2 + 1 = 25
        25 white tiles
        Growing figuresChallenge

        Figure 1 is a row of 2 identical squares, and its perimeter is 18 cm. Each figure after it has 2 more squares in the row than the one before. (a) Which figure has 40 squares? (b) Find the area of that figure.

        A row of 2 squares has a perimeter of 6 sides. Keep the count of squares apart from the area until the end.
        1. side of one square = 18 ÷ 6 = 3 cm
        2. squares added after figure 1 = 40 − 2 = 38
        3. 38 ÷ 2 = 19 gaps, so figure 19 + 1 = 20
        4. area of one square = 3 × 3 = 9 cm²
        5. area = 40 × 9 = 360 cm²
        (a) Figure 20 (b) 360 cm²

        Check yourself

        Five quick pattern questions. Nothing is saved; each reply names the matching question set.

        Figure 1 has 5 dots, figure 2 has 9 and figure 3 has 13. How many dots are in figure 4?

        Figure 1 has 3 counters and each figure adds 5. How many counters are in figure 21?

        Figure 1 uses 7 sticks and each figure adds 6. Which figure uses 67 sticks?

        A row of 40 shapes repeats: triangle, circle, circle, square. What is the 40th shape?

        A bracelet is a closed loop with 2 white beads between every 2 black beads. It has 9 black beads. How many white beads does it have?

        0/5
        For parents

        In Primary 6, patterns turn up inside problem-solving questions rather than as a chapter to revise on its own. The working is plain arithmetic: a table of counts, a change checked twice, and a division with a leftover. Your child does not need letters or formulas to reach a figure nobody has drawn.

        When your child is stuck, ask one question first: does something begin again, or is the same amount added each time? Then ask how many gaps sit between figure 1 and the figure wanted. Drawing three figures and writing their counts in a table often settles both.

        More study guides

        Before this: SolidsPrimary 4 Numbers to 100 000 study guidePrimary 3 Numbers up to 10 000 study guidePrimary 6 Algebra study guidePrimary 4 Area and Perimeter study guide
        Lessons and practice

        P6 Patterns lessons and practice

        2 lesson videos and 13 questions across two subtopics, from Basic to Challenge, each with a worked solution.

        Watch and practise →