Example 1
▲●■▲●■… What is the 20th shape?
- The block ▲●■ has 3 shapes.
- 18 shapes make 6 whole blocks, and 20 is 2 more.
- The 2nd shape in the block is ●.
Answer: ●
🦘 Kangaroo Grade 3 · session 3 of 24 · 60 minutes · ⭐ Plus
Repeating and growing patterns
What is the 100th bead on the necklace? What day of the week is the 31st? Find the repeating block or the growing rule, and you can jump straight to any position without drawing them all.
A complete lesson · 60 minutes
Teach it, see it, practise it, all on this page.
Open this page with your learner and work down it, or press Teach this lesson to go through it one step at a time on a big screen. Every section has something to do.
- Warm-up4 min
- Repeating8 min
- Growing numbers9 min
- Growing shapes7 min
- Calendars7 min
- Activity 17 min
- Activity 27 min
- Activity 36 min
- Quiz4 min
- Set the project1 min
By the end you can
- Find the repeating block and use it to find any position
- Find the rule of a growing number pattern
- Count the pieces in growing shape patterns
- Use the 7-day week to find days and dates
Before you start
- Times tables to 10
- Dividing with a remainder
Have ready
- Paper and pencil
- Beads or coloured counters
Grade 3 · ages 8 to 9 · contest level 3–4
Warm-up · think first
Monday is day 1, Tuesday is day 2, and so on. What day of the week is day 15?
Show the answer
Monday. The days repeat every 7: day 8 and day 15 are Mondays again.
Teacher tip: Let them count on their fingers first, then ask how they could do day 100 without counting.
Part 1 of 4 · learn, see, practise
Repeating patterns
A repeating pattern has a block that comes again and again. In ▲●■▲●■… the block is ▲●■, three shapes long.
To find the 20th shape, take away as many whole blocks as you can: 20 = 6 blocks of 3 (18 shapes) and 2 more. The 2nd shape of the block is ●.
Example 2
ABCDABCD… What is the 30th letter?
- The block has 4 letters.
- 28 is 7 blocks, and 30 is 2 more.
- The 2nd letter is B.
Answer: B
Practise it
Start with the warm-up and go as far as you can. The stretch questions are meant to be hard.
Warm-up
Warm-up
Core
Core
Stretch 🔥
Stretch 🔥
Answers (for the teacher)
- blue
- C
- 3
- 6
- G
- 40
⭐ Part of Pure Faith Plus
The rest of this lesson is in Plus
Already have Plus? Log in and the whole lesson opens.
You have seen the plan, the warm-up and part 1. With Plus you also get:
- Part 2: Growing number patterns, with practice at three levels
- Part 3: Shape patterns that grow, with practice at three levels
- Part 4: Weeks and calendars, with practice at three levels
- Class activity 1: Bead necklace
- Class activity 2: Matchstick houses
- Class activity 3: Calendar detective
- A 8-question quiz
- After-class project: My pattern necklace
- Homework and a printable practice sheet with answers
- Teach mode and the minute-by-minute teacher's plan
The first 2 lessons of every course, every game and all maths practice stay free.
That is ₹208 a month for every lesson of every course. Prefer a teacher? Ask about live classes.
FAQ
Repeating and growing patterns: questions
How do you find the 100th term of a repeating pattern?
Find the block length, take away as many whole blocks as fit into 100, and look at the leftover position in the block.
What pattern questions are in Math Kangaroo Grade 3?
Repeating shapes and letters, growing number patterns, matchstick and dot figures, and days of the week.
How do you find what day it will be in many days?
Take away whole weeks (7, 14, 21, 28 days) and count on the days that are left.
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