The Lumenary · K–2

Patterns

Name: ______________________

Date: ______________________

You will learn to

Copy, extend and create repeating patterns, and find the unit that repeats
Extend growing patterns such as 2, 4, 6, 8, … and describe the rule in words
Predict an item further along a repeating pattern without drawing every step
Explain why the first few items do not decide a pattern, so the rule must be stated

1.
What comes next? ● ■ ● ■ ● ■ ● ___
- A.■ square
- B.● circle
- C.▲ triangle
2.
Here is a repeating pattern: 🍎 🍌 🍌 🍎 🍌 🍌 🍎 🍌 🍌 … What is its unit — the part that repeats?
- A.🍎
- B.🍎 🍌
- C.🍎 🍌 🍌
- D.🍌 🍌
3.
What number comes next? 2, 4, 6, 8, ___
4.
The pattern 5, 10, 15, 20, … adds 5 each time. What is the 6th number in the pattern?
5.
Thandi's necklace goes red, blue, green, red, blue, green, … What colour is bead 20?
- A.Red
- B.Blue
- C.Green
6.
Today is Wednesday. What day of the week will it be in 14 days?
- A.Wednesday
- B.Thursday
- C.Tuesday
7.
A clapping game goes: clap, clap, stamp, clap, clap, stamp, … In the first 12 moves, how many claps are there?
8.
A pattern starts 1, 2, 4, … Nia says the next number is 8. Diego says it is 7. Who could be right?
- A.Only Nia — the numbers are doubling
- B.Only Diego
- C.Both, as long as each says their rule
- D.Neither
9.
Gideon's game: true or false? "In any repeating pattern whose unit has 4 items, item 5 and item 9 are the same."
- A.True
- B.False
10.
Margaret's computer checked the remainder shortcut for beads 1 to 1,000 and found no mistakes. Can we be sure the shortcut works for bead 5,000 too?
- A.Only if the computer checks bead 5,000 as well
- B.Yes — the reason (jumps of one whole unit never change the colour) works for every bead
- C.No — we can never know anything about bead 5,000

Answer key — Patterns

1.
The unit is ● ■ (circle, square), repeating. The last item shown is a circle, so the next item is a square ■.
2.
The pattern starts again at the fourth item, the second 🍎. So the unit is everything before it: 🍎 🍌 🍌, three items. A unit is the whole part that repeats, not a single item.
3.
Each number is 2 more than the one before: the rule is add 2. So after 8 comes $8 + 2 =$ 10.
4.
Keep adding 5: 5 (1st), 10 (2nd), 15 (3rd), 20 (4th), 25 (5th), 30 (6th). You can also see that the $n$ -th number is $5 \times n$ , so the 6th is $5 \times 6 = 30$ .
5.
The unit has 3 beads, so the green beads are 3, 6, 9, 12, 15, 18, … Bead 18 is green, bead 19 is red and bead 20 is blue. (For grown-ups: $20 = 3 \times 6 + 2$ , so bead 20 matches bead 2.)
6.
The week repeats every 7 days. 14 days is exactly 2 weeks, so we land on the same day: Wednesday.
7.
The unit clap, clap, stamp has 3 moves. 12 moves make 4 units (3, 6, 9, 12), and each unit has 2 claps. So there are $2 + 2 + 2 + 2 =$ 8 claps (and 4 stamps).
8.
Both could be right. Doubling: 1, 2, 4, 8, 16, … Adding one more each time: 1, 2, 4, 7, 11, … Both rules fit the first three numbers. That is why a pattern needs its rule to be stated.
9.
True. Item 9 is exactly 4 places after item 5, and the unit has 4 items, so item 9 is the same as item 5. (Both are also the same as item 1.) This works for every pattern with a 4-item unit — Lean proves the general fact in the lesson.
10.
Yes. The computer checked 1,000 beads — evidence for those beads. But the reason in the lesson works for any bead: jumping by a whole unit of 3 beads never changes the colour, so only the leftover steps matter. That reason (proved in Lean) covers bead 5,000 and every other bead.