CLASS 3 MATHS WORKSHEET LESSON 11

Patterns and Puzzles (Preparatory Stage Math)

Concepts • Computational Skills • Problem-Solving & Modeling • 10 questions each • 40% Easy, 40% Average, 20% Challenging • One toggle shows Answer + Solution

Worksheet A: Concepts

Easy

Q1. Complete the repeating pattern: AB AB AB __ __ (write the next two letters).

Show solution

Answer

AB.

Solution

The block “AB” repeats; after three blocks, the next block is again A then B.

Easy

Q2. Tick which is a 3-step repeat unit: ABCABC or ABAB (choose one and name the unit).

Show solution

Answer

ABCABC; unit = ABC.

Solution

ABC repeats as a 3-letter block; ABAB has a 2-step unit AB, not 3.

Easy

Q3. Odd-one-out by shape rule: circle, triangle, square, circle (which one differs by number of sides?).

Show solution

Answer

Circle (no straight sides).

Solution

Triangle has 3, square 4 sides; circle has none, so it breaks the “polygon with sides” rule.

Easy

Q4. Mirror idea: If the left half of a heart is drawn, what must the right half be (choose: same shape mirrored / same shape copied as is)?

Show solution

Answer

Same shape mirrored.

Solution

Mirror symmetry reflects across the middle line to complete the whole figure.

Average

Q5. Growing pattern by +2: 4, 6, 8, __, __ (write next two numbers).

Show solution

Answer

10, 12.

Solution

Add 2 each time; the sequence increases evenly by a fixed step.

Average

Q6. Border pattern repeats “straight, curve”: if the last three units are straight, curve, straight, what are the next two?

Show solution

Answer

curve, straight.

Solution

AB repeats; after straight (A) comes curve (B), then straight again.

Average

Q7. Complete a tiling idea: two small triangles make a square when joined along a side. How many triangles are needed to make two such squares?

Show solution

Answer

4 triangles.

Solution

Each square uses 2 triangles; two squares need 2×2 = 4 triangles.

Average

Q8. Odd-one-out by colouring rule: red circle, red square, blue triangle, red triangle (pick the one that breaks “red or square”).

Show solution

Answer

Blue triangle.

Solution

Others either are red or square; the blue triangle is neither, breaking the rule.

Challenging

Q9. Calendar-like cycle: If a 3-day cycle is A, B, C and today is A, what will it be after 8 days (write the letter)?

Show solution

Answer

B.

Solution

8 days is 2 cycles (6) plus 2 more: A→B→C→A→… After 8, land on B.

Challenging

Q10. Turn-and-flip: A triangle pointing up rotates 90° clockwise. Which way does it point now (choose: right/left/down)?

Show solution

Answer

Right.

Solution

Quarter-turn clockwise moves “up” to “right” in orientation.

Worksheet B: Computational Skills

Easy

Q1. Skip-count by 5s: 5, 10, 15, __, __, 30 (fill two blanks).

Show solution

Answer

20, 25.

Solution

Add 5 every step to extend the sequence correctly.

Easy

Q2. Fill by 10s: 20, 30, __, __, 60 (two numbers only).

Show solution

Answer

40, 50.

Solution

Place-value skip counting in tens gives the intermediate values.

Easy

Q3. Growing by +3: 2, 5, 8, __, __ (fill next two numbers).

Show solution

Answer

11, 14.

Solution

Add 3 repeatedly; the pattern increases linearly.

Easy

Q4. Machine rule: “add 4.” If input is 9 and 12, what are the outputs (two numbers)?

Show solution

Answer

13, 16.

Solution

Apply the same rule to each input; outputs follow the pattern consistently.

Average

Q5. Alternating pattern +2/−1 starting at 7: 7, 9, 8, 10, 9, __, __ (fill next two).

Show solution

Answer

11, 10.

Solution

Apply +2 then −1 alternately: …, 9 +2→11, then −1→10.

Average

Q6. Border count: a border uses “triangle, triangle, square” repeating. In 8 places, how many triangles and squares are used (write “tri = __, sq = __”).

Show solution

Answer

tri = 6, sq = 2.

Solution

Cycle length 3 with 2 triangles, 1 square; 8 items → two full cycles (6 items) + 2 more = 6 triangles, 2 squares.

Average

Q7. Complete: odd numbers from 1 up to 15 (list them in order).

Show solution

Answer

1, 3, 5, 7, 9, 11, 13, 15.

Solution

Odd numbers increase by +2 starting at 1 up to the limit.

Average

Q8. Fill missing: 12, __, 20, __, 28 (skip by +4; write the two blanks).

Show solution

Answer

16, 24.

Solution

Counting by 4s fills the intermediate values: 12, 16, 20, 24, 28.

Challenging

Q9. Find the rule: 3→9, 5→11, 7→13. What does 9 go to, and state a simple rule in words.

Show solution

Answer

15; “add 6 to odd inputs.”

Solution

Each output is input + 6; extend 9→15 accordingly.

Challenging

Q10. Two-step function: “double, then subtract 1.” What is the output for input 6, and what input would give output 13?

Show solution

Answer

Output for 6 = 11; input for 13 = 7.

Solution

6→2×6−1=11; to solve backward, (x×2)−1=13 → x×2=14 → x=7.

Worksheet C: Problem-Solving & Modeling

Easy

Q1. Make a week-cycle pattern with three colours repeated over 7 days (e.g., R, G, B, R, G, B, R). Which colour appears most often in 7 days (state the colour)?

Show solution

Answer

R (example shown).

Solution

With 7 days and a cycle of length 3, the first item (R) will appear one extra time.

Easy

Q2. “Complete the other half”: A butterfly’s left wing has 3 dots near the center and 2 at the edge. Describe where to place dots on the right wing to match.

Show solution

Answer

Mirror the positions: 3 near the centerline, 2 at the outer edge on the right wing.

Solution

Symmetry requires equal-distance mirrored placements across the midline.

Easy

Q3. Design a floor border using “square, circle, square” repeating. If the border has 10 shapes, how many circles will appear?

Show solution

Answer

About 3 or 4 depending on cut; with 10 places starting at square, circles appear at positions 2,5,8 → 3 circles.

Solution

Cycle length 3 with one circle per cycle; 10 items give 3 full cycles (3 circles) plus a start of the next cycle.

Easy

Q4. Create a “machine card”: input 0,1,2,3 under rule “×3.” Write outputs and name any skip-count it matches.

Show solution

Answer

0, 3, 6, 9; it matches skip-count by 3s.

Solution

Multiplying by 3 produces the 3-times table sequence used for skip counting.

Average

Q5. Puzzle condition: choose a number that is more than 20, less than 30, and odd. Give one example and explain in a phrase why it fits.

Show solution

Answer

25; it is >20, <30, and odd.

Solution

Check all conditions; 21, 23, 25, 27, 29 would also fit this rule.

Average

Q6. A shape-turn pattern rotates a square by 0°, 90°, 180°, 270°, then repeats. What comes after 270° in the cycle (name the degree)?

Show solution

Answer

0° (back to start).

Solution

After a full 360°, the orientation repeats; 270°→0° resets the cycle.

Average

Q7. “Two rules” pattern: +4, then ×2, starting at 2. Fill next three terms after 2: __, __, __.

Show solution

Answer

6, 12, 16.

Solution

Start 2; +4→6; ×2→12; +4→16; repeat the two-step rule.

Average

Q8. Border check: AABB pattern repeats. In the first 12 places, how many A and how many B appear (write counts “A=__, B=__”).

Show solution

Answer

A=6, B=6.

Solution

Block length 4 (AABB) has 2 As and 2 Bs each; 12 items = 3 full blocks → equal counts.

Challenging

Q9. Mystery rule: outputs jump 2, then 3, then 2, then 3… starting from 1. Write first seven terms of outputs (beginning at 1).

Show solution

Answer

1, 3, 6, 8, 11, 13, 16.

Solution

Add 2, then 3 alternately to extend: 1→3→6→8→11→13→16.

Challenging

Q10. Constraint puzzle: make a 3-long sequence using only numbers {2,4,6} with no repeats where the total is 12; list one valid sequence.

Show solution

Answer

2, 4, 6 (any order).

Solution

All three distinct values sum to 12; any permutation meets the constraint.

Two best activities

Activity 1: Border-and-Tiling Studio

Show solution

Answer

Create repeating borders (AB, ABB, AABB) and floor tilings with triangles/squares; label the smallest repeating block (unit) each time.

Solution

Provide paper shapes or stamps. Learners build borders and tilings, circle the repeat unit, and count how many of each tile appear in 10–12 places. They then swap designs and identify the unit in peers’ work, strengthening pattern recognition and communication.

Activity 2: Pattern Machines Lab

Show solution

Answer

Run “function machines” (+3, +5, ×2, double-then−1) on input cards, chart outputs, and match to skip-counts or growing patterns.

Solution

Set stations with machine cards. Teams feed inputs 0–12, record outputs, and draw a quick number line showing steps. They explain rules in words, compare machines that produce the same skip-count, and design one “two-rule” machine to share with the class.