Controller down. Builder mode on.
Mission:
Square Builders!
Square plazas made of tiles: how many tiles does each one need? With square numbers, you can tell at once.
Square turbo on!
How to practice: one mission a day (15 to 20 minutes) and 5 minutes in the trainer. Goal: all square numbers from 1² to 20², forward and backward.
Tablet tip: In the square trainer you practice forward, backward and spotting square numbers, with a hint for every mistake and a 10-problem test.
Open the trainerSquare numbers · the idea
Square Tiles
At the construction site, plazas are made of tiles: always as many rows as tiles in each row. The result is a square.
Careful: 4² means 4 × 4, not 4 × 2!
How many tiles does each plaza have?
Four plazas.
The first ten square numbers
| n | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| n² |
Ten boxes.
Square numbers from 11² to 20²
Big Squares
Starting at 11, the problems get more challenging. With two tricks you can build every big square number yourself.
Split
Twelve boxes.
Climb the square staircase
Ten steps.
Mixed up
Eight problems.
Thinking backwards · spotting square numbers
Square Detective
The detective knows square numbers backwards too. Which number is hiding behind them?
Which number times itself makes …?
Six problems.
Is it a square number?
Eight numbers.
Between which two consecutive square numbers does it lie?
Example: 49 < 50 < 64, because 7² = 49 and 8² = 64.
Eight boxes.
Greater or less?
Write < or >.
Six comparisons.
Pixel says: “7² = 14.” What is wrong? Explain.
Patterns · word problems
Pattern Garden
The garden is full of surprising patterns. Spot them, and you can calculate faster.
Odd numbers build squares
Each new square gets a corner made of the next odd number (red).
Six boxes.
Neighbors of the middle number
Compare the two answers in each row. What do you notice?
Seven boxes.
Word problems
1 A square plaza is laid with 15 rows of 15 tiles each. How many tiles are needed?
2 Pro: Wobbi has 200 tiles. He lays the largest square plaza he can. How many tiles go in each row, and how many are left over?
Compare your answer sentences with the answer key.
Everything mixed · like a test
Test Check
Show what you can do: lightning round, true or false and number riddles.
Lightning round: 12 problems, goal 3 minutes
Time: ______
True or false?
Six statements.
Number riddles
Three riddles.
Traffic light: how sure are you?
Extra · on a tablet or computer
Square Trainer
Pick a practice type. If you make a mistake, the trainer shows you a way to work it out.
Test: 10 problems
10 problems with a timer. Wrong ones go on your practice list.
Your last tests:
The check buttons count correct boxes. Compare explanations and answer sentences with the answer key yourself.
ANSWER KEY · Try first, then compare.
Answers
1 · Square Tiles
B 1² = 1 | 2² = 4 | 3² = 9 | 4² = 16 | 5² = 25 | 6² = 36 | 7² = 49 | 8² = 64 | 9² = 81 | 10² = 100
Typical mistake: 6² = 12. Correct: 6² = 6 × 6 = 36.
2 · Big Squares
14² = 140 + 56 = 196
16² = 160 + 96 = 256
18² = 180 + 144 = 324
B 11² = 121 | 12² = 144 | 13² = 169 | 14² = 196 | 15² = 225 | 16² = 256 | 17² = 289 | 18² = 324 | 19² = 361 | 20² = 400
C 17² = 289 | 13² = 169 | 19² = 361 | 11² = 121 | 15² = 225 | 20² = 400 | 14² = 196 | 16² = 256
3 · Square Detective
B 64: yes | 90: no | 121: yes | 150: no | 169: yes | 200: no | 256: yes | 324: yes
C 100 < 110 < 121 | 196 < 200 < 225 | 289 < 300 < 324 | 361 < 390 < 400
D 13² < 170 | 12 × 14 < 13² | 15² > 220 | 11² > 100 + 20 | 16² > 250 | 9² > 8 × 10
E 7² means 7 × 7 = 49. Pixel did 7 × 2.
4 · Pattern Garden
B 12 × 14 = 168, 13² = 169 | 14 × 16 = 224, 15² = 225 | 18 × 20 = 360, 19² = 361 | 16 × 18 = 288
Pattern: the product of the two neighbors is always 1 less than the square of the middle number.
1: 15 × 15 = 225. 225 tiles are needed.
2: 14 × 14 = 196 (15 × 15 = 225 would be too many), 200 − 196 = 4. He lays 14 tiles in each row, and 4 tiles are left over.
5 · Test Check
B 1: true | 2: false | 3: false | 4: true | 5: false | 6: true
C 1: 169 | 2: 289 | 3: 256
For grown-ups: what helps most
- The square numbers up to 20² should be known by heart, forward and backward. 5 minutes of the trainer a day is enough.
- Most common mistake: reading 7² as 7 × 2. Have the child say it out loud: “7 times 7”.
- The staircase (jumps 21, 23, 25, …) is a good self-check for the big square numbers.