Warm-ups for every class

7: 5 claps and 2 stamps.

Tip: Do it together and count every sound out loud.

5.

Tip: Then ask for 4 and 1, and 5 and 0.

7.

Tip: Draw the two shapes and touch each corner.

10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, blast off!

Tip: Crouch down lower with every number and jump at blast off.

Fingers: 10 is more than 2.

Tip: Ask how many more.

5 on one hand and 3 on the other (or 4 and 4).

Tip: Look for different ways to make 8.

A clock, a plate, a ball or a button: anything round.

Tip: Then hunt for a rectangle.

10, and then 20.

Tip: Count on together past 20.

4.

Tip: Use real socks or draw feet.

Red.

Tip: Make the pattern with toys and ask the child to continue it.

🍎 · 🍌 · 🚗 · 🍇

The car is not a fruit. But the banana is the only yellow one, and the grapes are the only ones in a bunch! Any answer is right if you can say why.

Tip: Ask 'why?' after every answer. There is no wrong one.

🍪🍪🍪 · 🍪🍪🍪🍪🍪

5 cookies: 5 is more than 3. Line them up to see the 2 extra!

Tip: Let them vote, then line real objects up to check.

2 are hiding: the 4 you can see and 2 under the splat make 6.

Tip: Count the ones you can see, then count on to 6 with fingers.

9 stars.

Tip: Ask for a guess in 3 seconds, then count together.

6 ways: 5 and 0, 4 and 1, 3 and 2, 2 and 3, 1 and 4, 0 and 5.

Tip: Show each way with fingers and say it as a number bond.

5 on one hand and 10 on two. Hands are a counting tool we always carry!

Tip: Wiggle each finger as you count it together. · from the lesson Counting objects to 10

You do: 5 is more than 3. Line them up side by side to see the extra 2.

Tip: Use real sweets or counters and line them up. · from the lesson Comparing: more, fewer and the same

5. One more is the next number after 4.

Tip: Act it out with toys. · from the lesson One more and one less

7. 3 and 7 make 10.

Tip: Try a few more: put 5 down, put 8 down. · from the lesson Number bonds to 5 and 10

5. Put them together and count: 1, 2, 3, 4, 5.

Tip: Use real apples or toys. · from the lesson Adding by counting on

3. Take 2 away and count what is left.

Tip: Use 5 counters and push 2 away. · from the lesson Taking away

A clock, a plate or a wheel are circles. Shapes are everywhere!

Tip: Go on a quick shape hunt around the room. · from the lesson 2D shapes

Many children wake up at about 7 o'clock. Let's learn how to show it on a clock.

Tip: Talk about times in the child's day: breakfast, school, bedtime. · from the lesson Time: o'clock and half past

47.

Tip: Ask which digit changed and why.

23.

Tip: List 20 to 29 and test the digit sums.

25.

Tip: Double 15 is 30; 30 − 5 = 25.

12.

Tip: Count in 4s: 4, 8, 12.

1 hour, which is 60 minutes.

Tip: Ask how much longer.

10.

Tip: Count them on fingers as you go.

Three quarters (3/4).

Tip: Draw the pizza.

10.

Tip: Ask for the 10th number too (20).

9.

Tip: Undo the + 4 with − 4.

10.

Tip: 3 + 3 + 4.

8 · 12 · 15 · 20

15 is the only odd number. 8 is the only one-digit number. 20 is the only one in the 10 times table. 12 is the only one whose digits add to 3. Every answer works with a reason!

Tip: Collect a reason for each number.

4 bags of 5 · 3 bags of 7

3 bags of 7: that is 21 sweets, and 4 bags of 5 is only 20.

Tip: Vote first, then work out both totals.

3 are hiding: 7 and 3 make 10.

Tip: Use the bonds to 10.

23 sweets.

Tip: Ask how they could count faster (in groups of 5 or 10).

Always · Sometimes · Never

Always. Two numbers made of pairs make a number made of pairs.

Tip: Ask for examples, then try to find one that breaks the rule.

100: four quarters make a whole, like four 25p make £1.

Tip: Ask for 25 × 8 next.

77.

Tip: List 11, 33, 55, 77, 99 and check.

On day 3: it is at 1 m after night 1, 2 m after night 2, and climbs to 5 m on day 3.

Tip: Draw the wall; most people say day 5.

150.

Tip: 60 + 60 + 30.

25.

Tip: Ask what a quarter of 100 is.

3/4 (9/12 is more than 8/12).

Tip: Draw two bars the same length.

Thursday: 14 days is 2 weeks, then 1 more day.

Tip: Take away whole weeks first.

One way: (4 − 2) × 3 × 4 = 24.

Tip: There are other ways; collect them.

5: 4 small and 1 big.

Tip: Then ask about a 3 by 3 grid (14).

9.

Tip: Ask for other square numbers.

36 · 45 · 64 · 81

45 is the only one that is not a square number. 64 is the only cube too (4 × 4 × 4). 81 is the only odd square. 36 is the only one in the 12 times table. Pick one and say why!

Tip: Push for two different reasons.

₹10 every day · Start at ₹1 and double

Doubling! 1 + 2 + 4 + 8 + 16 + 32 + 64 = ₹127, and ₹10 a day is only ₹70.

Tip: Most children pick ₹10. Work out the doubling day by day.

7 are hiding: 8 + 7 = 15.

Tip: Ask for two ways to work it out.

1,029. A good estimate is 50 × 20 = 1,000.

Tip: Ask how they rounded.

Always · Sometimes · Never

Always. A rectangle has 4 right angles and opposite sides equal, and a square has all of that.

Tip: Ask the opposite too: is a rectangle always a square? (Sometimes.)

4 numbers: 407, 470, 704 and 740. A 3-digit number cannot start with 0, so only 4 or 7 can go first.

Tip: Most learners say 6. Ask them to write every number down and check which ones are really 3-digit numbers. · from the lesson Place value and digit puzzles

6 hamsters. Swap each of the 3 rabbits for 2 hamsters: 3 × 2 = 6.

Tip: Draw the cat on one side and the rabbits on the other, then swap one rabbit at a time. · from the lesson Balance scales and missing numbers

Monday. The days repeat every 7: day 8 and day 15 are Mondays again.

Tip: Let them count on their fingers first, then ask how they could do day 100 without counting. · from the lesson Repeating and growing patterns

No. 1 + 2 + 3 + 4 + 5 + 6 = 21, which is odd, so it cannot be cut into two equal whole-number halves.

Tip: Let them try for a minute. When they get stuck, ask them to add all the numbers. This 'total first' idea runs through the whole lesson. · from the lesson Magic squares and number grids

6:15. One hour after 4:45 is 5:45, and 30 more minutes is 6:15.

Tip: Many learners say 5:75. Ask: how many minutes are in an hour, so what comes after 5:59? · from the lesson Clocks, time and calendars

No. There are 204 squares: 64 small ones and also 2 by 2, 3 by 3, … up to the whole 8 by 8 board. You will be able to count them by the end of the lesson.

Tip: Take a few guesses and write them down. Come back to them at the end of part 1. · from the lesson Counting squares, triangles and shapes

Cy. Draw a line from tall to short: Ann, Ben, Cy.

Tip: Ask them to draw it, even if they know the answer. The drawing is what makes harder puzzles easy. · from the lesson Ordering and logic puzzles

2 cows. If all 5 were hens there would be 10 legs. Each cow adds 2 extra legs, and there are 4 extra, so 2 cows.

Tip: Let them draw 5 heads with 2 legs each, then add legs until there are 14. · from the lesson Legs, heads and animals

30: 10% is 20 and 5% is 10.

Tip: Build it from 10% and 5%.

9: the three must add to 21.

Tip: Ask why we multiply 7 by 3.

60.

Tip: Ask why 120 is not the answer.

80 km: 20 km every 15 minutes.

Tip: Split the hour into quarters.

0.7 (it is 0.70).

Tip: Line up the decimal points.

15.

Tip: 5 + 4 + 3 + 2 + 1.

8 and 12.

Tip: Try pairs that add to 20.

53.

Tip: Check 48 to 52 one by one.

70°: the angles add to 180°.

Tip: Draw it.

210: 10 pairs of 21.

Tip: Pair the first and last numbers.

2 · 9 · 11 · 15

2 is the only even number. 9 is the only square number. 15 is the only multiple of 5. 11 is the only 2-digit prime. Every answer can be right!

Tip: Ask which reason was hardest to find.

1/3 of ₹120 · 25% of ₹200

25% of ₹200 = ₹50, and 1/3 of ₹120 = ₹40.

Tip: Vote, then work both out.

About 4,380 days: 12 × 365 = 4,380, plus about 3 leap days.

Tip: Ask how they estimated 12 × 365.

Always · Sometimes · Never

Sometimes. × 3 makes 5 bigger, but × 1, × 0 and × 0.5 do not.

Tip: Hunt for examples that break the rule.

400. For example 25 × 4 = 100 and 100 × 4 = 400, or 16 × 100 ÷ 4 = 400.

Tip: Write every method on the board without judging.

Day 19. It doubles every day, so the day before it was full it was half. Thinking backwards is often faster than thinking forwards, and that is a big Olympiad habit.

Tip: Most people say day 10 first. Let the learner say an answer, then ask: what happens between day 19 and day 20? · from the lesson Number patterns: find the rule

Yes. 1 + 0 + 0 + 0 + 0 + 0 + 2 = 3, and when the digits add to a multiple of 3, the number is a multiple of 3. Today you will learn why that works.

Tip: Let them try the long division first for a minute. Then show the digit trick and enjoy the surprise. · from the lesson Divisibility rules and missing digits

6 outfits: red with each of the 3 shorts, and blue with each of the 3 shorts. 2 × 3 = 6. Today you will learn why multiplying works, and how it saves time when there are hundreds of outfits.

Tip: Let them list freely first. Then ask: how can we be sure we did not miss one? That leads to listing in order. · from the lesson Counting without listing: the multiplication principle

Nobody on the island can say it. A knight would be lying (impossible), and a knave would be telling the truth (also impossible). So the speaker cannot be from the island! Testing both cases is today's big tool.

Tip: Ask the learner to try each case out loud: "Suppose they are a knight… then…". Let them find the contradiction themselves. · from the lesson Logic puzzles: knights, knaves and grids

They ate the same amount. Two pieces out of six is 2/6, and one third of six pieces is also two pieces, so 2/6 = 1/3.

Tip: Before you show the answer, ask everyone to vote: Asha, Ben or the same? Then ask one person from each side to explain. · from the lesson Fractions

x = 7.

Tip: Undo + 5, then ÷ 3.

7.

Tip: Negative times negative is positive: 12 − 5.

₹1,000: ₹800 is 80% of the price.

Tip: Most people say ₹960. Ask why that is wrong.

1,024.

Tip: Keep doubling from 2.

720°: it splits into 4 triangles.

Tip: Draw the triangles from one corner.

8 : 15.

Tip: Make b the same in both: 12.

20: 8 × 5 ÷ 2.

Tip: Each corner joins 5 others by a diagonal.

1: the last digits go 7, 9, 3, 1 and repeat every 4.

Tip: Write the first few powers.

8√2: 5√2 + 3√2.

Tip: Look for square factors.

1/6: 6 of the 36 outcomes.

Tip: List the pairs that make 7.

y = 2x · y = x² · y = 3x + 1 · y = −x

y = x² is the only curve. y = 3x + 1 is the only line that misses (0, 0). y = −x is the only one that goes down. y = 2x is the only one through (1, 2). Pick one and say why.

Tip: Sketch the four graphs if they get stuck.

20% off · 10% off, then 10% off

20% off. Two 10% discounts leave 0.9 × 0.9 = 0.81 of the price: only 19% off.

Tip: Try it on ₹100.

About 12.2: 12² = 144 and 13² = 169, and 150 is a little past 144.

Tip: Ask which two square numbers it sits between.

Always · Sometimes · Never

Sometimes. 3² = 9 is bigger, but 0.5² = 0.25 is smaller and 1² = 1 is equal.

Tip: Find a number for each case.

25/100 simplifies to 1/4; 1 ÷ 4 = 0.25; a quarter of ₹1 is 25 paise; shade a quarter of a 10 by 10 grid.

Tip: Collect pictures, sums and money.

5.

Tip: Ask what x holds after each line.

Usually 'put the bread in' or 'press the lever'. Computers need every step said.

Tip: Act out the robot doing exactly what is written.

4 times: 0, 1, 2 and 3.

Tip: Ask why it stops before 4.

The closing quote is missing: print('Hello world').

Tip: Ask what error message Python would show.

1: the remainder when 7 is divided by 3.

Tip: Ask what 10 % 2 is (0, so 10 is even).

20: counting starts at 0.

Tip: Ask for items[0] and items[-1].

False: 'and' needs both to be true.

Tip: Then ask about True or False.

5: 4 + 0 + 1.

Tip: Show the place values 4, 2, 1.

8.

Tip: Count the letters together.

4 swaps.

Tip: Swap neighbours that are in the wrong order, pass after pass.

print · input · len · banana

banana is not a Python word. print is the only one that shows something, input is the only one that waits for the user, and len is the only one that counts. Pick one and say why!

Tip: Ask what each one does.

One long, no comments · Three short, with comments

Most coders choose the short ones with comments: they are easier to read and to test one at a time.

Tip: There is no single right answer: ask for reasons.

6 times: i is 2, 5, 8, 11, 14 and 17.

Tip: List the values of i.

Always · Sometimes · Never

Sometimes. If the condition is false at the start, the loop never runs.

Tip: Write one that runs and one that never runs.

5 + 5 is the simplest. Others: 5 * 5 // 5 + 5, (5 + 5) * 5 // 5, and 55 // 5 - 5 // 5.

Tip: Run each idea in Python to check.

A program is a list of exact instructions that runs in order. If a step is missing ("open the tap") or two are swapped ("stir" before "add sugar"), the robot still follows them exactly, so the result is wrong. Computers are the same: they do what we write, not what we mean.

Tip: Let the learner read their steps aloud while you act as the robot and follow them literally. Then say: today we give instructions to Python. · from the lesson Hello, Python: print, text and comments

30. Only the latest value matters: 0 → 10 → 15 → 30. A variable is exactly that: a name with one value inside that can be replaced.

Tip: Do it physically: cross out and write the new value each time. · from the lesson Variables: boxes that remember

What you type arrives as text, like a word. Adding 5 to the word "11" makes no sense, so the program must first turn the text into a number.

Tip: Write "11" and 11 on paper: which is a word made of characters, and which is a number you can add to? · from the lesson Talking to the user: input() and types

Is height at least 120? Yes: open the gate. No: "Sorry, not yet". Every decision is a yes/no question with an action for each answer.

Tip: Act it out with different heights; ask what happens at exactly 120. · from the lesson Making decisions: if, elif and else