Controller down. Brain turbo on.
Mission:
Math Rally!
A go-kart. Lots of tens. And you at the wheel. Drive the route stop by stop!
Math turbo on!
Short on time? Express route (about 25 min): Stop 1 A+B → 2 A → 3 A → 5 (box 4) → 7 (case 1) → 8 (round A)
Tablet tip: In the mental math trainer you practice with big buttons, hints and a 10-problem test.
Open the trainerMental math · make a ten
Ten Buddies
Two numbers that make 10 together are ten buddies. They help you jump over any ten in a flash.
Who belongs together?
Eight pairs.
Count on to the next ten
The ones need their ten buddy. 48 + 2 = 50, because 8 + 2 = 10.
Eight problems.
Split the number
Four numbers.
Adding across a ten
Jump to the Ten
For 48 + 5 you don’t go in one go. You make a stop at the ten first.
2. Jump the rest (50 + 3 = 53).
To do this, split the 5: 5 = 2 + 3.
With a stop at the ten
First box: up to the ten.
On the number line
47 + 6 = ?
68 + 5 = ?
Fill in the jumps and the numbers.
Now in your head
Eight problems.
Subtracting across a ten
Jump Back
With minus you jump backwards. The stop at the ten helps here too.
2. Jump back the rest (50 − 2 = 48).
Split the 5: 5 = 3 + 2.
With a stop at the ten
First box: back to the ten.
On the number line (backwards)
62 − 5 = ?
81 − 7 = ?
Jump from right to left.
Now in your head
Eight problems.
Check trick: Add back to check. 53 − 5 = 48, because 48 + 5 = 53.
Strategies for adding and subtracting
Strategy Workshop
Build big problems from small steps. Three tools for your toolbox.
Step by step: tens first, then ones
47 + 36: 47 + 30 = 77 → 77 + 6 = 83
Three problems.
Place value: tens + tens, ones + ones
47 + 36: 40 + 30 = 70, 7 + 6 = 13 → 70 + 13 = 83
Two problems.
Subtract step by step
Three problems.
Use a friendly number: the 9 trick
Four problems.
Find the pattern · frog patterns
Frog Patterns
The frog hops from problem to problem. What changes? Solve, write the next problem and choose.
Solve, hop on, find the pattern
Below the dashed line, write the next problem. On the lines write: +1, −1, +10, −10 or stays the same.
Six boxes. Line 4 is the next problem in the pattern.
Tricky: why?
In box 4 the answer is always 48. Explain why.
Multiplication and division
Times Table Bakery
In the island bakery everything stands in neat rows. Perfect for multiplying!
How many cupcakes are on the tray?
Look at the picture above: 3 rows, 4 cupcakes in each row.
Two problems.
Multiplication blitz
Eight problems.
Division
Six problems.
Fact families: three numbers, four facts
Two families.
Double and halve
Eight problems.
Word problems
Detective Cases
Read carefully like a detective. What is the question? Then solve and answer with a sentence.
Case 1
48 people are on the Wobbly bus. At the stop, 7 more people get on. How many people are on the bus now?
Case 2
Pixel has 63 coins. She buys an ice cream for 6 coins. How many coins does she have left?
Case 3
Wobbi packs 4 parcels. Each parcel gets 5 balls. How many balls are there in all?
Case 4
Pro: The fishing boat catches 36 fish in the morning and 27 fish in the afternoon. Wobbi lets 9 fish go. How many fish are left?
Compare your answer sentences with the answer key.
Mental math like a test · 10 problems
Lightning Rally
Each round has 10 problems, like a mental math quiz. Do one round a day and watch yourself get better!
How it works: Round A without a timer: think of the ten jump for every problem. From round B on you can time yourself (goal: 3 minutes). Then compare with the answer key and write how many you got right.
Round ADate: ______
Round BDate: ______
Round CDate: ______
Extra · on a tablet or computer
Mental Math Trainer
Pick what to practice and tap your answer. If you make a mistake, the trainer shows you the ten jump.
Test: 10 problems
Like a mental math test: 10 problems, with a timer.
Your last tests:
The check buttons count correct boxes. Compare answer sentences and explanations with the answer key yourself.
ANSWER KEY · Try first, then compare.
Answers: stops 1 to 4
1 · Ten Buddies
B 48+2=50 · 76+4=80 · 33+7=40 · 61+9=70 · 85+5=90 · 27+3=30 · 54+6=60 · 19+1=20
C 5=2+3 · 7=4+3 · 8=3+5 · 9=5+4
2 · Ten Jump
78+4 = 78+2+2 = 82
67+5 = 67+3+2 = 72
39+7 = 39+1+6 = 46
56+9 = 56+4+5 = 65
26+8 = 26+4+4 = 34
B 47+6: +3 → 50, +3 → 53 · 68+5: +2 → 70, +3 → 73
C 58+6=64 · 37+9=46 · 74+8=82 · 29+6=35 · 46+7=53 · 83+9=92 · 65+8=73 · 18+5=23 · 49+3=52 · 77+6=83 · 35+9=44 · 88+4=92
Typical mistake: 48 + 5 = 43. The ten was forgotten. When you cross a ten, the tens digit always goes up by 1.
3 · Jump Back
71−4 = 71−1−3 = 67
64−7 = 64−4−3 = 57
35−8 = 35−5−3 = 27
93−5 = 93−3−2 = 88
B 62−5: −2 → 60, −3 → 57 · 81−7: −1 → 80, −6 → 74
C 91−3=88 · 54−8=46 · 33−6=27 · 82−7=75 · 45−9=36 · 76−8=68 · 61−5=56 · 27−9=18
Typical mistake: 53 − 5 = 52 (doing 5 − 3 instead of 3 − 5). Fix: jump back to the ten first.
4 · Workshop
B 30+40=70, 8+6=14 → 84 · 60+20=80, 5+7=12 → 92
C 83−30=53, −6 → 47 · 72−40=32, −5 → 27 · 91−50=41, −8 → 33
D 46+9=55 · 73−9=64 · 38+19=57 · 85−19=66
Answers: stops 5 to 8
5 · Frog Patterns
2: 42, 52, 62; next 68 + 4 = 72 (+10, stays the same, +10)
3: 33, 33, 33; next 30 + 3 = 33 (+1, −1, stays the same)
4: 48, 48, 48; next 55 − 7 = 48 (+1, +1, stays the same)
5: 78, 68, 58; next 51 − 3 = 48 (−10, stays the same, −10)
6: 38, 37, 36; next 45 − 10 = 35 (stays the same, +1, −1)
6 · Bakery
B 4×6=24 · 7×5=35 · 3×8=24 · 9×2=18 · 6×6=36 · 8×4=32 · 5×9=45 · 7×3=21
C 20÷4=5 · 35÷5=7 · 18÷3=6 · 24÷6=4 · 40÷8=5 · 27÷3=9
D 3×7=21, 7×3=21, 21÷3=7, 21÷7=3
5×8=40, 8×5=40, 40÷5=8, 40÷8=5
E double 14 = 28 · double 25 = 50 · double 37 = 74 · double 48 = 96
half of 36 = 18 · half of 50 = 25 · half of 84 = 42 · half of 70 = 35
7 · Detective Cases
2: 63 − 6 = 57. She has 57 coins left.
3: 4 × 5 = 20. There are 20 balls.
4: 36 + 27 = 63, 63 − 9 = 54. 54 fish are left.
8 · Lightning Rally
B: 84−8=76 · 63+9=72 · 89+3=92 · 15+8=23 · 75−8=67 · 36−7=29 · 14+7=21 · 24+8=32 · 64+8=72 · 28+3=31
C: 67+7=74 · 18+4=22 · 17+6=23 · 15−7=8 · 83+8=91 · 28−9=19 · 79+7=86 · 68+7=75 · 49+8=57 · 21−3=18
For grown-ups: what helps most
- Ten buddies (stop 1) need to be lightning fast. They are the base for every crossing.
- When there is a mistake, have the child explain out loud: “To the ten it’s …, then … more.” Don’t just correct the answer.
- 10 minutes every day beats one hour once. One rally round or a few minutes of the trainer a day is enough.
- Don’t forbid finger counting, but show the ten jump as the faster way.