Speak Maths Β· School
Plus, times, powers and brackets
The signs of arithmetic are the first words you will say aloud. Meet them while sharing and doubling sweets.
Draft: written by an AI helper and not yet checked by a teacher.
The alphabet
Read each sign aloud, the way it is written under it.
- Say: plusMeans: put amounts together
- Say: minusMeans: take an amount away
- Say: timesMeans: groups of; the cross and the dot both mean multiply
- Say: divided byMeans: share equally
- Say: a over bMeans: a divided by b, written as a fraction
- Say: a to the power nMeans: a multiplied by itself n times
- Say: the square root of aMeans: the number which, times itself, makes a
- Say: bracketsMeans: do what is inside first
The story: Sharing and doubling sweets
Tap a line to see its words.
- One bag holds 8 sweets and another holds 4. Pour them together: 12 sweets.
- Three are eaten, so 12 minus 3 leaves 9.
- Share the 9 sweets among 3 friends: 3 each.
- The same sharing, written as a fraction: 9 over 3 is 3.
- One friend doubles the pile: 2 times 3 makes 6.
- The 9 sweets make a square, 3 rows of 3. That is 3 to the power 2.
- Going back, the square root of 9 is the side of the square: 3.
- Two loose sweets and 3 packs of 4. Times comes first, so 2 plus 3 times 4 is 14.
- Put the 2 and the 3 in brackets first, then take 4 times: 20. Brackets change the answer.
In words this story is 564 letters long; in symbols, 53.
Read it
What does it say?
Write it
Which notation says this?
Twelve sweets shared among four friends is three each.
Add two and three first, then multiply the result by four.
The square root of forty-nine is seven.
Fifteen minus seven is eight.
Six packs of five pencils make thirty pencils.
Two to the power three is eight.
Half of twenty, written as a fraction, is ten.
The square root of eighty-one is nine.
Take three from ten, then double the result.
Twenty biscuits shared among five is four each.
Nine, plus the square root of nine, is twelve.
Four times four is four squared.
Build it
Tap the tiles in order. One tile does not belong.
Three squared equals nine.
Two plus three, in brackets, times four.
Twelve divided by three equals four.
Two to the power four equals sixteen.
The square root of thirty-six, minus one.
Ten minus, in brackets, two plus three.
Challenges
Creative puzzles that use every sign of this chapter. Take your time; there is no clock.
1 Three bags of sweets
Bags p, q and r hold the numbers of sweets shown. Judge each sentence: true or false?
| β | |||||
| β | |||||
| β |
A tick under a number shows how many sweets that bag holds.
p is 4, q is 9, r is 6. The only difference between the first two lines is the brackets: 3 Β· 4 = 12, but 9 β 24 is not.
2 Same digits, different story
Pair each line with what it says.
Tap a line, then its meaning.
Times comes before plus; brackets override that; and the small raised number counts how many times the big one is used.
3 Brackets first
Add 3 and 4 first, then take two times that: 14. One tile is wrong. Find it, then fix it.
Tap the tile that is wrong.
(3 + 4) is 7, and 7 Γ 2 is 14. Plus, minus or division would give 9, 5 or 3.5.
4 Going back and forth
The square root of 16 is 4, and squaring 4 should take us back to 16. One tile is wrong.
Tap the tile that is wrong.
Squaring and square root undo each other: 4Β² = 16.
5 The long fraction
Work out this fraction. Powers first, then the top, then divide.
2Β³ = 8, then 20 β 8 = 12, then 12 Γ· 3 = 4. The fraction bar works like brackets around the top.
6 Which square?
What was a, if its square root is 6?
The square root of a is 6 when 6 times 6 gives a: 36.
7 The square carpet
A square carpet has side s. Its area A is the side times itself. Write this as a formula.
One way:
Multiplying a number by itself is squaring it, so A = sΒ².
8 Share and check
Twelve sweets shared among three friends give four each. Write the sharing and then the check that gets you back to twelve.
One way:
Division and multiplication undo each other: 12 Γ· 3 = 4 and 4 Γ 3 = 12.
9 Three jars of buttons
Jars a, b and c hold the numbers of buttons shown. Judge each sentence: true or false?
| β | ||||
| β | ||||
| β |
A tick under a number shows how many buttons that jar holds.
a is 2, b is 5, c is 8. Brackets make (2 + 5) Γ 2 = 14, but without them 2 + 5 Γ 2 = 12. And cΒ² is 64, not 2 Γ 8.
10 Three dice
Three dice have been thrown. Judge each sentence about the faces showing: true or false?
| β | ||||||
| β | ||||||
| β |
A tick under a number means that die shows that number.
The dice show 3, 4 and 6. Times before plus: 3 + 4 Γ 6 = 27, but with brackets (3 + 4) Γ 6 = 42.
11 Eight meets a half
Pair each line with what it says and what it makes.
Tap a line, then its meaning.
Multiplying by a half shrinks, dividing by a half grows. Two different lines can still make the same four.
12 The pizza slices
Eight slices shared among four friends gives two each. One tile is wrong. Find it, then fix it.
Tap the tile that is wrong.
Sharing is division: 8 Γ· 4 = 2. Eight times four would be 32, and 8 β 4 is 4.
13 Brackets, then square
Add 3 and 2 inside the brackets, then square the result. One tile is wrong.
Tap the tile that is wrong.
(3 + 2)Β² = 5Β² = 25. Squaring each number separately gives 9 + 4 = 13, and 3 + 2Β² is 7.
14 Under the root
Work out what is under the root first, then take the root.
2Β² = 4 and 3 Γ 4 = 12; together 16, whose square root is 4.
15 Halve, halve, halve
Halve 64 three times. The result is a power of two: which power?
64 becomes 32, then 16, then 8; and 8 = 2 Γ 2 Γ 2 = 2Β³.
16 The rug
A rectangular rug has length l and width w. Its area A is length times width; its perimeter P is twice the sum of length and width. Write both formulas.
One way:
Area multiplies the two sides; the perimeter adds them in brackets first, then doubles.
17 The square field
A square field has area 49. Write how its side s is found, and what it is.
One way:
The side squared is the area, so the side is the square root of 49: 7.
18 Splitting the bill
Three friends split a bill of 60 equally, and each adds 2 as a tip. Write what each one pays.
One way:
Share first: 60 Γ· 3 = 20; then add the tip: 22. The fraction bar and Γ· say the same thing.
Chapter finished. The symbols are yours.
Tell your own
Tell a three-line story about sharing or doubling sweets, in signs only. Use brackets once. Then read it aloud.
Kept on this device only.