Speak Maths · School
Equal, bigger, smaller
Seven small signs compare two things. Each one is a whole sentence you can say aloud.
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: equalsMeans: both sides are the same amount
- Say: is not equal toMeans: the two sides are different amounts
- Say: is less thanMeans: the left side is smaller; the open mouth faces the bigger side
- Say: is greater thanMeans: the left side is bigger
- Say: is less than or equal toMeans: smaller, or the same: “at most”
- Say: is greater than or equal toMeans: bigger, or the same: “at least”
- Say: is approximately equal toMeans: nearly the same, close enough for now
The story: The balance
Tap a line to see its words.
- A bag of apples weighs 3 kilograms.
- A bag of pears weighs 5 kilograms.
- The apples are lighter than the pears.
- Put a 2-kilogram weight beside the apples, and the balance is level.
- With only a 1-kilogram weight, it is not level.
- The little basket can hold 4 kilograms or less.
- The pears weigh more than 4 kilograms, so they will not fit.
- A melon weighs a little under 2 kilograms: about 2.
In words this story is 387 letters long; in symbols, 28.
Read it
What does it say?
Write it
Which notation says this?
Nine is about ten.
Five is less than six.
The number of children, n, is at least twenty.
A dozen, d, is exactly twelve.
The bus ride, t, takes about forty minutes.
To go on the ride, your age a must be at least eight.
The room holds fewer than thirty chairs, c.
Six times seven is not forty-eight.
The speed limit: the speed v is at most fifty.
Three quarters is greater than one half.
The temperature T is between 18 and 22 degrees, and may be 18 or 22 itself.
A half plus a half is exactly one.
Build it
Tap the tiles in order. One tile does not belong.
Two plus three equals five.
Ten is greater than or equal to y.
Seven is not equal to eight.
Two is less than x, and x is less than or equal to nine.
Pi is approximately 3.14.
Four plus six is greater than or equal to ten.
Challenges
Creative puzzles that use every sign of this chapter. Take your time; there is no clock.
1 The parcel shelf
Four parcels have been weighed. Judge each sentence about them: true or false?
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A tick under a number means the parcel weighs that many kilograms.
The weights are 2, 3, 3 and 5. Note that 2 + 3 is exactly 5, so “not equal” fails, and 3 + 3 beats 5.
2 Which way does the mouth face?
x is a number. Pair each line with what it says about x.
Tap a line, then its meaning.
The open side faces the bigger number, and the little line underneath means “or equal”.
3 The crooked scale
Two plus two makes four, and four is at most five. One tile is wrong. Find it, then fix it.
Tap the tile that is wrong.
“At most” allows smaller or equal, so it is ≤. The signs = and > are both false for 4 and 5.
4 Squeezed in
x is a whole number. Which value satisfies both conditions?
3 < x ≤ 5 leaves 4 and 5, and x ≠ 4 throws out 4.
5 Close enough
A scale shows 9.98 kilograms. Which x makes the sentence sensible?
≈ means nearly the same: 9.98 is almost 10, not 9 and not ten times too big.
6 The small lift
The lift carries at most 8 people, so 9 people are too many. Write both facts with n for the number of people on board.
One way:
“At most 8” is ≤ 8, and “9 is too many” says 9 is greater than 8.
7 About how tall?
Your height h is about 150 centimetres, at least 140 but less than 160, and not exactly 145. Write it in symbols.
One way:
Three different comparisons side by side: ≈ for roughly, ≤ and < for the two ends of the range, ≠ to rule one value out.
8 The tin tower
Four tins stand on a shelf, each with its height in centimetres. Judge each sentence: true or false?
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A tick under a number means the tin is that many centimetres tall.
The heights are 2, 4, 4 and 1. Tins 2 and 3 are the same height, so “greater than” fails but “greater than or equal to” holds.
9 Three jars of marbles
Three jars hold marbles. Judge each sentence: true or false?
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A tick under a number means the jar holds that many marbles.
The jars hold 3, 6 and 6. The second and third are equal, so “not equal” is false, and 6 is not “5 or less”.
10 Exactly, roughly, or not at all
x is a number. Pair each line with what it says.
Tap a line, then its meaning.
Four signs that all mention seven: one says exactly, one says nearly, one says never, and one allows seven or anything smaller.
11 Inside or outside?
A number x and the stretch from zero to one. Pair each line with where x is.
Tap a line, then its meaning.
A double inequality squeezes x between two numbers; the little line under the sign decides whether the ends count.
12 The crooked ladder
Three is less than five, and five is greater than four. One tile is wrong. Find it, then fix it.
Tap the tile that is wrong.
5 < 4 is false; the mouth must open towards the bigger number, so 5 > 4.
13 The cake recipe
The cake needs at least 3 eggs, e, and 2 is less than 3, so 2 eggs are not enough. One tile is wrong.
Tap the tile that is wrong.
“At least 3” means 3 or more: e ≥ 3. With ≤ the recipe would accept zero eggs.
14 Squeezed from both sides
Both sentences are true. What do they say together?
At least 4 and at most 4 leaves only one number: x = 4.
15 Not true!
A friend claims this sentence about x. It turns out to be false. Which sentence is then certainly true?
If x is not greater than 10, it is 10 or smaller: x ≤ 10. “x < 10” forgets that x could be exactly 10.
16 Nearly a hundred
x is a whole number. Which value fits all three sentences?
About 100 but not 100, and above it: 101. 99 is below, and 100 is ruled out.
17 Half a loaf
“Half a loaf is better than none.” Write the proverb as a comparison of two amounts.
One way:
Half is 1/2 and none is 0; “better” here means more: 1/2 > 0.
18 Half full
A glass holds g millilitres. The water in it, w, is about half of that, not exactly half, and of course less than a full glass. Write all three facts.
One way:
≈ for about half, ≠ to say not exactly, and < because the glass is not full.
Chapter finished. The symbols are yours.
Tell your own
Tell a three-line story about weighing two things, in signs only. Then read it aloud.
Kept on this device only.