Speak Maths Β· School
Letters for unknown numbers
A letter is a name for a number. Sometimes the number is hidden, sometimes it is simply not said yet.
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: box plus three equals eightMeans: a box holds a number we do not know yet
- Say: xMeans: a letter taking the place of the unknown number
- Say: a, b, cMeans: constants: fixed numbers we choose not to write out
- Say: three xMeans: 3 times x; the times sign is left out
- Say: a bMeans: a times b; letters side by side are multiplied
- Say: x one, x twoMeans: the first and the second of several numbers, all called x
- Say: is defined asMeans: a name we choose, not something to be solved
The story: The unknown box
Tap a line to see its words.
- A closed box holds some counters. Put in 3 more, and there are 8.
- Call the number inside the box x. Now the box is a letter.
- Take 3 from 8 to find x: it is 5.
- From now on, let k be a name for 5. It is defined, not solved.
- Three boxes of k counters each hold 3 times 5, which is 15.
- A tray has a rows with b boxes in each row. Here a is 3 and b is 4.
- The tray holds a times b boxes: 12.
- Two different boxes: the first holds 5, the second holds 8.
- Together they hold 13 counters. One letter, many boxes, one story.
In words this story is 512 letters long; in symbols, 50.
Read it
What does it say?
Write it
Which notation says this?
Four times a number n.
Let m be a name for twelve.
The first number plus the second number.
Some number, plus five, makes nine.
Seven times a number t.
The third number in the list y.
Let p be a name for one hundred.
The length l times the width w.
A number x, minus four, is ten.
Half of a number n.
The first number minus the second number, in the list a.
Constants a and b: a is three, and b is twice a.
Build it
Tap the tiles in order. One tile does not belong.
Three x plus two equals eleven.
k is defined as a times b.
Box times two equals ten.
Five y minus one.
x one plus x two equals twenty.
c is defined as two a.
Challenges
Creative puzzles that use every sign of this chapter. Take your time; there is no clock.
1 Three closed boxes
Each box holds some counters. Judge each sentence about them: true or false?
| β | |||
| β | |||
| β |
A tick under a number means the box holds that many counters.
x_1 and x_3 hold 5 each, x_2 holds 8. The small number below a letter is only a label, not something to multiply.
2 Look-alikes
Pair each line with what it says.
Tap a line, then its meaning.
A number in front multiplies, a small number below labels, letters side by side multiply, and := gives a name.
3 Naming a number
From now on k is a name for 5, and then three k is 15. One tile is wrong. Find it, then fix it.
Tap the tile that is wrong.
We are not solving for k; we are choosing its name, so the sign is := and not an equation to check.
4 The tray of boxes
A tray has a rows with b boxes in each row. Here a is 3 and b is 4, and the tray holds 12 boxes. One tile is wrong.
Tap the tile that is wrong.
The number of boxes is a times b, written ab. 3 + 4 would only give 7.
5 The mystery box
Two of the hidden number, plus 1, makes 9. What is in the box?
2 Γ 4 + 1 = 9. Try 5 and you get 11; try 3 and you get 7.
6 Letters side by side
Here a and b are named numbers. What is ab + a?
ab means a times b, not the number 23: 2 Γ 3 + 2 = 8.
7 Think of a number
Think of a number, double it, add 3, and you get 11. Write this as an equation, using x for your number.
One way:
Doubling x is 2x, adding 3 gives 2x + 3, and that equals 11. So x is 4.
8 Rows and columns
A tray has a rows of b boxes. Name the total number of boxes n, and write how it is found.
One way:
Letters side by side are multiplied, so the total is ab. Writing n := ab names it.
9 Three named numbers
a, b and c are constants: fixed numbers shown in the table. Judge each sentence: true or false?
| β | |||||
| β | |||||
| β |
A tick under a number means the letter stands for that number.
a = 2, b = 3, c = 6. Letters side by side multiply: ab = 6 = c, but a + b is only 5.
10 Four cups in a row
Four cups stand in a row; x_1 is the number of sugar lumps in the first, x_2 in the second, and so on. Judge each sentence: true or false?
| β | |||||
| β | |||||
| β | |||||
| β |
A tick under a number means the cup holds that many lumps.
The cups hold 1, 3, 0 and 5. The small number only says which cup; x_2 x_4 is 3 Γ 5 = 15, and 5 β 3 is 2, not 1.
11 x and the number four
Five ways to put x next to a four. Pair each line with what it says.
Tap a line, then its meaning.
Where the four sits changes everything: in front it multiplies, below it labels, above it is a power, and := names rather than solves.
12 Twice the flour
A recipe takes s cups of sugar and twice as much flour, f. With s named 3, f comes to 6. One tile is wrong.
Tap the tile that is wrong.
Twice s is 2s = 6. s + 2 would be 5, and sΒ² would be 9.
13 The second box
The first box holds 5, the second holds 7, and together they hold 12. One tile is wrong.
Tap the tile that is wrong.
The second number in the list is x_2, with the 2 written low as a label. xΒ² would mean x times x.
14 Twin boxes
Two boxes hold the same hidden number, and together they make 14. What is in each?
The same box twice is two of the number: 2 Γ 7 = 14.
15 Named in a chain
a is named first, then b is named using a. What is 2b β a?
b is 5, so 2b is 10 and 10 β 4 = 6.
16 A growing list
Each number in the list is made from the earlier ones. What is the third?
x_1 x_1 = 4, then x_1 x_2 = 2 Γ 4 = 8. Side by side means multiply, not add.
17 The lost marbles
You had some marbles, lost 4, and have 9 left. Write this with a box for the number you started with, or with x.
One way:
The unknown is the starting number: box minus 4 equals 9, so the box held 13.
18 The shared gift
Three friends each pay the same amount p for a gift that costs 24. Write the equation.
One way:
Three equal amounts: a 3 in front of the letter, 3p = 24, so p = 8.
19 Two throws
A die is thrown twice: call the first result t_1 and the second t_2. Together they make 9. Write it.
One way:
The same letter with labels 1 and 2 keeps the two throws apart: t_1 + t_2 = 9.
Chapter finished. The symbols are yours.
Tell your own
Tell a three-line story about a box with a hidden number in it, using a letter. Define one name with colon-equals. Then read it aloud.
Kept on this device only.