Printing: use your browser's print (Ctrl+P / ⌘P). The whole week is 16 A4 sheets (8 pieces of paper double-sided) — the same content as the single days.

time yourself

Maths A (new)Tue 8 September1 / 4

Using common multiples and common factors

Last week you learned the words. This week they become tools

Name Date

Try this first

List every factor of 12, and every factor of 18.
Then circle the numbers that appear in both lists.

1Factors of 12:

Factors of 18:

In both:

The largest circled number is the greatest common divisor.

Lowest common multiple → for adding fractions　/　Greatest common divisor → for cancellingThese two lines are the whole of this week

Now you

2Find both the greatest common divisor and the lowest common multiple of 8 and 12.

time yourself

Maths A (new)Tue 8 September2 / 4

Using common multiples and common factors

Name Date

3Find the greatest common divisor of 15 and 20.

4Find the lowest common multiple of 6 and 9. Explain in words how it differs from 6 x 9 ＝ 54.

5A sheet of paper is 18 cm by 24 cm. It is cut into identical squares with nothing left over. What is the largest possible side length, and how many squares are there?

What kind of number divides both 18 and 24 exactly?

6A red lamp flashes every 12 seconds and a blue lamp every 18 seconds. They have just flashed together. After how many seconds do they flash together again?

time yourself

Maths A (new)Tue 8 September3 / 4

Using common multiples and common factors

Name Date

7List every whole number from 1 to 50 that is a multiple of both 4 and 6.

8Two whole numbers have greatest common divisor 8 and lowest common multiple 48. What could the two numbers be?

The product of two numbers equals GCD x LCM.

Which tool is it

9Find both the greatest common divisor and the lowest common multiple of 16 and 24.

10Of the whole numbers 1 to 60, write every one that is a multiple of both 5 and 6.

time yourself

Maths A (new)Tue 8 September4 / 4

Using common multiples and common factors

Name Date

1136 pencils and 24 erasers are shared out equally with none left over. What is the largest number of people, and what does each get?

12Question 5 (cutting squares) and question 6 (flashing together) used different tools. Which used the greatest common divisor and which the lowest common multiple? Say why.

The important question today. Naming it matters more than doing it.

Extra · you may skip this

Find the lowest common multiple of 3, 4 and 6. Three numbers work the same way.

Costume 1 · ITWed 9 September1 / 4

Screen resolution

Cancelling a fraction is also how a screen's shape gets its name

Name Date

Think about this

A computer screen is 1920 dots across and 1080 down.

We call that screen 16 : 9.

Where did 16 and 9 come from?

1Write down what you think.

Both numbers are divided by the same thing, and the shape does not change. It is exactly the same move as cancelling a fraction.

Now you

2The greatest common divisor of 1920 and 1080 is 120. Do the division and check that you get 16 : 9.

Costume 1 · ITWed 9 September2 / 4

Screen resolution

Name Date

3An older screen was 1024 by 768, and their GCD is 256. Find the ratio.

4A phone screen is 1170 by 2532, and their GCD is 6. Find the ratio.

5Which of the shapes in questions 2 and 3 is wider? Answer from the ratio alone, and say how you can tell.

16 : 9 and 4 : 3. Try dividing the width by the height.

6A 4K screen is 3840 by 2160. Is that the same shape as 1920 by 1080? Cancel it down and check.

Costume 1 · ITWed 9 September3 / 4

Screen resolution

Name Date

7A photo is 6000 by 4000. Write the ratio in its simplest form.

8A screen is 1280 by 720 and their GCD is 80. Find the ratio.

Ratios and cancelling

9A screen is 2048 by 1536 and their GCD is 512. Find the ratio.

10On a 16 : 9 screen the height is 1440. How wide is it?

Costume 1 · ITWed 9 September4 / 4

Screen resolution

Name Date

11Which is the wider shape, a 4 : 3 photo or a 16 : 9 screen? Say why.

12Is putting a ratio in its simplest form the same thing as cancelling a fraction, or different? Explain in words.

Set today's ratios beside Friday's cancelling.

Extra · you may skip this

On a 16 : 9 screen, if the width is 2560 dots, what is the height?

time yourself

Maths B (word problems)Fri 11 September1 / 4

Common denominators and cancelling

Read the theory page first and this goes much faster

Name Date

First, the most common mistake

¹⁄₄ ＋ ¹⁄₆ ＝ ²⁄₁₀　This is wrong.

¹⁄₄ on its own is already bigger than ²⁄₁₀, so adding ¹⁄₆ cannot give something smaller.

Example

¹⁄₄ ＋ ¹⁄₆

① LCM of 4 and 6 → 12
② ¹⁄₄ ＝ ³⁄₁₂　¹⁄₆ ＝ ²⁄₁₂
③ ³⁄₁₂ ＋ ²⁄₁₂ ＝ ⁵⁄₁₂

Now you

1¹⁄₂ ＋ ¹⁄₃

2³⁄₄ ＋ ¹⁄₆

time yourself

Maths B (word problems)Fri 11 September2 / 4

Common denominators and cancelling

Name Date

3⁵⁄₆ − ²⁄₉

4Simplify ²⁴⁄₃₆.

5¹⁄₄ ＋ ¹⁄₁₂　(simplify if you can)

6Which is larger, ²⁄₃ or ⁵⁄₈ ? Use a common denominator.

7A ribbon is ³⁄₄ m long. ¹⁄₆ m is used. How much is left?

Draw the picture before writing the calculation.

time yourself

Maths B (word problems)Fri 11 September3 / 4

Common denominators and cancelling

Name Date

8Explain by meaning, not by method, why ¹⁄₂ ＋ ¹⁄₃ ＝ ²⁄₅ must be wrong.

This wants a sentence, not a number.

9With denominators 6 and 8 you could use 24 or 48. Why is 24 the usual choice?

A little further

10⁵⁄₈ ＋ ⁷⁄₁₂

The answer comes out bigger than 1.

time yourself

Maths B (word problems)Fri 11 September4 / 4

Common denominators and cancelling

Name Date

11Put ³⁄₄, ⁵⁄₆ and ⁷⁄₉ in order, largest first.

12There is ²⁄₃ L of milk. ¹⁄₄ L is drunk in the morning and ¹⁄₆ L at night. How much is left?

Extra · you may skip this

Work out ¹⁄₂ ＋ ¹⁄₃ ＋ ¹⁄₆. Look at the answer and write down what you notice.

Costume 2 · machines + correctionsSun 13 September1 / 4

Gears, and this week's corrections

A lowest common multiple you can actually watch turning

Name Date

Think about this

A 12-tooth gear meshes with an 18-tooth gear. Both marks start pointing straight up.

After how many teeth do both marks point up again?

1Answer the question above.

2By then, how many turns has the 12-tooth gear made? And the 18-tooth one?

Once you have both numbers, look at them carefully. Notice anything?

This is the important part today

Not 12 x 18 ＝ 216.

Multiplying takes you far past the first time they line up. Make sure you can say in words why the answer is 36 and not 216.

Costume 2 · machines + correctionsSun 13 September2 / 4

Gears, and this week's corrections

Name Date

3Write, in words, why the answer to question 1 is not 216.

Different gears

4With an 8-tooth and a 12-tooth gear, after how many teeth do they line up again?

5A bicycle has 48 teeth on the front gear and 16 on the back. One turn of the pedals turns the back gear how many times?

48 ÷ 16. This one is division, not a common multiple.

This week's corrections

6Pick two questions you got wrong this week and do them again.

Solve them again — do not copy the answer across.

Costume 2 · machines + correctionsSun 13 September3 / 4

Gears, and this week's corrections

Name Date

Classic problem — cycles

7Red, blue and yellow lights flash in that order, over and over. The 1st is red. What colour is the 50th?

Think about the remainder when you divide by 3.

8With the same three lights, what colour is the 100th?

More of it — reading the remainder

9Red, blue, yellow, green repeat in that order, starting with red. What colour is the 60th?

Costume 2 · machines + correctionsSun 13 September4 / 4

Gears, and this week's corrections

Name Date

10In question 9 the remainder came out 0. What does a remainder of 0 mean here? Say it in words.

The important question today.

11If 1 January is a Thursday, what day is 29 January?

12The gear questions used the lowest common multiple. What did the repeating-colour questions use? One phrase is enough.

Extra · you may skip this

Add a third gear with 36 teeth. After how many teeth are all three back where they started?