Fraction Wall Explorer — Interactive Tool

1

Select the fraction 2/4 and toggle Equivalents on. Which rows light up? Write down all the equivalent fractions you can see on the wall. What do you notice about the relationship between the numerators and denominators?

2

Find two different fractions that are equivalent to 1/3. Now find two that are equivalent to 2/3. How can you tell from the wall whether two fractions are equivalent without doing any calculation?

3

Select 6/12. The banner shows the simplified form. Now select 4/12, then 3/12. Which of these simplify and which are already in simplest form? What must be true about the numerator and denominator for a fraction to be in its simplest form?

4

Drag the sixths row so it sits directly beneath the thirds row. Select 2/3. What do you notice about how the shaded regions line up? Now drag the twelfths row underneath the sixths. How does this help you see the chain of equivalence 2/3 = 4/6 = 8/12?

5

Which row has the most fractions equivalent to 1/2? Which rows have no fraction equivalent to 1/2? What do the denominators of these rows have in common?

6

Can you find a fraction on the wall that has no equivalents on any other row? Why does this happen for some fractions but not others?

7

Without using compare mode, look at the wall and decide which is larger: 3/5 or 2/3. Explain how the wall helps you see this. Now check your answer using compare mode.

8

Turn on compare mode. Select 1/3 and 1/4. Look at the number line. Which fraction is further from zero? Now try 2/3 and 3/4. Which is closer to 1? How does the number line help you see this?

9

Using compare mode, find two fractions from different rows that are very close together but not equal. What is the smallest difference you can find between two non-equivalent fractions on the wall?

10

Select 1/2 as fraction A, then try each of these as fraction B: 3/7, 4/9, 5/11. Without calculating, use the wall and number line to put them in order from smallest to largest. Which are less than 1/2 and which are greater?

11

Drag the rows into order from largest unit fraction at the top to smallest at the bottom. What do you notice about the visual pattern? Why does a larger denominator mean a smaller unit fraction?

12

Toggle Decimals on. Look at the unit fractions 1/2, 1/3, 1/4, 1/5. Which of these have terminating decimals (they end) and which have recurring decimals (they go on forever)? Can you spot a pattern in which denominators give terminating decimals?

13

Toggle Percentages on. Select 3/8. The banner shows the percentage. Now find a fraction on a different row whose percentage is as close as possible to 3/8. What is the closest you can get?

14

Toggle Decimals on and look at the sevenths row. What do you notice about the decimal for each seventh? Write down 1/7, 2/7, 3/7, 4/7, 5/7, 6/7 as decimals. What is special about the digits that appear?

15

Using the percentage display, find all the fractions on the wall that are greater than 30% but less than 40%. How many are there? Do any of them simplify to the same fraction?

16

Toggle both Decimals and Percentages on. Select 1/3. The decimal shows 0.3333 and the percentage shows 33.3%. Now select 2/6. Are the decimal and percentage the same or different? Explain why this makes sense.

17

Turn on compare mode. Select 1/3 then 1/4. Look at the banner carefully. It shows the addition working: 1/3 + 1/4 = 4/12 + 3/12 = 7/12. Explain in your own words what happened to each fraction and why.

18

Using compare mode, add 1/2 + 1/3. What row does the sum appear on? Now try 1/2 + 1/4. What row does that sum appear on? Why are the sum rows different?

19

Find two fractions that add up to exactly 1 (a whole). How many different pairs can you find? What do you notice about the two fractions in each pair?

20

Using compare mode, add 1/6 + 1/6. What is the result? Now try 2/6 + 1/6, then 3/6 + 1/6. What pattern do you see? Does the sum ever appear on a row other than sixths?

21

Try adding 1/3 + 1/6. The banner shows the common denominator step. Now try 1/4 + 1/6. Which of these needs a bigger common denominator? How does the wall help you see why 1/4 + 1/6 is harder to add than 1/3 + 1/6?

22

Find two fractions whose sum is as close to 1/2 as possible without equalling it. Use the number line to check how close you got.

23

What happens when you try to add two fractions whose sum is greater than 1? Try 2/3 + 1/2. What does the banner tell you? Why can’t the wall show this sum visually?

24

Select 1/4 and look at where its marker appears on the number line. Now select 3/12. Does the marker move? Why or why not?

25

Turn on compare mode and select 1/3 and 2/5. Look at the number line. The markers are quite close together. Now look at the wall. Can you see which is larger from the wall alone? Which representation — the wall or the number line — makes it easier to compare fractions that are close in value?

26

Without clicking, estimate where 5/8 would appear on the number line. Is it closer to 1/2 or to 3/4? Now click to check. Was your estimate accurate?

27

In compare mode, select two fractions and look at all three markers (A, B, and their sum). The sum marker should always be to the right of both A and B. Can you explain why this must be true?

28

Look at the wall with no fraction selected. How many segments does each row have? What is the total number of segments across the entire wall (with the default 12 rows)? Can you find a formula?

29

How many fractions on the wall are equivalent to 1/2? How many are equivalent to 1/3? How many are equivalent to 1/4? Can you predict how many fractions on the wall are equivalent to 1/5 without counting?

30

Using manual shading, shade all the fractions on the wall that are in their simplest form (cannot be simplified). Which row has the most fractions in simplest form? Which has the fewest? Can you explain the pattern?

31

The halves row divides the wall into 2 equal parts, the thirds into 3, and so on. If you drew vertical lines at every segment boundary across all rows, how many distinct positions between 0 and 1 would be marked? (Hint: think about which boundaries overlap.)

32

Using manual shading with different colours, shade all fractions equivalent to 1/2 in one colour, all fractions equivalent to 1/3 in another, and all fractions equivalent to 1/4 in a third. What proportion of the wall is left unshaded? Are there any fractions that could be shaded in more than one colour?

33

A unit fraction is a fraction with 1 as the numerator. The Ancient Egyptians wrote all fractions as sums of distinct unit fractions. Using compare mode, can you write 3/4 as the sum of two different unit fractions? What about 5/6? Can you always do this?

34

Investigate: for which pairs of rows on the wall can you always find equivalent fractions? For example, can you always find a fraction in the sixths row equivalent to one in the thirds row? What about the sixths and the fourths? What mathematical concept determines this?

35

Using the wall and compare mode, investigate this claim: when you add two unit fractions 1/a + 1/b, the sum is always (a+b)/(a×b). Test it with at least five examples. Does the wall always confirm this? When does the result simplify?

36

Design your own fraction wall investigation. Choose which display options to turn on, which rows to reorder, and write a question that another student could explore. Test it yourself first, then exchange with a partner.