Fraction bars - mr barton maths

1

Set up 1/5 + 2/5 using the builder. Look at the Question line — both bars are the same colour and divided into the same size pieces. How many pieces are shaded altogether? Press = ? to check.

2

Now try 3/8 + 4/8. Before pressing = ?, count the shaded pieces and predict the answer. Were you right? What do you notice about the denominator of the answer?

3

Set up 2/6 + 3/6. The answer is 5/6. Now try 2/6 + 4/6. What happens when the total number of pieces equals the denominator? What fraction is this equal to?

4

When you add two fractions with the same denominator, do you add the numerators, the denominators, or both? Use the tool to test your answer with three examples.

5

Try 1/7 + 1/7, then 2/7 + 2/7, then 3/7 + 3/7. Without using the tool, predict the answer to 4/7 + 4/7. What will be different about this answer compared to the others?

6

Set up 1/2 using the builder. Tap the bar, then look at the conversion panel. Convert it to fourths, then to sixths, then to eighths. Each time, what happens to the number of pieces? What stays the same about the bar?

7

Convert 1/3 to sixths. Now use the “Reset” button and convert it to ninths instead. Compare: 2/6 and 3/9. Are these the same fraction? How can you tell by looking at the bars?

8

Set up 2/3 and convert it to twelfths. How many twelfths is this? Now set up 3/4 and convert it to twelfths too. Why is 12 a useful denominator for both of these fractions?

9

Set up 1/4 and look at the conversion targets. Which denominators can you convert to? Now try 1/3. Are the targets the same? Why does 1/4 have different conversion options to 1/3?

10

A student says “to find an equivalent fraction, you just double the numerator and denominator.” Set up 1/5 and convert it. Is doubling the only option? How many different equivalent fractions can you make? What is the rule that connects all of them?

11

Set up 3/5 and try to convert it to eighths. Can you? Why not? What must be true about the new denominator for a conversion to work?

12

Set up 1/2 + 1/4. The amber message tells you the pieces are different sizes. Tap the 1/2 bar and convert it to fourths. What happens on the Working line? Can you now see the answer by counting pieces?

13

Try 1/3 + 1/6. Which fraction needs converting — the thirds or the sixths? Why do you only need to convert one of them?

14

Set up 1/3 + 1/4. This time, both fractions need converting. Before tapping anything, can you think of a denominator that works for both? Tap a bar and look at the conversion targets — is your denominator one of them? Convert both fractions and check your answer.

15

Set up 2/3 + 3/5. Convert both to the same denominator. Now clear and try again, but this time choose a different common denominator. Do you get the same answer? Which common denominator made the arithmetic easier?

16

Set up 1/2 + 1/3. The smallest common denominator is 6. But you could also use 12, 18, or 24. Try using 12 instead of 6. Is the answer harder or easier to simplify? Why is the smallest common denominator usually the best choice?

17

Set up 1/2 + 1/3 + 1/6. You have three fractions with three different denominators. Can you find one denominator that works for all of them? Convert each fraction and find the total. Does the answer simplify?

18

Switch to Subtraction mode. Set up 3/5 − 1/5. Look at the Difference row — the hatched zone shows the overlap and the purple zone shows the difference. How many pieces is the purple zone? Press = ? to check.

19

Set up 3/4 − 1/3. The pieces are different sizes, so you cannot subtract yet. Convert both fractions to the same denominator. Watch the Difference row change — when does the piece count appear inside the purple zone?

20

Set up 1/2 − 2/3. The tool shows a warning because B is larger than A. Use the Swap button. Now it reads 2/3 − 1/2. Why does the order matter in subtraction but not in addition?

21

Set up 5/6 − 1/3. Before converting anything, estimate: is the answer more or less than 1/2? Now convert and check. Was your estimate correct?

22

Try 7/8 − 3/8, then 7/8 − 4/8, then 7/8 − 5/8. What happens to the purple Difference zone each time? Without using the tool, what would 7/8 − 7/8 look like?

23

Set up 3/4 + 1/2. Convert to the same denominator and reveal the answer. The tool shows three forms: 5/4 = 5/4 = 1¼. What does the whole number “1” represent? How does the bar model show this — what happens to the bar when the total is greater than 1?

24

Try 2/3 + 2/3. The answer is 4/3. The tool shows this equals 1⅓. Now try 2/3 + 5/6. Does this also give an improper fraction? Can you predict before revealing?

25

What is the largest answer you can make by adding two proper fractions using denominators up to 10? (Hint: what are the two largest proper fractions you can make?)

26

Can you find two fractions where the answer is exactly 1? Try it with the same denominator first (easy), then with different denominators (harder). What must be true about the two fractions for their sum to equal exactly 1?

27

Use the generator on Level 1 (Same denominator). Generate five questions and solve each one. Time yourself. Now switch to Level 2 (One is a multiple). Are these harder? What extra step do you need each time?

28

Generate a Level 3 question (Share a factor). Look at the two denominators. Can you spot the common factor? Use this to find the smallest common denominator before tapping any bars.

29

Generate a Level 4 question (Co-prime). The denominators share no common factor, so the smallest common denominator is their product. For example, thirds and fifths need fifteenths (3 × 5 = 15). Generate five questions and find the common denominator for each by multiplying. Does this always give the smallest possible denominator?

30

Generate a Level 2 subtraction question. Before converting, estimate whether the answer is more or less than 1/2. Now convert and check. Try this five times. How often was your estimate correct?

31

Investigate: is 1/2 + 1/3 the same as 1/3 + 1/2? Try it both ways. What about 2/5 + 1/3 and 1/3 + 2/5? Does the order matter in fraction addition? Does the order matter in fraction subtraction? Use the tool to test your claims.

32

A student says “when you add fractions, you add the tops and add the bottoms.” So they think 1/3 + 1/4 = 2/7. Set up 1/3 + 1/4 in the tool. Is 2/7 correct? Look at the bars — why does the student’s method give the wrong answer?

33

Find two fractions that add to exactly 1/2. Now find a different pair. How many pairs can you find? Is there a pattern?

34

Investigate: for which pairs of denominators is the common denominator not equal to their product? For example, thirds and sixths need sixths (not eighteenths). Test at least five pairs. What do the denominators have in common when this happens?

35

Using subtraction, find two different fractions where the difference is exactly 1/6. Now find a pair where the difference is 1/12. Can you find a pair for any unit fraction difference?

36

Design three fraction addition questions: one that is easy, one that is medium, and one that is hard. Give them to a partner to solve using the tool. What made your hard question hard?