Year 4: Solving problems and reasoning with charts
Part of the Year 4 pictograms, bar charts and time graphs chapter. Chapter overview · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)
Solving problems and reasoning with charts
Now you can read tally charts, pictograms, bar charts, tables and time graphs. In this section you will use them to solve problems. Many questions ask you to compare things (“how many more”), to find a sum (“how many altogether”) or to find a difference (“what is the difference between the tallest and the shortest”).
The best way is to do it in steps. 1. Read the question: what is it asking? 2. Find the numbers you need on the chart (read the key or scale first!). 3. Decide: add, subtract or multiply? 4. Write the answer with its unit and check it makes sense.
Which chart? Use a tally chart to collect data as it comes in. Use a pictogram or a bar chart to compare things you have counted (discrete data), such as favourite fruit. Use a table when you need exact numbers. Use a time graph when something changes over time and you measure it (continuous data), such as temperature or height.
Key ideas
- Read the question. Find what it asks and which numbers you need.
- Read the key (pictogram) or the scale (bar chart, time graph) first.
- “How many more” and “the difference” → subtract. “Altogether” and “in total” → add.
- Tally and bar chart or pictogram: counted data. Time graph: measured data over time.
- To decide if a statement is true: find the numbers and check them. Then give a reason.
Key words. The difference between two numbers is how much bigger one is than the other. We find it by subtracting. “How many more” and “how many fewer” questions are difference questions. A bar chart uses bars to show data. The height (or length) of a bar shows how many. The scale is the row of numbers on the side. It tells you how much each gridline is worth.
Method. Work out each total first. Then subtract the smaller total from the bigger total.
- Find the scale. The numbers up the side are the scale. Not every gridline has a number, so we must work out what each small gap is worth.The numbers go up in 10s: 0, 10, 20...
Between two numbers there are 2 gaps.
10 ÷ 2 = 5, so each small gap is worth 5. - Read the numbers we need from the picture. We need these numbers for the calculation.Football = 35
Swimming = 25
Chess = 15
Art = 20 - Add the numbers for football and swimming. Together means add.35 + 25 = 60
- Add the numbers for chess and art. Together means add.15 + 20 = 35
- Subtract. How many more means the bigger total minus the smaller total.60 − 35 = 25
Check. 35 + 25 = 60. ✓
Watch out. There are three steps here: add, add, then subtract.
Key words. A pictogram uses small pictures (symbols) to show data. The key tells you how many each symbol stands for. A half symbol stands for half of that number.
Method. Find the number for the first one, double it, then look for that number in the chart.
- Read the key. The key tells us what one symbol is worth. Here a symbol is not worth 1.1 symbol = 5 books
- Read the numbers we need from the picture. Multiply the number of symbols by what one symbol is worth.Mon = 20
- Double the number. Twice as many means two times as many.2 × 20 = 40
- Find the number 40 in the chart. Look for the row or bar with this number.Tue = 40
- Write the answer. Tue
Check. 40 ÷ 2 = 20. ✓
Watch out. Twice as many means × 2, not + 2.
Key words. A table shows information in rows (going across) and columns (going down). A total is the answer when you add all the numbers together. A pictogram uses small pictures (symbols) to show data. The key tells you how many each symbol stands for. A half symbol stands for half of that number.
Method. Read the number from the chart. Then multiply by the price of one.
- Read the key. The key tells us what one symbol is worth. Here a symbol is not worth 1.1 symbol = 5 lunches
- Read the numbers we need from the picture. Multiply the number of symbols by what one symbol is worth.Wrap = 20
- Multiply by the price. Each one costs £3, so multiply the number sold by £3.20 × £3 = £60
- Write the answer. £60
Check. £60 ÷ 20 = £3. ✓
Watch out. Check you use the right price for the right item.
Key words. Discrete data is data you count. It jumps from one whole number to the next (you cannot have 2½ pupils). Continuous data is data you measure. It can take any value in between, like a height or a time. Continuous data changes smoothly.
Method. Think about what kind of data it is, and what we want to show.
- Is it counted or measured? Counted data is discrete. Measured data that changes over time is continuous.The temperature is measured, and it keeps changing. It is continuous data.
- What do we want to show? Compare amounts, or show how something changes?We want to show how the temperature changes through the day.
- Choose the chart. A time graph
Check. This chart fits the data. ✓
Watch out. A time graph is for data that changes over time. Bar charts and pictograms compare separate groups.
Key words. A time graph (or line graph) shows how something changes over time. The points are joined by lines. The numbers along the bottom show the time. The numbers up the side show the measurement.
Method. Find how much the graph goes up each time. Then carry on the pattern.
- Find the scale. The scale up the side tells us what each gridline is worth.The numbers up the side go up in 4s.
Between two numbers there are 2 gaps.
4 ÷ 2 = 2, so each small gap is worth 2. - Read the points. We need the numbers on the graph.9am = 4, 10am = 8, 11am = 12, 12pm = 16, 1pm = 20, 2pm = 24
- Look for the pattern. Find how much the number changes each time.9am to 10am: 8 − 4 = 4
10am to 11am: 12 − 8 = 4
11am to 12pm: 16 − 12 = 4
It goes up by 4 every time. - Carry on the pattern. If the pattern continues, add the same amount again.24 + 4 = 28
Check. 28 − 4 × 1 = 24. ✓
Watch out. This is a prediction. It only works if the pattern carries on.
Key words. The difference between two numbers is how much bigger one is than the other. We find it by subtracting. “How many more” and “how many fewer” questions are difference questions. A bar chart uses bars to show data. The height (or length) of a bar shows how many. The scale is the row of numbers on the side. It tells you how much each gridline is worth.
Method. Find the biggest and the smallest numbers, then subtract.
- Find the scale. The numbers up the side are the scale. Not every gridline has a number, so we must work out what each small gap is worth.The numbers go up in 20s: 0, 20, 40...
Between two numbers there are 2 gaps.
20 ÷ 2 = 10, so each small gap is worth 10. - Find the biggest and the smallest. We need these numbers for the calculation.Dev = 160
Chloe = 120 - Subtract. The difference between two numbers is the bigger minus the smaller.160 − 120 = 40
- Write the answer. 40
Check. 120 + 40 = 160. ✓
Watch out. Be sure you have found the biggest and the smallest of all the numbers.
Key words. A pictogram uses small pictures (symbols) to show data. The key tells you how many each symbol stands for. A half symbol stands for half of that number.
Method. Read both numbers. Double the smaller one and see if it matches the bigger one.
- Read the key. The key tells us what one symbol is worth. Here a symbol is not worth 1.1 symbol = 5 books
- Read the numbers we need from the picture. We need these numbers for the calculation.Tue = 40
Mon = 20 - Double the smaller number. “Twice as many” means two times as many.2 × 20 = 40
- Compare. Is Tue equal to 40?40 = 40
- Decide. The statement is true.
Check. 40 ÷ 2 = 20. ✓
Watch out. Twice as many means × 2, not + 2.
Watch out
Do not stop after the first step! In a two-step problem, check you have answered the whole question. Also check the unit (books, children, centimetres, £). And read the key or scale before you read any numbers.Exercise 11G Problems and reasoning
Non-calculatorKey words. Discrete data is data you count. It jumps from one whole number to the next (you cannot have 2½ pupils). Continuous data is data you measure. It can take any value in between, like a height or a time. Continuous data changes smoothly.
Method. Think about what kind of data it is, and what we want to show.
- Is it counted or measured? Counted data is discrete. Measured data that changes over time is continuous.The flavours are counted. It is discrete data.
- What do we want to show? Compare amounts, or show how something changes?We want to compare how many children chose each flavour.
- Choose the chart. A bar chart or a pictogram
Check. This chart fits the data. ✓
Watch out. A time graph is for data that changes over time. Bar charts and pictograms compare separate groups.
Key words. Discrete data is data you count. It jumps from one whole number to the next (you cannot have 2½ pupils). Continuous data is data you measure. It can take any value in between, like a height or a time. Continuous data changes smoothly.
Method. Think about what kind of data it is, and what we want to show.
- Is it counted or measured? Counted data is discrete. Measured data that changes over time is continuous.Height is measured, and it changes over time. It is continuous data.
- What do we want to show? Compare amounts, or show how something changes?We want to show how the height changes.
- Choose the chart. A time graph
Check. This chart fits the data. ✓
Watch out. A time graph is for data that changes over time. Bar charts and pictograms compare separate groups.
Key words. Discrete data is data you count. It jumps from one whole number to the next (you cannot have 2½ pupils). Continuous data is data you measure. It can take any value in between, like a height or a time. Continuous data changes smoothly.
Method. Think about what kind of data it is, and what we want to show.
- Is it counted or measured? Counted data is discrete. Measured data that changes over time is continuous.We are counting, one at a time, as each vote is called out.
- What do we want to show? Compare amounts, or show how something changes?We want to record each vote quickly while we count.
- Choose the chart. A tally chart
Check. This chart fits the data. ✓
Watch out. A time graph is for data that changes over time. Bar charts and pictograms compare separate groups.
Key words. Discrete data is data you count. It jumps from one whole number to the next (you cannot have 2½ pupils). Continuous data is data you measure. It can take any value in between, like a height or a time. Continuous data changes smoothly.
Method. Think about what kind of data it is, and what we want to show.
- Is it counted or measured? Counted data is discrete. Measured data that changes over time is continuous.Temperature is measured, and it keeps changing. It is continuous data.
- What do we want to show? Compare amounts, or show how something changes?We want to show how the temperature falls over time.
- Choose the chart. A time graph
Check. This chart fits the data. ✓
Watch out. A time graph is for data that changes over time. Bar charts and pictograms compare separate groups.
Key words. The difference between two numbers is how much bigger one is than the other. We find it by subtracting. “How many more” and “how many fewer” questions are difference questions. A bar chart uses bars to show data. The height (or length) of a bar shows how many. The scale is the row of numbers on the side. It tells you how much each gridline is worth.
Method. To find “how many more”, read both numbers and then subtract the smaller from the bigger.
- Find the scale. The numbers up the side are the scale. Not every gridline has a number, so we must work out what each small gap is worth.The numbers go up in 10s: 0, 10, 20...
Between two numbers there are 2 gaps.
10 ÷ 2 = 5, so each small gap is worth 5. - Read the numbers we need from the picture. We need these numbers for the calculation.Dance = 30
Art = 20 - Find the difference. To find how many more (or fewer), subtract the smaller number from the bigger number.30 − 20 = 10
- Write the answer. 10 more
Check. Add back: 20 + 10 = 30. ✓
Watch out. Subtract: do not add. The question asks for the difference.
Key words. A bar chart uses bars to show data. The height (or length) of a bar shows how many. The scale is the row of numbers on the side. It tells you how much each gridline is worth.
Method. Find each number on the picture, then add.
- Find the scale. The numbers up the side are the scale. Not every gridline has a number, so we must work out what each small gap is worth.The numbers go up in 10s: 0, 10, 20...
Between two numbers there are 2 gaps.
10 ÷ 2 = 5, so each small gap is worth 5. - Read the numbers we need from the picture. We need these numbers for the calculation.Chess = 15
Art = 20
Dance = 30 - Add them. Together means add.15 + 20 + 30 = 65
- Write the answer. 65 children
Check. Subtract one number back: 65 − 15 = 50, which is the rest. ✓
Watch out. Make sure you read the right bars.
Key words. The difference between two numbers is how much bigger one is than the other. We find it by subtracting. “How many more” and “how many fewer” questions are difference questions. A bar chart uses bars to show data. The height (or length) of a bar shows how many. The scale is the row of numbers on the side. It tells you how much each gridline is worth.
Method. Work out each total first. Then subtract the smaller total from the bigger total.
- Find the scale. The numbers up the side are the scale. Not every gridline has a number, so we must work out what each small gap is worth.The numbers go up in 10s: 0, 10, 20...
Between two numbers there are 2 gaps.
10 ÷ 2 = 5, so each small gap is worth 5. - Read the numbers we need from the picture. We need these numbers for the calculation.Football = 35
Dance = 30
Swimming = 25
Art = 20 - Add the numbers for football and dance. Together means add.35 + 30 = 65
- Add the numbers for swimming and art. Together means add.25 + 20 = 45
- Subtract. How many more means the bigger total minus the smaller total.65 − 45 = 20
Check. 45 + 20 = 65. ✓
Watch out. There are three steps here: add, add, then subtract.
Key words. A pictogram uses small pictures (symbols) to show data. The key tells you how many each symbol stands for. A half symbol stands for half of that number.
Method. Find the number for the first one, double it, then look for that number in the chart.
- Read the key. The key tells us what one symbol is worth. Here a symbol is not worth 1.1 symbol = 5 books
- Read the numbers we need from the picture. Multiply the number of symbols by what one symbol is worth.Mon = 20
- Double the number. Twice as many means two times as many.2 × 20 = 40
- Find the number 40 in the chart. Look for the row or bar with this number.Tue = 40
- Write the answer. Tue
Check. 40 ÷ 2 = 20. ✓
Watch out. Twice as many means × 2, not + 2.
Key words. A pictogram uses small pictures (symbols) to show data. The key tells you how many each symbol stands for. A half symbol stands for half of that number.
Method. Read each number from the picture, then add them all.
- Read the key. The key tells us what one symbol is worth. Here a symbol is not worth 1.1 symbol = 5 books
- Read every number. We need these numbers for the calculation.Mon = 20
Tue = 40
Wed = 25
Thu = 10
Fri = 30 - Add the numbers together. Altogether means add everything. Add one number at a time.20 + 40 + 25 + 10 + 30
20 + 40 = 60
60 + 25 = 85
85 + 10 = 95
95 + 30 = 125 - Write the answer. Total = 125 books
Check. Add in the opposite order: 30 + 10 + 25 + 40 + 20 = 125. ✓
Watch out. Do not leave out a row or a bar. Check you have used every one.
Key words. The difference between two numbers is how much bigger one is than the other. We find it by subtracting. “How many more” and “how many fewer” questions are difference questions. A pictogram uses small pictures (symbols) to show data. The key tells you how many each symbol stands for. A half symbol stands for half of that number.
Method. To find “how many more”, read both numbers and then subtract the smaller from the bigger.
- Read the key. The key tells us what one symbol is worth. Here a symbol is not worth 1.1 symbol = 5 books
- Read the numbers we need from the picture. We need these numbers for the calculation.Tue = 40
Thu = 10 - Find the difference. To find how many more (or fewer), subtract the smaller number from the bigger number.40 − 10 = 30
- Write the answer. 30 more
Check. Add back: 10 + 30 = 40. ✓
Watch out. Subtract: do not add. The question asks for the difference.
Key words. A table shows information in rows (going across) and columns (going down). A total is the answer when you add all the numbers together. A pictogram uses small pictures (symbols) to show data. The key tells you how many each symbol stands for. A half symbol stands for half of that number.
Method. Read the number from the chart. Then multiply by the price of one.
- Read the key. The key tells us what one symbol is worth. Here a symbol is not worth 1.1 symbol = 5 lunches
- Read the numbers we need from the picture. Multiply the number of symbols by what one symbol is worth.Pizza = 30
- Multiply by the price. Each one costs £2, so multiply the number sold by £2.30 × £2 = £60
- Write the answer. £60
Check. £60 ÷ 30 = £2. ✓
Watch out. Check you use the right price for the right item.
Key words. A table shows information in rows (going across) and columns (going down). A total is the answer when you add all the numbers together. A pictogram uses small pictures (symbols) to show data. The key tells you how many each symbol stands for. A half symbol stands for half of that number.
Method. Read the number from the chart. Then multiply by the price of one.
- Read the key. The key tells us what one symbol is worth. Here a symbol is not worth 1.1 symbol = 5 lunches
- Read the numbers we need from the picture. Multiply the number of symbols by what one symbol is worth.Soup = 15
- Multiply by the price. Each one costs £1, so multiply the number sold by £1.15 × £1 = £15
- Write the answer. £15
Check. £15 ÷ 15 = £1. ✓
Watch out. Check you use the right price for the right item.
Key words. A table shows information in rows (going across) and columns (going down). A total is the answer when you add all the numbers together. A pictogram uses small pictures (symbols) to show data. The key tells you how many each symbol stands for. A half symbol stands for half of that number.
Method. Read the number from the chart. Then multiply by the price of one.
- Read the key. The key tells us what one symbol is worth. Here a symbol is not worth 1.1 symbol = 5 lunches
- Read the numbers we need from the picture. Multiply the number of symbols by what one symbol is worth.Wrap = 20
- Multiply by the price. Each one costs £3, so multiply the number sold by £3.20 × £3 = £60
- Write the answer. £60
Check. £60 ÷ 20 = £3. ✓
Watch out. Check you use the right price for the right item.
Key words. A time graph (or line graph) shows how something changes over time. The points are joined by lines. The numbers along the bottom show the time. The numbers up the side show the measurement.
Method. Find how much the graph goes up each time. Then carry on the pattern.
- Find the scale. The scale up the side tells us what each gridline is worth.The numbers up the side go up in 4s.
Between two numbers there are 2 gaps.
4 ÷ 2 = 2, so each small gap is worth 2. - Read the points. We need the numbers on the graph.9am = 4, 10am = 8, 11am = 12, 12pm = 16, 1pm = 20, 2pm = 24
- Look for the pattern. Find how much the number changes each time.9am to 10am: 8 − 4 = 4
10am to 11am: 12 − 8 = 4
11am to 12pm: 16 − 12 = 4
It goes up by 4 every time. - Carry on the pattern. If the pattern continues, add the same amount again.24 + 4 = 28
Check. 28 − 4 × 1 = 24. ✓
Watch out. This is a prediction. It only works if the pattern carries on.
Key words. A time graph (or line graph) shows how something changes over time. The points are joined by lines. The numbers along the bottom show the time. The numbers up the side show the measurement.
Method. Find how much the graph goes up each time. Then carry on the pattern.
- Find the scale. The scale up the side tells us what each gridline is worth.The numbers up the side go up in 4s.
Between two numbers there are 2 gaps.
4 ÷ 2 = 2, so each small gap is worth 2. - Read the points. We need the numbers on the graph.9am = 4, 10am = 8, 11am = 12, 12pm = 16, 1pm = 20, 2pm = 24
- Look for the pattern. Find how much the number changes each time.9am to 10am: 8 − 4 = 4
10am to 11am: 12 − 8 = 4
11am to 12pm: 16 − 12 = 4
It goes up by 4 every time. - Carry on the pattern. If the pattern continues, add the same amount again.24 + 4 × 3 = 36
Check. 36 − 4 × 3 = 24. ✓
Watch out. This is a prediction. It only works if the pattern carries on.
Key words. The difference between two numbers is how much bigger one is than the other. We find it by subtracting. “How many more” and “how many fewer” questions are difference questions. A bar chart uses bars to show data. The height (or length) of a bar shows how many. The scale is the row of numbers on the side. It tells you how much each gridline is worth.
Method. Find the biggest and the smallest numbers, then subtract.
- Find the scale. The numbers up the side are the scale. Not every gridline has a number, so we must work out what each small gap is worth.The numbers go up in 20s: 0, 20, 40...
Between two numbers there are 2 gaps.
20 ÷ 2 = 10, so each small gap is worth 10. - Find the biggest and the smallest. We need these numbers for the calculation.Dev = 160
Chloe = 120 - Subtract. The difference between two numbers is the bigger minus the smaller.160 − 120 = 40
- Write the answer. 40
Check. 120 + 40 = 160. ✓
Watch out. Be sure you have found the biggest and the smallest of all the numbers.
Key words. A bar chart uses bars to show data. The height (or length) of a bar shows how many. The scale is the row of numbers on the side. It tells you how much each gridline is worth.
Method. Look at the bar carefully and read off the number for Chloe.
- Find the scale. The numbers up the side are the scale. Not every gridline has a number, so we must work out what each small gap is worth.The numbers go up in 20s: 0, 20, 40...
Between two numbers there are 2 gaps.
20 ÷ 2 = 10, so each small gap is worth 10. - Read the bar for Chloe. Find the top of the bar, then look across to the scale (follow the orange dotted line).The top of the bar for Chloe is exactly on the line for 120.
- Write the answer. Chloe = 120 cm
Check. Look again at the picture: Chloe is 120. ✓
Watch out. Work out what each gridline is worth before you read a bar. The scale does not always go up in 1s.
Key words. The difference between two numbers is how much bigger one is than the other. We find it by subtracting. “How many more” and “how many fewer” questions are difference questions. A bar chart uses bars to show data. The height (or length) of a bar shows how many. The scale is the row of numbers on the side. It tells you how much each gridline is worth.
Method. To find “how many more”, read both numbers and then subtract the smaller from the bigger.
- Find the scale. The numbers up the side are the scale. Not every gridline has a number, so we must work out what each small gap is worth.The numbers go up in 20s: 0, 20, 40...
Between two numbers there are 2 gaps.
20 ÷ 2 = 10, so each small gap is worth 10. - Read the numbers we need from the picture. We need these numbers for the calculation.Ben = 150
Amira = 130 - Find the difference. To find how many more (or fewer), subtract the smaller number from the bigger number.150 − 130 = 20
- Write the answer. 20 cm taller
Check. Add back: 130 + 20 = 150. ✓
Watch out. Subtract: do not add. The question asks for the difference.
Key words. Data is information we collect, like a list of numbers. A frequency is how many times something happens (how many there are of one kind). A chart or graph is a picture that shows data.
Method. Read every chart, write the numbers, then compare the lists.
- Read the numbers on each chart. Write the numbers for each in the same order.A: Dog 8, Cat 12, Fish 6
B: Dog 8, Cat 10, Fish 6
C: Dog 8, Cat 12, Fish 6 - Compare the lists. Two charts show the same data if all the numbers match.A and B: different
A and C: all the same
B and C: different - Write the answer. A and C
Check. Both lists are 8, 12, 6. ✓
Watch out. Read each key and scale carefully. A pictogram with a different key looks different but can show the same data.
Key words. A pictogram uses small pictures (symbols) to show data. The key tells you how many each symbol stands for. A half symbol stands for half of that number.
Method. Read the key first. Then count the symbols and multiply by the key.
- Read the key. The key tells us what one symbol is worth. Here a symbol is not worth 1.1 symbol = 2 stickers
- Count the symbols for Tuesday. Priya counted these correctly.Tuesday has 9 symbols.
- Multiply by the key. Each symbol is worth 2.9 × 2 = 18
- Find the mistake. Priya forgot to use the key. She wrote the number of symbols.She should have written 18.
Check. 18 ÷ 2 = 9 symbols. ✓
Watch out. Always multiply the symbols by the key.
Key words. A bar chart uses bars to show data. The height (or length) of a bar shows how many. The scale is the row of numbers on the side. It tells you how much each gridline is worth.
Method. Read the scale first. Then read the bar. Then compare with what Noah said.
- Find the scale. The numbers up the side are the scale. We must know what one gridline is worth.The numbers go up in 10s: 0, 10, 20, 30...
- Read the bar for Wed. Find the top of the bar, then look across to the scale (follow the orange dotted line).The top of the bar for Wed is exactly on the line for 20.
- Compare. Noah said 2. The bar shows 20.Noah is wrong. Wednesday is 20.
- Find the mistake. Noah counted the gridlines. He did not look at the numbers.Wednesday’s bar reaches the 2nd gridline, and each gridline is worth 10.
Check. 2 × 10 = 20. ✓
Watch out. The numbers on the scale tell you what each gridline is worth.
Key words. A pictogram uses small pictures (symbols) to show data. The key tells you how many each symbol stands for. A half symbol stands for half of that number.
Method. Find the numbers on the chart and check the statement. Then explain.
- Read the key. The key tells us what one symbol is worth. Here a symbol is not worth 1.1 symbol = 5 books
- Read all the days. Each symbol is 5 books.Mon 20, Tue 40, Wed 25, Thu 10, Fri 30
- Find the smallest. The smallest is 10, on Thursday.
- Decide. The statement is true.
Check. We used the numbers on the chart. ✓
Watch out. A reason should use numbers from the chart.
Key words. A pictogram uses small pictures (symbols) to show data. The key tells you how many each symbol stands for. A half symbol stands for half of that number.
Method. Find the numbers on the chart and check the statement. Then explain.
- Read the key. The key tells us what one symbol is worth. Here a symbol is not worth 1.1 symbol = 5 books
- Read Wednesday and Friday. Count the symbols and multiply by 5.Wednesday = 25, Friday = 30
- Compare. 25 < 30, so Wednesday had fewer.
- Decide. The statement is false.
Check. We used the numbers on the chart. ✓
Watch out. A reason should use numbers from the chart.
Key words. A pictogram uses small pictures (symbols) to show data. The key tells you how many each symbol stands for. A half symbol stands for half of that number.
Method. Find the numbers on the chart and check the statement. Then explain.
- Read the key. The key tells us what one symbol is worth. Here a symbol is not worth 1.1 symbol = 5 books
- Add the days. Read each day, then add.20 + 40 + 25 + 10 + 30 = 125
- Compare. 125 = 125
- Decide. The statement is true.
Check. We used the numbers on the chart. ✓
Watch out. A reason should use numbers from the chart.
Key words. A bar chart uses bars to show data. The height (or length) of a bar shows how many. The scale is the row of numbers on the side. It tells you how much each gridline is worth.
Method. Find the total for each class and compare.
- Find the scale. The numbers up the side are the scale. We must know what one gridline is worth.The numbers go up in 2s: 0, 2, 4, 6...
- Total for 4A. Add the four bars.10 + 14 + 8 + 12 = 44
- Total for 4B. Add the four bars.12 + 6 + 10 + 14 = 42
- Compare. The bigger total is the winner.44 > 42, so Class 4A earned more.
Check. The difference is 2. ✓
Watch out. Add all four bars for each class.
Key words. The difference between two numbers is how much bigger one is than the other. We find it by subtracting. “How many more” and “how many fewer” questions are difference questions.
Method. Subtract the totals.
- Find each total. Add the bars.Class 4A: 44
Class 4B: 42 - Subtract. The difference is the bigger total minus the smaller total.44 − 42 = 2
Check. 42 + 2 = 44. ✓
Watch out. Subtract: do not add.
Key words. A bar chart uses bars to show data. The height (or length) of a bar shows how many. The scale is the row of numbers on the side. It tells you how much each gridline is worth.
Method. Work out Monday and Wednesday from Tuesday, add the three days, then subtract from the total.
- Find Monday. Twice as many as Tuesday.2 × 10 = 20
- Find Wednesday. 10 more than Tuesday.10 + 10 = 20
- Add Monday, Tuesday and Wednesday. We need all the days we know.20 + 10 + 20 = 50
- Subtract from the total. Thursday is what is left.60 − 50 = 10
Check. 20 + 10 + 20 + 10 = 60. ✓
Watch out. Read each clue carefully: “twice as many” is not the same as “10 more”.
Key words. Discrete data is data you count. It jumps from one whole number to the next (you cannot have 2½ pupils). Continuous data is data you measure. It can take any value in between, like a height or a time. Continuous data changes smoothly.
Method. Think about what a time graph is for.
- What is the data? The number of children who like each fruit is counted. It is discrete data in separate groups.Fruits are separate groups: apples, bananas, and so on.
- What is a time graph for? A time graph shows how a measurement changes over time.There is no time in this data.
- Decide. No, I do not agree. A bar chart or a pictogram is better.
Check. A bar chart can compare the number of children for each fruit. ✓
Watch out. Use a time graph only when something changes over time.