Year 4 Pictograms, Bar Charts and Time Graphs: check-up and SATs-style questions

Key words. A tally mark is a small stroke we draw for each thing we count. Every fifth stroke goes across the other four, so each group of 5 is easy to see. The frequency is the total number of tally marks in one row.

Method. Count the groups of five first (count in 5s), then add on the single strokes.

1. Count the groups of five. Each group is four strokes with one across them. That group is worth 5.
   3 groups: count in fives: 5, 10, 15
   3 × 5 = 15
2. Count the single strokes at the end. These are not in a group of five yet.
   3 single strokes = 3
3. Add the two amounts. The groups and the single strokes make the total.
   15 + 3 = 18

Check. Count the strokes one by one: you should reach 18. ✓

Watch out. A group with a line across is worth 5, not 1.

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. Look at the picto carefully and read off the number for Mon.

1. Read the key. The key tells us what one symbol is worth. Here a symbol is not worth 1.
   1 symbol = 5 pizzas
2. Count the symbols in the row for Mon. Multiply the number of symbols by what one symbol is worth.
   Mon: 7 symbols
   7 × 5 = 35
3. Write the answer.
   Mon = 35 pizzas

Check. Count back: 35 ÷ 5 = 7 symbols. ✓

Watch out. Do not forget the key. A symbol is not always worth 1. A half symbol is worth half.

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. Divide the number by what one symbol is worth. A remainder that is half the key needs a half symbol.

1. Look at the key. One symbol stands for 10. A half symbol stands for 5.
   1 symbol = 10
2. Divide by the key. Dividing tells us how many symbols we need.
   30 ÷ 10 = 3
3. Write the answer.
   3 symbols

Check. 3 × 10 = 30. ✓

Watch out. A symbol is not always 1. Always divide 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. Look at the bar carefully and read off the number for Thu.

1. 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.
2. Read the bar for Thu. Find the top of the bar, then look across to the scale (follow the orange dotted line).
   The top of the bar for Thu is between 30 and 40.
   It is 1 small gap after 30: 30 + 5 = 35
3. Write the answer.
   Thu = 35 visitors

Check. Look again at the picture: Thu is 35. ✓

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.

1. 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.
2. Read the numbers we need from the picture. We need these numbers for the calculation.
   Tue = 40
   Wed = 15
3. Find the difference. To find how many more (or fewer), subtract the smaller number from the bigger number.
   40 − 15 = 25
4. Write the answer.
   25 more

Check. Add back: 15 + 25 = 40. ✓

Watch out. Subtract: do not add. The question asks for the difference.

Key words. In a table, a row goes across and a column goes down. A two-way table shows two things at once, for example boys and girls, and how they travel. The total of a row or column is all its numbers added together.

Method. Find the right row and the right column. The answer is the number where they meet.

1. Find the row. Look down the left-hand side for Girls.
   Row: Girls
2. Find the column. Look along the top for Milk.
   Column: Milk
3. Find where the row and column meet. The number in that box is the answer.
   Girls and Milk: 10

   Drink	Tea	Juice	Milk	Total
   Boys	6	9	8	23
   Girls	7	5	10	22
   Total	13	14	18	45

Check. Look again: row Girls, column Milk, number 10. ✓

Watch out. Make sure you use the right row and the right column.

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. Look at the graph carefully and read off the number for Day 3.

1. Find the scale. The scale up the side tells us what each gridline is worth.
   The numbers up the side go up in 2s: 0, 2, 4, 6...
2. Find Day 3 along the bottom and read the point. Go up from the time to the point on the line, then look across to the scale (follow the orange dotted lines).
   At Day 3, the point is exactly on the line for 14 cm.
3. Write the answer.
   Day 3 = 14 cm

Check. Look again at the picture: Day 3 is 14. ✓

Watch out. Read the scale up the side carefully. Check which time you are looking at along the bottom.

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. Start at 10 on the scale, go across to the line, then go down to find the time.

1. Find the scale. The scale up the side tells us what each gridline is worth.
   The numbers up the side go up in 2s: 0, 2, 4, 6...
2. Find 10 on the scale up the side. Then go across to the line.
   Look across from 10 until you reach the line.
3. Go down to the time. Look straight down from the point to the numbers along the bottom.
   The point is above Day 2.
4. Write the answer.
   Day 2

Check. At Day 2 the snow depth is 10. ✓

Watch out. Go across first, then down.

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 how we get the numbers. We count discrete data. We measure continuous data.

1. Ask: do we count it, or measure it? Counting gives whole numbers that jump. Measuring gives numbers that can be anywhere between.
   We measure weight on scales. It can be any value in between.
2. Decide. If we count it, it is discrete. If we measure it, it is continuous.
   It is continuous data.
3. Choose a graph. Different data suits different graphs.
   Continuous data is often shown on a time graph (line graph).

Check. Can there be a value in between? Yes: for example, halfway between two values. ✓

Watch out. Money is counted in pence, so it is discrete. Time, height and temperature are measured, so they are continuous.

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.

1. Is it counted or measured? Counted data is discrete. Measured data that changes over time is continuous.
   The height of a plant is measured, and it grows over time. It is continuous data.
2. What do we want to show? Compare amounts, or show how something changes?
   We want to show how the height changes over time.
3. 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 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 Rugby.

1. Find the scale. The numbers up the side are the scale. We must know what one gridline is worth.
   The numbers go up in 5s: 0, 5, 10, 15...
2. Read the bar for Rugby. Find the top of the bar, then look across to the scale (follow the orange dotted line).
   The top of the bar for Rugby is exactly on the line for 45.
3. Write the answer.
   Rugby = 45 pupils

Check. Look again at the picture: Rugby is 45. ✓

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. 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. Look at the picto carefully and read off the number for Cats.

1. Read the key. The key tells us what one symbol is worth. Here a symbol is not worth 1.
   1 symbol = 10 pets
   Half a symbol = 10 ÷ 2 = 5 pets
2. Count the symbols in the row for Cats. Multiply the number of symbols by what one symbol is worth.
   Cats: 2 whole symbols and 1 half symbol
   2 × 10 = 20
   Half symbol = 5
   20 + 5 = 25
3. Write the answer.
   Cats = 25 pets

Check. Count back: 25 ÷ 10 = 2 and a half symbols. ✓

Watch out. Do not forget the key. A symbol is not always worth 1. A half symbol is worth half.

Key words. A tally mark is a small stroke we draw for each thing we count. Every fifth stroke goes across the other four, so each group of 5 is easy to see. The frequency is the total number of tally marks in one row.

Method. Count the groups of five first (count in 5s), then add on the single strokes.

1. Count the groups of five. Each group is four strokes with one across them. That group is worth 5.
   4 groups: count in fives: 5, 10, 15, 20
   4 × 5 = 20
2. Count the single strokes at the end. These are not in a group of five yet.
   3 single strokes = 3
3. Add the two amounts. The groups and the single strokes make the total.
   20 + 3 = 23

Check. Count the strokes one by one: you should reach 23. ✓

Watch out. A group with a line across is worth 5, not 1.

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.

1. Find the scale. The numbers up the side are the scale. We must know what one gridline is worth.
   The numbers go up in 5s: 0, 5, 10, 15...
2. Read the numbers we need from the picture. We need these numbers for the calculation.
   Rugby = 45
   Hockey = 30
3. Find the difference. To find how many more (or fewer), subtract the smaller number from the bigger number.
   45 − 30 = 15
4. Write the answer.
   15 more

Check. Add back: 30 + 15 = 45. ✓

Watch out. Subtract: do not add. The question asks for the difference.

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. Divide each number by the key to find how many symbols to draw.

1. Read the key. The key tells us what one symbol is worth. Here a symbol is not worth 1.
   1 symbol = 5 sandwiches
2. Work out how many symbols each row needs. Divide each number by the key. A half symbol is used for half a key.
   Tue: 45 ÷ 5 = 9, so 9 symbols
   Wed: 20 ÷ 5 = 4, so 4 symbols
3. Draw the symbols. Draw them neatly in a line, with the same size and the same gaps.

Check. Count the symbols you drew. They should be worth 45, 20. ✓

Watch out. Use a half symbol if the number is half way between two whole symbols.

Key words. In a table, a row goes across and a column goes down. A two-way table shows two things at once, for example boys and girls, and how they travel. The total of a row or column is all its numbers added together.

Method. The numbers in a row (or column) add up to its total. Add the numbers you know, then subtract from the total.

1. Look at the row or column with the missing number. We use the row for Year 4. It has a total.

   Club	Chess	Art	Choir	Total
   Year 3	8	12	10	30
   Year 4	9	?	14	30
   Total	17	19	24	60

2. Add the numbers we know. The missing number is the part of the total that is left.
   9 + 14 = 23
3. Subtract from the total. Total minus the known parts leaves the missing part.
   30 − 23 = 7

Check. 9 + 14 + 7 = 30. ✓

Watch out. Use subtraction to find the missing number.

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 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. To find “how many more”, read both numbers and then subtract the smaller from the bigger.

1. 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.
2. Read the numbers we need from the picture. We need these numbers for the calculation.
   1pm = 20
   10am = 8
3. Find the difference. To find how many more (or fewer), subtract the smaller number from the bigger number.
   20 − 8 = 12
4. Write the answer.
   12 litres

Check. Add back: 8 + 12 = 20. ✓

Watch out. Subtract: do not add. The question asks for the difference.

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. Count the symbols for each day. Then compare.

1. Read the key. The key tells us what one symbol is worth. Here a symbol is not worth 1.
   1 symbol = 2 children
2. Count Tuesday. Count the symbols and multiply by 2.
   7 symbols: 7 × 2 = 14
3. Count Monday. Count the symbols and multiply by 2.
   5 symbols: 5 × 2 = 10
4. Compare. Is Tuesday twice Monday? Double Monday.
   2 × 10 = 20, and 14 is not 20.
5. Decide.
   Amira is wrong. Tuesday is 14, not 20.

Check. 14 ÷ 2 = 7. ✓

Watch out. Twice as many means double.

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. Draw the two missing bars, then add all five days.

1. Find the scale. The numbers up the side are the scale. We must know what one gridline is worth.
   The numbers go up in 5s: 0, 5, 10, 15...
2. Draw the bar for Tuesday. Tuesday is 35, which is on the line for 35.
   Draw the bar to 35.
3. Draw the bar for Thursday. Thursday is 30, which is on the line for 30.
   Draw the bar to 30.
4. Add the five days. Altogether means add.
   20 + 35 + 15 + 30 + 25 = 125

Check. Add in the opposite order: 25 + 30 + 15 + 35 + 20 = 125. ✓

Watch out. Draw each bar up from the 0 line.

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. 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. Read the temperatures for each part, then give the answers.

1. Find the scale. The scale up the side tells us what each gridline is worth.
   The numbers up the side go up in 2s: 0, 2, 4, 6...
2. Part (a): read 10am. Go up from 10am to the dot, then across to the scale.
   10am = 14°C
3. Part (b): the flat part. The line is flat from 10am to 11am, so the temperature stayed at 14°C.
   The temperature stayed the same.
4. Part (c): the rise. Subtract the 8am reading from the 12pm reading.
   18 − 6 = 12
5. Part (d): the data. Temperature is measured.
   It is continuous data.

Check. 6 + 12 = 18. ✓

Watch out. Read the scale carefully.