Statistics

Key words. A table puts information in rows and columns. Read across a row and down a column to find the number where they meet.

Method. Find the column and the row, then read the number where they meet.

1. Find the column heading. Look along the top row for Children.
   Column: Children
2. Find the row heading. Look down the left-hand side for Wraps.
   Row: Wraps
3. Read the number where they meet. Read across the row and down the column until they meet.
   Wraps, Children = 7
4. Write the answer. Write the number only.
   7

Check. 7 is the number in the Wraps row under Children. ✓

Watch out. Read across the row, not down the column next to it.

Key words. A table puts information in rows and columns. Read across a row and down a column to find the number where they meet.

Method. Find the column and the row, then read the number where they meet.

1. Find the column heading. Look along the top row for Children.
   Column: Children
2. Find the row heading. Look down the left-hand side for Jacket potato.
   Row: Jacket potato
3. Read the number where they meet. Read across the row and down the column until they meet.
   Jacket potato, Children = 4
4. Write the answer. Write the number only.
   4

Check. 4 is the number in the Jacket potato row under Children. ✓

Watch out. Read across the row, not down the column next to it.

Method. Read the number for each lunch, then add them together to find the class total.

1. Read the number for Pizza. Read it from the table, chart or list.
   Pizza = 9
2. Read the number for Pasta. Read it from the table, chart or list.
   Pasta = 6
3. Read the number for Jacket potato. Read it from the table, chart or list.
   Jacket potato = 4
4. Read the number for Wraps. Read it from the table, chart or list.
   Wraps = 7
5. Add the numbers together. Add every number to find the total.
   9 + 6 + 4 + 7 = 26
6. Write the answer. The total is the answer.
   26

Check. 26 − 7 = 19, which is the total of the other numbers. ✓

Watch out. Add every number, not only the first two.

Key words. A table puts information in rows and columns. Read across a row and down a column to find the number where they meet.

Method. Find the column and the row, then read the number where they meet.

1. Find the column heading. Look along the top row for Wednesday.
   Column: Wednesday
2. Find the row heading. Look down the left-hand side for Girls.
   Row: Girls
3. Read the number where they meet. Read across the row and down the column until they meet.
   Girls, Wednesday = 7
4. Write the answer. Write the number only.
   7

Check. 7 is the number in the Girls row under Wednesday. ✓

Watch out. Read across the row, not down the column next to it.

Key words. A table puts information in rows and columns. Read across a row and down a column to find the number where they meet.

Method. Find the column and the row, then read the number where they meet.

1. Find the column heading. Look along the top row for Friday.
   Column: Friday
2. Find the row heading. Look down the left-hand side for Boys.
   Row: Boys
3. Read the number where they meet. Read across the row and down the column until they meet.
   Boys, Friday = 8
4. Write the answer. Write the number only.
   8

Check. 8 is the number in the Boys row under Friday. ✓

Watch out. Read across the row, not down the column next to it.

Method. Read each number, then add them together to find the total.

1. Read the number for the boys on Tuesday. Read it from the table, chart or list.
   the boys on Tuesday = 7
2. Read the number for the girls on Tuesday. Read it from the table, chart or list.
   the girls on Tuesday = 5
3. Add the numbers together. Add every number to find the total.
   7 + 5 = 12
4. Write the answer. The total is the answer.
   12

Check. 12 − 5 = 7, which is the total of the other numbers. ✓

Watch out. Add every number, not only the first two.

Key words. A table puts information in rows and columns. Read across a row and down a column to find the number where they meet.

Method. Find the total for each day by adding the boys and girls, then choose the biggest total.

1. Add the boys and the girls on Monday. Add the two numbers in that column.
   5 + 6 = 11
2. Add the boys and the girls on Tuesday. Add the two numbers in that column.
   7 + 5 = 12
3. Add the boys and the girls on Wednesday. Add the two numbers in that column.
   4 + 7 = 11
4. Add the boys and the girls on Thursday. Add the two numbers in that column.
   6 + 4 = 10
5. Add the boys and the girls on Friday. Add the two numbers in that column.
   8 + 6 = 14
6. Find the biggest total. Friday has the biggest total, 14.
   biggest = 14
7. Write the answer. Write the day with the biggest total.
   Friday

Check. 14 is bigger than every other day total. ✓

Watch out. Add the boys and the girls first. Do not compare only the boys or only the girls.

Method. Find the total for Monday and the total for Friday, then add them together.

1. Read the number for the boys on Monday. Read it from the table, chart or list.
   the boys on Monday = 5
2. Read the number for the girls on Monday. Read it from the table, chart or list.
   the girls on Monday = 6
3. Read the number for the boys on Friday. Read it from the table, chart or list.
   the boys on Friday = 8
4. Read the number for the girls on Friday. Read it from the table, chart or list.
   the girls on Friday = 6
5. Add the numbers together. Add every number to find the total.
   5 + 6 + 8 + 6 = 25
6. Write the answer. The total is the answer.
   25

Check. 25 − 6 = 19, which is the total of the other numbers. ✓

Watch out. Add every number, not only the first two.

Key words. A table puts information in rows and columns. Read across a row and down a column to find the number where they meet.

Method. Take the number of girls away from the total for Monday. The rest are boys.

1. Write the total for Monday. The table gives the total for the whole day.
   11 children
2. Write the number of girls. The girls are part of the total.
   6 girls
3. Take the girls away from the total. What is left must be the boys.
   11 − 6 = 5
4. Write the answer. This is the number of boys on Monday.
   5

Check. 5 boys and 6 girls make 11 children. ✓

Watch out. Use the total you are given. Do not add the girls to the total.

Key words. A table puts information in rows and columns. Read across a row and down a column to find the number where they meet.

Method. Find the total number of boys and the total number of girls, then compare them.

1. Find the total number of boys. Add the boys for every day.
   5 + 7 + 4 + 6 + 8 = 30
2. Find the total number of girls. Add the girls for every day.
   6 + 5 + 7 + 4 + 6 = 28
3. Compare the two totals. 30 is more than 28, so more boys came altogether.
   30 > 28
4. Decide. Sam said more girls came, which is not true.
   No

Check. 28 + 2 = 30, so the boys had 2 more. ✓

Watch out. Add all five days for each group. Do not compare only one day.

Key words. A pictogram uses pictures to show numbers. The key tells you how many one picture stands for. A half picture is half of the key.

Method. Count the whole pictures, multiply by the key, then add any half picture.

1. Find the row for Dogs. Read along the row to see all of its pictures.
   Row: Dogs
2. Count the whole pictures and multiply by the key. Each whole picture stands for 2 children.
   5 × 2 = 10
3. Write the answer. The whole pictures make the whole number.
   10

Check. 5 × 2 = 10. ✓

Watch out. Do not stop at the number of pictures. Multiply by the key first.

Key words. A pictogram uses pictures to show numbers. The key tells you how many one picture stands for. A half picture is half of the key.

Method. Count the whole pictures, multiply by the key, then add any half picture.

1. Find the row for Cats. Read along the row to see all of its pictures.
   Row: Cats
2. Count the whole pictures and multiply by the key. Each whole picture stands for 2 children.
   3 × 2 = 6
3. Count the half picture. A half picture is half of the key, so it stands for 1.
   half picture = 1
4. Add the half picture. Add it to the whole pictures.
   6 + 1 = 7

Check. 3 × 2 + 1 = 7. ✓

Watch out. Do not stop at the number of pictures. Multiply by the key first.

Key words. A pictogram uses pictures to show numbers. The key tells you how many one picture stands for. A half picture is half of the key.

Method. Count the whole pictures, multiply by the key, then add any half picture.

1. Find the row for Hamsters. Read along the row to see all of its pictures.
   Row: Hamsters
2. Count the whole pictures and multiply by the key. Each whole picture stands for 2 children.
   2 × 2 = 4
3. Write the answer. The whole pictures make the whole number.
   4

Check. 2 × 2 = 4. ✓

Watch out. Do not stop at the number of pictures. Multiply by the key first.

Key words. A pictogram uses pictures to show numbers. The key tells you how many one picture stands for. A half picture is half of the key.

Method. Count the whole pictures, multiply by the key, then add any half picture.

1. Find the row for Fish. Read along the row to see all of its pictures.
   Row: Fish
2. Count the whole pictures and multiply by the key. Each whole picture stands for 2 children.
   1 × 2 = 2
3. Count the half picture. A half picture is half of the key, so it stands for 1.
   half picture = 1
4. Add the half picture. Add it to the whole pictures.
   2 + 1 = 3

Check. 1 × 2 + 1 = 3. ✓

Watch out. Do not stop at the number of pictures. Multiply by the key first.

Method. Work out the number for each row of the pictogram, then add them together.

1. Read the number for Dogs. Read it from the table, chart or list.
   Dogs = 10
2. Read the number for Cats. Read it from the table, chart or list.
   Cats = 7
3. Read the number for Hamsters. Read it from the table, chart or list.
   Hamsters = 4
4. Read the number for Fish. Read it from the table, chart or list.
   Fish = 3
5. Add the numbers together. Add every number to find the total.
   10 + 7 + 4 + 3 = 24
6. Write the answer. The total is the answer.
   24

Check. 24 − 3 = 21, which is the total of the other numbers. ✓

Watch out. Add every number, not only the first two.

Key words. A pictogram uses pictures to show numbers. The key tells you how many one picture stands for. A half picture is half of the key.

Method. Count the whole pictures, multiply by the key, then add any half picture.

1. Find the row for Thursday. Read along the row to see all of its pictures.
   Row: Thursday
2. Count the whole pictures and multiply by the key. Each whole picture stands for 5 books.
   6 × 5 = 30
3. Write the answer. The whole pictures make the whole number.
   30

Check. 6 × 5 = 30. ✓

Watch out. Do not stop at the number of pictures. Multiply by the key first.

Key words. A pictogram uses pictures to show numbers. The key tells you how many one picture stands for. A half picture is half of the key.

Method. Count the whole pictures, multiply by the key, then add any half picture.

1. Find the row for Monday. Read along the row to see all of its pictures.
   Row: Monday
2. Count the whole pictures and multiply by the key. Each whole picture stands for 5 books.
   3 × 5 = 15
3. Write the answer. The whole pictures make the whole number.
   15

Check. 3 × 5 = 15. ✓

Watch out. Do not stop at the number of pictures. Multiply by the key first.

Key words. A pictogram uses pictures to show numbers. The key tells you how many one picture stands for. A half picture is half of the key.

Method. Count the whole pictures, multiply by the key, then add any half picture.

1. Find the row for Class 3C. Read along the row to see all of its pictures.
   Row: Class 3C
2. Count the whole pictures and multiply by the key. Each whole picture stands for 2 children.
   7 × 2 = 14
3. Count the half picture. A half picture is half of the key, so it stands for 1.
   half picture = 1
4. Add the half picture. Add it to the whole pictures.
   14 + 1 = 15

Check. 7 × 2 + 1 = 15. ✓

Watch out. Do not stop at the number of pictures. Multiply by the key first.

Key words. A pictogram uses pictures to show numbers. The key tells you how many one picture stands for. A half picture is half of the key.

Method. Count the whole pictures, multiply by the key, then add any half picture.

1. Find the row for Class 3D. Read along the row to see all of its pictures.
   Row: Class 3D
2. Count the whole pictures and multiply by the key. Each whole picture stands for 2 children.
   2 × 2 = 4
3. Count the half picture. A half picture is half of the key, so it stands for 1.
   half picture = 1
4. Add the half picture. Add it to the whole pictures.
   4 + 1 = 5

Check. 2 × 2 + 1 = 5. ✓

Watch out. Do not stop at the number of pictures. Multiply by the key first.

Key words. A pictogram uses pictures to show numbers. The key tells you how many one picture stands for. A half picture is half of the key.

Method. Read every number, then find the most one.

1. Read the number for Monday. Read it from the chart.
   Monday = 15
2. Read the number for Tuesday. Read it from the chart.
   Tuesday = 20
3. Read the number for Wednesday. Read it from the chart.
   Wednesday = 5
4. Read the number for Thursday. Read it from the chart.
   Thursday = 30
5. Read the number for Friday. Read it from the chart.
   Friday = 10
6. Find the biggest number. The most is the biggest number.
   biggest = 30
7. Write the answer. Write the name with the number.
   Thursday

Check. 30 is bigger than all the other numbers. ✓

Watch out. Read every bar or picture row before you choose. Check the key first.

Key words. A pictogram uses pictures to show numbers. The key tells you how many one picture stands for. A half picture is half of the key.

Method. Count the pictures in the Wednesday row, then multiply by the key. Compare the answer with what Tom said.

1. Count the pictures in the Wednesday row. There is one picture in the row.
   1 picture
2. Multiply by the key. Each picture stands for 5 books.
   1 × 5 = 5
3. Compare with what Tom said. Tom said 10 books, but the row shows 5 books.
   5 is not 10
4. Decide. So Tom is not right.
   No

Check. Two pictures would be 10 books, but there is only one picture, so 5 books. ✓

Watch out. Count the pictures in the row, then use the key. Do not use the number of pictures on another row.

Key words. In a scaled bar chart, one square stands for more than one unit. The key tells you how many one square stands for.

Method. Count the squares up to the top of the bar, then multiply by the scale.

1. Find the bar for Eagles. Find the label under the bar.
   Bar: Eagles
2. Count the squares up to the top of the bar. Each square stands for 2 goals.
   4 squares
3. Multiply the squares by the scale. Each square is worth 2, so multiply the squares by 2.
   4 × 2 = 8
4. Write the answer. This is the number of goals.
   8

Check. 4 squares of 2 make 8. ✓

Watch out. Count the squares, then multiply. Do not write the number of squares as the answer.

Key words. In a scaled bar chart, one square stands for more than one unit. The key tells you how many one square stands for.

Method. Count the squares up to the top of the bar, then multiply by the scale.

1. Find the bar for Owls. Find the label under the bar.
   Bar: Owls
2. Count the squares up to the top of the bar. Each square stands for 2 goals.
   3 squares
3. Multiply the squares by the scale. Each square is worth 2, so multiply the squares by 2.
   3 × 2 = 6
4. Write the answer. This is the number of goals.
   6

Check. 3 squares of 2 make 6. ✓

Watch out. Count the squares, then multiply. Do not write the number of squares as the answer.

Key words. In a scaled bar chart, one square stands for more than one unit. The key tells you how many one square stands for.

Method. Count the squares up to the top of the bar, then multiply by the scale.

1. Find the bar for Falcons. Find the label under the bar.
   Bar: Falcons
2. Count the squares up to the top of the bar. Each square stands for 2 goals.
   5 squares
3. Multiply the squares by the scale. Each square is worth 2, so multiply the squares by 2.
   5 × 2 = 10
4. Write the answer. This is the number of goals.
   10

Check. 5 squares of 2 make 10. ✓

Watch out. Count the squares, then multiply. Do not write the number of squares as the answer.

Key words. In a scaled bar chart, one square stands for more than one unit. The key tells you how many one square stands for.

Method. Count the squares up to the top of the bar, then multiply by the scale.

1. Find the bar for Class 3A. Find the label under the bar.
   Bar: Class 3A
2. Count the squares up to the top of the bar. Each square stands for 5 bottles.
   5 squares
3. Multiply the squares by the scale. Each square is worth 5, so multiply the squares by 5.
   5 × 5 = 25
4. Write the answer. This is the number of bottles.
   25

Check. 5 squares of 5 make 25. ✓

Watch out. Count the squares, then multiply. Do not write the number of squares as the answer.

Key words. In a scaled bar chart, one square stands for more than one unit. The key tells you how many one square stands for.

Method. Count the squares up to the top of the bar, then multiply by the scale.

1. Find the bar for Class 3D. Find the label under the bar.
   Bar: Class 3D
2. Count the squares up to the top of the bar. Each square stands for 5 bottles.
   6 squares
3. Multiply the squares by the scale. Each square is worth 5, so multiply the squares by 5.
   6 × 5 = 30
4. Write the answer. This is the number of bottles.
   30

Check. 6 squares of 5 make 30. ✓

Watch out. Count the squares, then multiply. Do not write the number of squares as the answer.

Key words. In a scaled bar chart, one square stands for more than one unit. The key tells you how many one square stands for.

Method. Count the squares up to the top of the bar, then multiply by the scale.

1. Find the bar for Bea. Find the label under the bar.
   Bar: Bea
2. Count the squares up to the top of the bar. Each square stands for 2 books.
   8 squares
3. Multiply the squares by the scale. Each square is worth 2, so multiply the squares by 2.
   8 × 2 = 16
4. Write the answer. This is the number of books.
   16

Check. 8 squares of 2 make 16. ✓

Watch out. Count the squares, then multiply. Do not write the number of squares as the answer.

Key words. In a scaled bar chart, one square stands for more than one unit. The key tells you how many one square stands for.

Method. Count the squares up to the top of the bar, then multiply by the scale.

1. Find the bar for Eva. Find the label under the bar.
   Bar: Eva
2. Count the squares up to the top of the bar. Each square stands for 2 books.
   2 squares
3. Multiply the squares by the scale. Each square is worth 2, so multiply the squares by 2.
   2 × 2 = 4
4. Write the answer. This is the number of books.
   4

Check. 2 squares of 2 make 4. ✓

Watch out. Count the squares, then multiply. Do not write the number of squares as the answer.

Key words. In a scaled bar chart, one square stands for more than one unit. The key tells you how many one square stands for.

Method. Read every number, then find the fewest one.

1. Read the number for Ali. Read it from the chart.
   Ali = 12
2. Read the number for Bea. Read it from the chart.
   Bea = 16
3. Read the number for Cal. Read it from the chart.
   Cal = 6
4. Read the number for Dev. Read it from the chart.
   Dev = 10
5. Read the number for Eva. Read it from the chart.
   Eva = 4
6. Find the smallest number. The fewest is the smallest number.
   smallest = 4
7. Write the answer. Write the name with the number.
   Eva

Check. 4 is smaller than all the other numbers. ✓

Watch out. Read every bar or picture row before you choose. Check the key first.

Key words. In a scaled bar chart, one square stands for more than one unit. The key tells you how many one square stands for.

Method. Count the squares up to the top of the bar, then multiply by the scale.

1. Find the bar for Team B. Find the label under the bar.
   Bar: Team B
2. Count the squares up to the top of the bar. Each square stands for 5 points.
   4 squares
3. Multiply the squares by the scale. Each square is worth 5, so multiply the squares by 5.
   4 × 5 = 20
4. Write the answer. This is the number of points.
   20

Check. 4 squares of 5 make 20. ✓

Watch out. Count the squares, then multiply. Do not write the number of squares as the answer.

Key words. In a scaled bar chart, one square stands for more than one unit. The key tells you how many one square stands for.

Method. Read every number, then find the most one.

1. Read the number for Team A. Read it from the chart.
   Team A = 35
2. Read the number for Team B. Read it from the chart.
   Team B = 20
3. Read the number for Team C. Read it from the chart.
   Team C = 45
4. Find the biggest number. The most is the biggest number.
   biggest = 45
5. Write the answer. Write the name with the number.
   Team C

Check. 45 is bigger than all the other numbers. ✓

Watch out. Read every bar or picture row before you choose. Check the key first.

Key words. In a scaled bar chart, one square stands for more than one unit. The key tells you how many one square stands for.

Method. Count the squares on the Team C bar, then multiply by the key. Compare the answer with what Ali said.

1. Count the squares on the Team C bar. Count the squares up to the top of the bar.
   9 squares
2. Multiply the squares by the key. Each square stands for 5 points.
   9 × 5 = 45
3. Compare with what Ali said. Ali said Team C scored 45 points.
   45 = 45
4. Decide. The bar shows 45 points, so Ali is right.
   Yes

Check. 9 squares of 5 points make 45 points. ✓

Watch out. Count the squares, then multiply by the key. The bar is not the same as the number of squares.

Key words. A tally counts in groups of five. Four upright marks and one line across them make a group of five.

Method. Count the groups of five, then count the single marks and add them.

1. Look at the tally marks for Blue. There are no full groups of five.
   4 marks altogether
2. Count the marks. Count each single mark.
   4 marks
3. Write the answer. The answer is the number of marks.
   4

Check. Counting the marks one at a time also gives 4. ✓

Watch out. A group of five has four upright marks and one line across them. Count each group as five.

Key words. A tally counts in groups of five. Four upright marks and one line across them make a group of five.

Method. Count the groups of five, then count the single marks and add them.

1. Look at the tally marks for Red. Count the groups of five first.
   1 group of five and 2 single marks
2. Count the marks in the groups. Each group of five has five marks.
   1 × 5 = 5
3. Add the single marks. Add the marks that are not in a group.
   5 + 2 = 7
4. Write the answer. The answer is the total number of marks.
   7

Check. Counting the marks one at a time also gives 7. ✓

Watch out. A group of five has four upright marks and one line across them. Count each group as five.

Method. Count the votes for each colour, then add them together.

1. Read the number for Red. Read it from the table, chart or list.
   Red = 7
2. Read the number for Blue. Read it from the table, chart or list.
   Blue = 4
3. Read the number for Yellow. Read it from the table, chart or list.
   Yellow = 6
4. Read the number for Green. Read it from the table, chart or list.
   Green = 3
5. Add the numbers together. Add every number to find the total.
   7 + 4 + 6 + 3 = 20
6. Write the answer. The total is the answer.
   20

Check. 20 − 3 = 17, which is the total of the other numbers. ✓

Watch out. Add every number, not only the first two.

Key words. Data is information that we collect and count, such as the number of children who chose each pet.

Method. Go through the list and count each apple.

1. Read the list. Each word is one child.
   20 words in the list
2. Count the words that say apple. Go through the list and count each one.
   apple = 7
3. Write the answer. The answer is the number of times the word appears.
   7

Check. The other 13 words are not apple, and 7 + 13 = 20. ✓

Watch out. Count every word, even when the same word is in the list many times.

Key words. Data is information that we collect and count, such as the number of children who chose each pet.

Method. Go through the list and count each banana.

1. Read the list. Each word is one child.
   20 words in the list
2. Count the words that say banana. Go through the list and count each one.
   banana = 6
3. Write the answer. The answer is the number of times the word appears.
   6

Check. The other 14 words are not banana, and 6 + 14 = 20. ✓

Watch out. Count every word, even when the same word is in the list many times.

Key words. Data is information that we collect and count, such as the number of children who chose each pet.

Method. Go through the list and count each pear.

1. Read the list. Each word is one child.
   20 words in the list
2. Count the words that say pear. Go through the list and count each one.
   pear = 4
3. Write the answer. The answer is the number of times the word appears.
   4

Check. The other 16 words are not pear, and 4 + 16 = 20. ✓

Watch out. Count every word, even when the same word is in the list many times.

Key words. A pictogram uses pictures to show numbers. The key tells you how many one picture stands for. A half picture is half of the key.

Method. Divide the total by what one picture stands for.

1. Write the total. We need to show 14 children.
   14 children
2. Divide by how many one picture stands for. One picture stands for 2 children.
   14 ÷ 2 = 7
3. Write the number of pictures. 7 whole pictures.
   7

Check. 7 × 2 = 14. ✓

Watch out. Divide, do not multiply. A bigger number of children needs more pictures.

Key words. In a scaled bar chart, one square stands for more than one unit. The key tells you how many one square stands for.

Method. Divide the total by what one square stands for.

1. Write the total. We need to show 25 books.
   25 books
2. Divide by how many one square stands for. One square stands for 5 books.
   25 ÷ 5 = 5
3. Write the number of squares. 5 whole squares.
   5

Check. 5 × 5 = 25. ✓

Watch out. Divide, do not multiply. A bigger number of books needs more squares.

Key words. In a scaled bar chart, one square stands for more than one unit. The key tells you how many one square stands for.

Method. Divide the total by what one square stands for.

1. Write the total. We need to show 24 goals.
   24 goals
2. Divide by how many one square stands for. One square stands for 2 goals.
   24 ÷ 2 = 12
3. Write the number of squares. 12 whole squares.
   12

Check. 12 × 2 = 24. ✓

Watch out. Divide, do not multiply. A bigger number of goals needs more squares.

Key words. A pictogram uses pictures to show numbers. The key tells you how many one picture stands for. A half picture is half of the key.

Method. Divide the total by what one picture stands for.

1. Write the total. We need to show 15 children.
   15 children
2. Divide by how many one picture stands for. One picture stands for 2 children.
   15 ÷ 2 = 7 remainder 1
3. Write the number of pictures. 7 whole pictures and one half.
   7 and a half

Check. 7 × 2 + 1 = 15. ✓

Watch out. Divide, do not multiply. A bigger number of children needs more pictures.

Key words. In a scaled bar chart, one square stands for more than one unit. The key tells you how many one square stands for.

Method. Divide 9 by 2 to find the number of whole squares, then look at what is left over.

1. Divide 9 by 2. Divide the total by the scale.
   9 ÷ 2 = 4 remainder 1
2. Look at the remainder. A remainder of 1 means half a square is left over. Whole squares cannot show it exactly.
   1 left over = half a square
3. Decide. So a bar for 9 goals cannot be drawn exactly with whole squares. Ali is not right.
   No

Check. 4 × 2 = 8, and 8 + 1 = 9, so one half square is needed. ✓

Watch out. Check the remainder. An odd number needs a half square when the scale is 2.

Key words. How many more and how many fewer both ask for the difference between two numbers. Subtract the smaller number from the bigger number.

Method. Find both numbers, then subtract the smaller from the bigger to find how many more.

1. Find the number for Dogs. The number for Dogs is 10 children.
   Dogs = 10
2. Find the number for Hamsters. The number for Hamsters is 4 children.
   Hamsters = 4
3. Subtract the smaller number from the bigger number. 10 is more than 4, so take 4 away from 10.
   10 − 4 = 6
4. Write the answer. The difference is 6 children.
   6

Check. 4 + 6 = 10. ✓

Watch out. Subtract the smaller number from the bigger one, not the other way round.

Key words. How many more and how many fewer both ask for the difference between two numbers. Subtract the smaller number from the bigger number.

Method. Find both numbers, then subtract the smaller from the bigger to find how many fewer.

1. Find the number for Cats. The number for Cats is 7 children.
   Cats = 7
2. Find the number for Fish. The number for Fish is 3 children.
   Fish = 3
3. Subtract the smaller number from the bigger number. 7 is more than 3, so take 3 away from 7.
   7 − 3 = 4
4. Write the answer. The difference is 4 children.
   4

Check. 3 + 4 = 7. ✓

Watch out. Subtract the smaller number from the bigger one, not the other way round.

Key words. How many more and how many fewer both ask for the difference between two numbers. Subtract the smaller number from the bigger number.

Method. Find both numbers, then subtract the smaller from the bigger to find how many fewer.

1. Find the number for Friday. The number for Friday is 10 books.
   Friday = 10
2. Find the number for Wednesday. The number for Wednesday is 5 books.
   Wednesday = 5
3. Subtract the smaller number from the bigger number. 10 is more than 5, so take 5 away from 10.
   10 − 5 = 5
4. Write the answer. The difference is 5 books.
   5

Check. 5 + 5 = 10. ✓

Watch out. Subtract the smaller number from the bigger one, not the other way round.

Key words. How many more and how many fewer both ask for the difference between two numbers. Subtract the smaller number from the bigger number.

Method. Find both numbers, then subtract the smaller from the bigger to find how many more.

1. Find the number for Pizza. The number for Pizza is 9 children.
   Pizza = 9
2. Find the number for Wraps. The number for Wraps is 7 children.
   Wraps = 7
3. Subtract the smaller number from the bigger number. 9 is more than 7, so take 7 away from 9.
   9 − 7 = 2
4. Write the answer. The difference is 2 children.
   2

Check. 7 + 2 = 9. ✓

Watch out. Subtract the smaller number from the bigger one, not the other way round.

Key words. How many more and how many fewer both ask for the difference between two numbers. Subtract the smaller number from the bigger number.

Method. Find both numbers, then subtract the smaller from the bigger to find how many fewer.

1. Find the number for Pizza. The number for Pizza is 9 children.
   Pizza = 9
2. Find the number for Jacket potato. The number for Jacket potato is 4 children.
   Jacket potato = 4
3. Subtract the smaller number from the bigger number. 9 is more than 4, so take 4 away from 9.
   9 − 4 = 5
4. Write the answer. The difference is 5 children.
   5

Check. 4 + 5 = 9. ✓

Watch out. Subtract the smaller number from the bigger one, not the other way round.

Key words. How many more and how many fewer both ask for the difference between two numbers. Subtract the smaller number from the bigger number.

Method. Find both numbers, then subtract the smaller from the bigger to find how many more.

1. Find the number for the boys on Friday. The number for the boys on Friday is 8 children.
   the boys on Friday = 8
2. Find the number for the girls on Friday. The number for the girls on Friday is 6 children.
   the girls on Friday = 6
3. Subtract the smaller number from the bigger number. 8 is more than 6, so take 6 away from 8.
   8 − 6 = 2
4. Write the answer. The difference is 2 children.
   2

Check. 6 + 2 = 8. ✓

Watch out. Subtract the smaller number from the bigger one, not the other way round.

Key words. How many more and how many fewer both ask for the difference between two numbers. Subtract the smaller number from the bigger number.

Method. Find both numbers, then subtract the smaller from the bigger to find how many more.

1. Find the number for Bea. The number for Bea is 16 books.
   Bea = 16
2. Find the number for Ali. The number for Ali is 12 books.
   Ali = 12
3. Subtract the smaller number from the bigger number. 16 is more than 12, so take 12 away from 16.
   16 − 12 = 4
4. Write the answer. The difference is 4 books.
   4

Check. 12 + 4 = 16. ✓

Watch out. Subtract the smaller number from the bigger one, not the other way round.

Key words. How many more and how many fewer both ask for the difference between two numbers. Subtract the smaller number from the bigger number.

Method. Find both numbers, then subtract the smaller from the bigger to find how many more.

1. Find the number for Class 3B. The number for Class 3B is 40 bottles.
   Class 3B = 40
2. Find the number for Class 3C. The number for Class 3C is 15 bottles.
   Class 3C = 15
3. Subtract the smaller number from the bigger number. 40 is more than 15, so take 15 away from 40.
   40 − 15 = 25
4. Write the answer. The difference is 25 bottles.
   25

Check. 15 + 25 = 40. ✓

Watch out. Subtract the smaller number from the bigger one, not the other way round.

Key words. How many more and how many fewer both ask for the difference between two numbers. Subtract the smaller number from the bigger number.

Method. Find both numbers, then subtract the smaller from the bigger to find how many more.

1. Find the number for Class 3C. The number for Class 3C is 15 children.
   Class 3C = 15
2. Find the number for Class 3D. The number for Class 3D is 5 children.
   Class 3D = 5
3. Subtract the smaller number from the bigger number. 15 is more than 5, so take 5 away from 15.
   15 − 5 = 10
4. Write the answer. The difference is 10 children.
   10

Check. 5 + 10 = 15. ✓

Watch out. Subtract the smaller number from the bigger one, not the other way round.

Key words. How many more and how many fewer both ask for the difference between two numbers. Subtract the smaller number from the bigger number.

Method. Find both numbers, then subtract the smaller from the bigger to find how many fewer.

1. Find the number for Eagles. The number for Eagles is 8 goals.
   Eagles = 8
2. Find the number for Owls. The number for Owls is 6 goals.
   Owls = 6
3. Subtract the smaller number from the bigger number. 8 is more than 6, so take 6 away from 8.
   8 − 6 = 2
4. Write the answer. The difference is 2 goals.
   2

Check. 6 + 2 = 8. ✓

Watch out. Subtract the smaller number from the bigger one, not the other way round.

Key words. How many more and how many fewer both ask for the difference between two numbers. Subtract the smaller number from the bigger number.

Method. Find both numbers, then subtract the smaller from the bigger to find how many more.

1. Find the number for Thursday. The number for Thursday is 30 books.
   Thursday = 30
2. Find the number for Tuesday. The number for Tuesday is 20 books.
   Tuesday = 20
3. Subtract the smaller number from the bigger number. 30 is more than 20, so take 20 away from 30.
   30 − 20 = 10
4. Write the answer. The difference is 10 books.
   10

Check. 20 + 10 = 30. ✓

Watch out. Subtract the smaller number from the bigger one, not the other way round.

Key words. A two-step question needs two calculations. Use the answer from the first step in the second step.

Method. Find the total for Monday and Tuesday, then compare it with the total for Friday.

1. Add the totals for Monday and Tuesday. Each day total is the boys and girls added together.
   11 + 12 = 23
2. Read the total for Friday. Use the total for Friday from the table.
   Friday = 14
3. Compare the two numbers. 23 is more than 14, so the statement is not right.
   23 > 14
4. Decide. Mia is not right. Monday and Tuesday together had more children than Friday.
   No

Check. 14 is less than 23, so the answer is No. ✓

Watch out. Use the day totals from the table. Do not compare the boys with the girls.

Key words. A table puts information in rows and columns. Read across a row and down a column to find the number where they meet.

Method. Find the column and the row, then read the number where they meet.

1. Find the column heading. Look along the top row for Tickets.
   Column: Tickets
2. Find the row heading. Look down the left-hand side for Class 3B.
   Row: Class 3B
3. Read the number where they meet. Read across the row and down the column until they meet.
   Class 3B, Tickets = 23
4. Write the answer. Write the number only.
   23

Check. 23 is the number in the Class 3B row under Tickets. ✓

Watch out. Read across the row, not down the column next to it.

Key words. A pictogram uses pictures to show numbers. The key tells you how many one picture stands for. A half picture is half of the key.

Method. Count the whole pictures, multiply by the key, then add any half picture.

1. Find the row for Tuesday. Read along the row to see all of its pictures.
   Row: Tuesday
2. Count the whole pictures and multiply by the key. Each whole picture stands for 5 stickers.
   5 × 5 = 25
3. Write the answer. The whole pictures make the whole number.
   25

Check. 5 × 5 = 25. ✓

Watch out. Do not stop at the number of pictures. Multiply by the key first.

Key words. In a scaled bar chart, one square stands for more than one unit. The key tells you how many one square stands for.

Method. Count the squares up to the top of the bar, then multiply by the scale.

1. Find the bar for Wednesday. Find the label under the bar.
   Bar: Wednesday
2. Count the squares up to the top of the bar. Each square stands for 2 cups.
   8 squares
3. Multiply the squares by the scale. Each square is worth 2, so multiply the squares by 2.
   8 × 2 = 16
4. Write the answer. This is the number of cups.
   16

Check. 8 squares of 2 make 16. ✓

Watch out. Count the squares, then multiply. Do not write the number of squares as the answer.

Method. Read the number of tickets for each class, then add them together.

1. Read the number for Class 3A. Read it from the table, chart or list.
   Class 3A = 18
2. Read the number for Class 3B. Read it from the table, chart or list.
   Class 3B = 23
3. Read the number for Class 3C. Read it from the table, chart or list.
   Class 3C = 9
4. Add the numbers together. Add every number to find the total.
   18 + 23 + 9 = 50
5. Write the answer. The total is the answer.
   50

Check. 50 − 9 = 41, which is the total of the other numbers. ✓

Watch out. Add every number, not only the first two.

Key words. How many more and how many fewer both ask for the difference between two numbers. Subtract the smaller number from the bigger number.

Method. Find both numbers, then subtract the smaller from the bigger to find how many more.

1. Find the number for Tuesday. The number for Tuesday is 25 stickers.
   Tuesday = 25
2. Find the number for Wednesday. The number for Wednesday is 5 stickers.
   Wednesday = 5
3. Subtract the smaller number from the bigger number. 25 is more than 5, so take 5 away from 25.
   25 − 5 = 20
4. Write the answer. The difference is 20 stickers.
   20

Check. 5 + 20 = 25. ✓

Watch out. Subtract the smaller number from the bigger one, not the other way round.

Key words. How many more and how many fewer both ask for the difference between two numbers. Subtract the smaller number from the bigger number.

Method. Find both numbers, then subtract the smaller from the bigger to find how many fewer.

1. Find the number for Monday. The number for Monday is 12 cups.
   Monday = 12
2. Find the number for Thursday. The number for Thursday is 6 cups.
   Thursday = 6
3. Subtract the smaller number from the bigger number. 12 is more than 6, so take 6 away from 12.
   12 − 6 = 6
4. Write the answer. The difference is 6 cups.
   6

Check. 6 + 6 = 12. ✓

Watch out. Subtract the smaller number from the bigger one, not the other way round.

Method. Read the number for Monday and for Friday, then add them together.

1. Read the number for Monday. Read it from the table, chart or list.
   Monday = 10
2. Read the number for Friday. Read it from the table, chart or list.
   Friday = 20
3. Add the numbers together. Add every number to find the total.
   10 + 20 = 30
4. Write the answer. The total is the answer.
   30

Check. 30 − 20 = 10, which is the total of the other numbers. ✓

Watch out. Add every number, not only the first two.

Key words. A pictogram uses pictures to show numbers. The key tells you how many one picture stands for. A half picture is half of the key.

Method. Divide the total by what one picture stands for.

1. Write the total. We need to show 35 stickers.
   35 stickers
2. Divide by how many one picture stands for. One picture stands for 5 stickers.
   35 ÷ 5 = 7
3. Write the number of pictures. 7 whole pictures.
   7

Check. 7 × 5 = 35. ✓

Watch out. Divide, do not multiply. A bigger number of stickers needs more pictures.

Key words. A two-step question needs two calculations. Use the answer from the first step in the second step.

Method. Do the first step, then use its answer in the second step.

1. Step 1: read the number for Class 3B. Read it from the chart or table.
   Class 3B = 23
2. Step 1: read the number for Class 3C. Read it from the chart or table.
   Class 3C = 9
3. Step 1: add the numbers together. This is the total for Class 3B and Class 3C.
   23 + 9 = 32
4. Step 2: read the number for Class 3A. This is the number to compare with.
   Class 3A = 18
5. Step 2: subtract the smaller number from the bigger number. The total of 32 is more than 18, so take 18 away from 32.
   32 − 18 = 14
6. Write the answer. Both answers are needed: 32 tickets altogether, and 14 tickets more.
   14

Check. 18 + 14 = 32. ✓

Watch out. Check that both steps are done. Many answers stop after the first step.

Key words. In a scaled bar chart, one square stands for more than one unit. The key tells you how many one square stands for.

Method. Count the squares on the Tuesday bar, then multiply by the scale.

1. Count the squares on the Tuesday bar. Count the squares up to the top of the bar.
   4 squares
2. Multiply the squares by the scale. Each square stands for 2 cups.
   4 × 2 = 8
3. Compare with what Ali said. Ali said 8 cups, which is the same.
   8 = 8
4. Decide. So Ali is right.
   Yes

Check. 4 squares of 2 cups make 8 cups. ✓

Watch out. Count the squares, then multiply by the scale.

Key words. A pictogram uses pictures to show numbers. The key tells you how many one picture stands for. A half picture is half of the key.

Method. Read every number, then find the fewest one.

1. Read the number for Dogs. Read it from the chart.
   Dogs = 10
2. Read the number for Cats. Read it from the chart.
   Cats = 7
3. Read the number for Hamsters. Read it from the chart.
   Hamsters = 4
4. Read the number for Fish. Read it from the chart.
   Fish = 3
5. Find the smallest number. The fewest is the smallest number.
   smallest = 3
6. Write the answer. Write the name with the number.
   Fish

Check. 3 is smaller than all the other numbers. ✓

Watch out. Read every bar or picture row before you choose. Check the key first.

Key words. In a scaled bar chart, one square stands for more than one unit. The key tells you how many one square stands for.

Method. Divide the total by what one square stands for.

1. Write the total. We need to show 10 goals.
   10 goals
2. Divide by how many one square stands for. One square stands for 2 goals.
   10 ÷ 2 = 5
3. Write the number of squares. 5 whole squares.
   5

Check. 5 × 2 = 10. ✓

Watch out. Divide, do not multiply. A bigger number of goals needs more squares.

Key words. A table puts information in rows and columns. Read across a row and down a column to find the number where they meet.

Method. Find the total for each day, then add the five totals together.

1. Add the boys and the girls on Monday. Add the two numbers in that column.
   5 + 6 = 11
2. Add the boys and the girls on Tuesday. Add the two numbers in that column.
   7 + 5 = 12
3. Add the boys and the girls on Wednesday. Add the two numbers in that column.
   4 + 7 = 11
4. Add the boys and the girls on Thursday. Add the two numbers in that column.
   6 + 4 = 10
5. Add the boys and the girls on Friday. Add the two numbers in that column.
   8 + 6 = 14
6. Add the five day totals. Add the totals for each day.
   11 + 12 + 11 + 10 + 14 = 58
7. Write the answer. This is the number of children altogether.
   58

Check. The Friday total is 14, and the other days add to 44. ✓

Watch out. Add all five days. Do not add only the boys or only the girls.

Key words. A pictogram uses pictures to show numbers. The key tells you how many one picture stands for. A half picture is half of the key.

Method. Divide the total by what one picture stands for.

1. Write the total. We need to show 45 books.
   45 books
2. Divide by how many one picture stands for. One picture stands for 5 books.
   45 ÷ 5 = 9
3. Write the number of pictures. 9 whole pictures.
   9

Check. 9 × 5 = 45. ✓

Watch out. Divide, do not multiply. A bigger number of books needs more pictures.

Key words. In a scaled bar chart, one square stands for more than one unit. The key tells you how many one square stands for.

Method. Take 15 away from the bottles for Class 3B, then find the class with that number.

1. Read the number for Class 3B. Read it from the bar chart.
   Class 3B = 40
2. Take 15 away. We want 15 fewer than Class 3B.
   40 − 15 = 25
3. Find the class with that number. Look for the bar that reaches the same number.
   25 bottles = Class 3A
4. Write the answer. Write the name of the class.
   Class 3A

Check. Class 3A has 25 bottles, and 25 + 15 = 40. ✓

Watch out. Check the bar for each class, not only the tallest bar.

Key words. How many more and how many fewer both ask for the difference between two numbers. Subtract the smaller number from the bigger number.

Method. Find both numbers, then subtract the smaller from the bigger to find how many more.

1. Find the number for Class 3B. The number for Class 3B is 8 children.
   Class 3B = 8
2. Find the number for Class 3D. The number for Class 3D is 5 children.
   Class 3D = 5
3. Subtract the smaller number from the bigger number. 8 is more than 5, so take 5 away from 8.
   8 − 5 = 3
4. Write the answer. The difference is 3 children.
   3

Check. 5 + 3 = 8. ✓

Watch out. Subtract the smaller number from the bigger one, not the other way round.

Key words. A table puts information in rows and columns. Read across a row and down a column to find the number where they meet.

Method. Find the total for the class and half of it, then compare the number for Pizza with half.

1. Find the total for the class. Add all the lunches.
   9 + 6 + 4 + 7 = 26
2. Find half of the class. Halve the total.
   26 ÷ 2 = 13
3. Read the number for Pizza. Pizza is in the lunch table.
   Pizza = 9
4. Compare. 9 is less than 13, so fewer than half chose Pizza.
   9 < 13
5. Decide. So Ruby is not right.
   No

Check. 9 + 17 = 26. ✓

Watch out. Half is the total divided by 2. Compare the Pizza number with half of the class, not with the total.

Key words. A tally counts in groups of five. Four upright marks and one line across them make a group of five.

Method. Count the votes for each colour, then add them together. Compare the total with what Tom said.

1. Read the votes for each colour. Count the tally marks for each colour.
   Red 7, Blue 4, Yellow 6, Green 3
2. Add the votes together. This is the total number of children who voted.
   7 + 4 + 6 + 3 = 20
3. Compare with what Tom said. Tom said 22, but the total is 20.
   20 is not 22
4. Decide. So Tom is not right.
   No