Year 4: Tally charts and frequency tables
Part of the Year 4 pictograms, bar charts and time graphs chapter. Chapter overview · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)
Tally charts and frequency tables
Data is information. When we collect data we find things out. Priya wants to know which fruit is the most popular in her class. She asks every child and writes down their answer. But counting a long list is hard, so she makes a tally chart.
| Fruit | Tally | Frequency |
|---|---|---|
| Apple | 8 | |
| Banana | 13 | |
| Grapes | 6 | |
| Orange | 11 |
Each time a child chooses a fruit, Priya draws one tally mark in that row. She draws four strokes and then the fifth stroke goes across the four. That makes a group of 5. Groups of five are quick to count: 5, 10, 15, 20 … and then you add the single strokes.
When the voting is finished, Priya counts the tally marks in each row and writes the number in the Frequency column. The frequency is how many there are of one kind. A chart with the Item, Tally and Frequency columns is called a frequency table. Always check the frequencies: they must add up to the number of children asked.
Key ideas
- A tally mark is one stroke for each thing you count. The fifth stroke goes across the first four to make a group of 5.
- To count a tally: count in fives for the groups, then count on the single strokes.
- The frequency is the total number in a row. Write it as a number.
- The frequencies add up to the total number of things counted.
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.
- Count the groups of five. Each group is four strokes with one across them. That group is worth 5.2 groups: count in fives: 5, 10
2 × 5 = 10 - Count the single strokes at the end. These are not in a group of five yet.4 single strokes = 4
- Add the two amounts. The groups and the single strokes make the total.10 + 4 = 14
Check. Count the strokes one by one: you should reach 14. ✓
Watch out. A group with a line across is worth 5, not 1.
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. Draw one group of five for every five, then draw the strokes that are left.
- Split the number into groups of five. Tally marks are drawn in fives, so we find how many fives there are.18 ÷ 5 = 3 remainder 3
- Draw the groups of five. Draw four strokes, then a fifth stroke across the four.3 groups of five
- Draw the strokes that are left. These make an unfinished group. Do not draw a line across.3 single strokes
- Put it together and check. Count in fives, then count on.5, 10, 15, then 3 more: 18
Check. 15 + 3 = 18. ✓
Watch out. The fifth stroke goes across the other four. Do not draw five strokes in a row.
| Game | Tally |
|---|---|
| Skipping | |
| Football | |
| Tag | |
| Hopscotch |
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. Look at the tally carefully and read off the number for Football.
- Count in fives. Each group of 4 strokes with a line across is 5 tally marks. Count the fives first, then the single strokes.Count: 5, 10, 15, 20 ...
- Count the tally marks for Football. Groups of five first, then the strokes left over.Football: 2 groups of 5 = 10, and 4 more = 10 + 4 = 14
- Write the answer. Football = 14 children
Game Tally Skipping Football Tag Hopscotch
Check. Look again at the picture: Football is 14. ✓
Watch out. Count each crossed group as 5, not as 1. Then add the single marks.
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. Go through the list once. Make a tally mark for each item, then count the marks in each row.
- Make a table with a row for each kind. We need a place to put the tally marks for each kind.Rows: red, blue, white, silver
- Go through the list one item at a time. Make one tally mark in the right row for each item. Cross off each item as you go, so you do not count it twice.red, blue, white, red, silver
white, blue, red, white, white
silver, red, blue, white, silver
white, red, blue, white, silver - Count the tally marks in each row. Count in fives, then add the single strokes. Write each total in the Frequency column.
Colour Tally Frequency red 5 blue 4 white 7 silver 4 - Check the total. Every item in the list is in one row, so the frequencies must add up to 20.5 + 4 + 7 + 4 = 20, and the list has 20 items.
Check. The frequencies add up to 20, the same as the number of items in the list. ✓
Watch out. Cross off each item as you tally it. Then you will not miss one or count one twice.
| Game | Tally |
|---|---|
| Skipping | |
| Football | |
| Tag | |
| Hopscotch |
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. Read each number from the picture, then add them all.
- Count in fives. Each group of 4 strokes with a line across is 5 tally marks. Count the fives first, then the single strokes.Count: 5, 10, 15, 20 ...
- Read every number. We need these numbers for the calculation.Skipping = 9
Football = 14
Tag = 11
Hopscotch = 6Game Tally Skipping Football Tag Hopscotch - Add the numbers together. Altogether means add everything. Add one number at a time.9 + 14 + 11 + 6
9 + 14 = 23
23 + 11 = 34
34 + 6 = 40 - Write the answer. Total = 40 children
Check. Add in the opposite order: 6 + 11 + 14 + 9 = 40. ✓
Watch out. Do not leave out a row or a bar. Check you have used every one.
| Game | Tally |
|---|---|
| Skipping | |
| Football | |
| Tag | |
| Hopscotch |
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 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. To find “how many more”, read both numbers and then subtract the smaller from the bigger.
- Count in fives. Each group of 4 strokes with a line across is 5 tally marks. Count the fives first, then the single strokes.Count: 5, 10, 15, 20 ...
- Read the numbers we need from the picture. We need these numbers for the calculation.Football = 14
Hopscotch = 6Game Tally Skipping Football Tag Hopscotch - Find the difference. To find how many more (or fewer), subtract the smaller number from the bigger number.14 − 6 = 8
- Write the answer. 8 more
Check. Add back: 6 + 8 = 14. ✓
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.
Method. The numbers in the table must add up to the total. Add the numbers we know, then subtract from the total.
- Add the numbers we know. The missing number is the part of the total that is left.8 + 11 + 6 = 25
- Subtract from the total. Total minus the parts we know leaves the missing part.30 − 25 = 5
- Write the answer. Green = 5
Check. Add them all: 8 + 11 + 6 + 5 = 30. ✓
Watch out. Use subtraction to find a missing part. Do not add the total.
Watch out
A group of five has a line across it, and it counts as 5, not 1. Also, do not stop counting early: add the single strokes at the end. Check that your frequencies add up to the total.Exercise 11A Tally charts and frequency tables
Non-calculatorKey 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.
- Count the groups of five. Each group is four strokes with one across them. That group is worth 5.1 group: count in fives: 5
1 × 5 = 5 - Count the single strokes at the end. These are not in a group of five yet.2 single strokes = 2
- Add the two amounts. The groups and the single strokes make the total.5 + 2 = 7
Check. Count the strokes one by one: you should reach 7. ✓
Watch out. A group with a line across is worth 5, not 1.
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.
- Count the groups of five. Each group is four strokes with one across them. That group is worth 5.2 groups: count in fives: 5, 10
2 × 5 = 10 - Count the single strokes at the end. These are not in a group of five yet.2 single strokes = 2
- Add the two amounts. The groups and the single strokes make the total.10 + 2 = 12
Check. Count the strokes one by one: you should reach 12. ✓
Watch out. A group with a line across is worth 5, not 1.
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.
- 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 - Count the single strokes at the end. These are not in a group of five yet.1 single stroke = 1
- Add the two amounts. The groups and the single strokes make the total.15 + 1 = 16
Check. Count the strokes one by one: you should reach 16. ✓
Watch out. A group with a line across is worth 5, not 1.
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.
- 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 - Count the single strokes at the end. These are not in a group of five yet.3 single strokes = 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. 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. Draw one group of five for every five, then draw the strokes that are left.
- Split the number into groups of five. Tally marks are drawn in fives, so we find how many fives there are.6 ÷ 5 = 1 remainder 1
- Draw the groups of five. Draw four strokes, then a fifth stroke across the four.1 group of five
- Draw the strokes that are left. These make an unfinished group. Do not draw a line across.1 single stroke
- Put it together and check. Count in fives, then count on.5, then 1 more: 6
Check. 5 + 1 = 6. ✓
Watch out. The fifth stroke goes across the other four. Do not draw five strokes in a row.
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. Draw one group of five for every five, then draw the strokes that are left.
- Split the number into groups of five. Tally marks are drawn in fives, so we find how many fives there are.9 ÷ 5 = 1 remainder 4
- Draw the groups of five. Draw four strokes, then a fifth stroke across the four.1 group of five
- Draw the strokes that are left. These make an unfinished group. Do not draw a line across.4 single strokes
- Put it together and check. Count in fives, then count on.5, then 4 more: 9
Check. 5 + 4 = 9. ✓
Watch out. The fifth stroke goes across the other four. Do not draw five strokes in a row.
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. Draw one group of five for every five, then draw the strokes that are left.
- Split the number into groups of five. Tally marks are drawn in fives, so we find how many fives there are.15 ÷ 5 = 3
- Draw the groups of five. Draw four strokes, then a fifth stroke across the four.3 groups of five
- Put it together and check. Count in fives, then count on.5, 10, 15, 15
Check. 15 + 0 = 15. ✓
Watch out. The fifth stroke goes across the other four. Do not draw five strokes in a row.
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. Draw one group of five for every five, then draw the strokes that are left.
- Split the number into groups of five. Tally marks are drawn in fives, so we find how many fives there are.21 ÷ 5 = 4 remainder 1
- Draw the groups of five. Draw four strokes, then a fifth stroke across the four.4 groups of five
- Draw the strokes that are left. These make an unfinished group. Do not draw a line across.1 single stroke
- Put it together and check. Count in fives, then count on.5, 10, 15, 20, then 1 more: 21
Check. 20 + 1 = 21. ✓
Watch out. The fifth stroke goes across the other four. Do not draw five strokes in a row.
| Pet | Tally |
|---|---|
| Dog | |
| Cat | |
| Rabbit | |
| Fish |
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. Look at the tally carefully and read off the number for Cat.
- Count in fives. Each group of 4 strokes with a line across is 5 tally marks. Count the fives first, then the single strokes.Count: 5, 10, 15, 20 ...
- Count the tally marks for Cat. Groups of five first, then the strokes left over.Cat: 3 groups of 5 = 15
- Write the answer. Cat = 15 children
Pet Tally Dog Cat Rabbit Fish
Check. Look again at the picture: Cat is 15. ✓
Watch out. Count each crossed group as 5, not as 1. Then add the single marks.
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. Read every number, then find the smallest one.
- Count in fives. Each group of 4 strokes with a line across is 5 tally marks. Count the fives first, then the single strokes.Count: 5, 10, 15, 20 ...
- Read every number. We need these numbers for the calculation.Dog = 12
Cat = 15
Rabbit = 7
Fish = 9Pet Tally Dog Cat Rabbit Fish - Compare the numbers. Look for the smallest number.The smallest number is 7.
- Write the answer. The question asks for the name, not the number.Rabbit
Check. No other number is smaller than 7. ✓
Watch out. The question asks which one, so write the name.
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. Read each number from the picture, then add them all.
- Count in fives. Each group of 4 strokes with a line across is 5 tally marks. Count the fives first, then the single strokes.Count: 5, 10, 15, 20 ...
- Read every number. We need these numbers for the calculation.Dog = 12
Cat = 15
Rabbit = 7
Fish = 9Pet Tally Dog Cat Rabbit Fish - Add the numbers together. Altogether means add everything. Add one number at a time.12 + 15 + 7 + 9
12 + 15 = 27
27 + 7 = 34
34 + 9 = 43 - Write the answer. Total = 43 children
Check. Add in the opposite order: 9 + 7 + 15 + 12 = 43. ✓
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 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. To find “how many more”, read both numbers and then subtract the smaller from the bigger.
- Count in fives. Each group of 4 strokes with a line across is 5 tally marks. Count the fives first, then the single strokes.Count: 5, 10, 15, 20 ...
- Read the numbers we need from the picture. We need these numbers for the calculation.Dog = 12
Fish = 9Pet Tally Dog Cat Rabbit Fish - Find the difference. To find how many more (or fewer), subtract the smaller number from the bigger number.12 − 9 = 3
- Write the answer. 3 more
Check. Add back: 9 + 3 = 12. ✓
Watch out. Subtract: do not add. The question asks for the difference.
| Colour | Tally | Frequency |
|---|---|---|
| Red | ? | |
| Blue | ? | |
| Green | ? | |
| Yellow | ? |
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. Look at the tally carefully and read off the number for Red.
- Count in fives. Each group of 4 strokes with a line across is 5 tally marks. Count the fives first, then the single strokes.Count: 5, 10, 15, 20 ...
- Count the tally marks for Red. Groups of five first, then the strokes left over.Red: 1 group of 5 = 5, and 1 more = 5 + 1 = 6
- Write the answer. Red = 6 children
Colour Tally Red Blue Green Yellow
Check. Look again at the picture: Red is 6. ✓
Watch out. Count each crossed group as 5, not as 1. Then add the single marks.
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. Look at the tally carefully and read off the number for Blue.
- Count in fives. Each group of 4 strokes with a line across is 5 tally marks. Count the fives first, then the single strokes.Count: 5, 10, 15, 20 ...
- Count the tally marks for Blue. Groups of five first, then the strokes left over.Blue: 2 groups of 5 = 10
- Write the answer. Blue = 10 children
Colour Tally Red Blue Green Yellow
Check. Look again at the picture: Blue is 10. ✓
Watch out. Count each crossed group as 5, not as 1. Then add the single marks.
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. Look at the tally carefully and read off the number for Green.
- Count in fives. Each group of 4 strokes with a line across is 5 tally marks. Count the fives first, then the single strokes.Count: 5, 10, 15, 20 ...
- Count the tally marks for Green. Groups of five first, then the strokes left over.Green: 2 groups of 5 = 10, and 4 more = 10 + 4 = 14
- Write the answer. Green = 14 children
Colour Tally Red Blue Green Yellow
Check. Look again at the picture: Green is 14. ✓
Watch out. Count each crossed group as 5, not as 1. Then add the single marks.
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. Look at the tally carefully and read off the number for Yellow.
- Count in fives. Each group of 4 strokes with a line across is 5 tally marks. Count the fives first, then the single strokes.Count: 5, 10, 15, 20 ...
- Count the tally marks for Yellow. Groups of five first, then the strokes left over.Yellow: 1 group of 5 = 5, and 4 more = 5 + 4 = 9
- Write the answer. Yellow = 9 children
Colour Tally Red Blue Green Yellow
Check. Look again at the picture: Yellow is 9. ✓
Watch out. Count each crossed group as 5, not as 1. Then add the single marks.
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. Go through the list once. Make a tally mark for each item, then count the marks in each row.
- Make a table with a row for each kind. We need a place to put the tally marks for each kind.Rows: circle, square, triangle
- Go through the list one item at a time. Make one tally mark in the right row for each item. Cross off each item as you go, so you do not count it twice.circle, square, triangle, circle, circle
square, triangle, circle, square, circle
triangle, square, circle, triangle, circle - Count the tally marks in each row. Count in fives, then add the single strokes. Write each total in the Frequency column.
Shape Tally Frequency circle 7 square 4 triangle 4 - Check the total. Every item in the list is in one row, so the frequencies must add up to 15.7 + 4 + 4 = 15, and the list has 15 items.
Check. The frequencies add up to 15, the same as the number of items in the list. ✓
Watch out. Cross off each item as you tally it. Then you will not miss one or count one twice.
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. Go through the list. Look for 6 each time and count them.
- Look at the list and find every 6. We will count only these items.3, 5, 1, 6, 2, 4, 6, 3, 3, 5, 2, 6, 1, 4, 5, 6, 3, 2, 6, 4, 1, 5, 6, 3
- Count the 6s. Count each one in red. Counting in fives with tally marks helps.6
Check. Count again, slowly, from the beginning. You should find 6 again. ✓
Watch out. Do not miss one. Cross each one off as you count it.
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. Go through the list once. Make a tally mark for each item, then count the marks in each row.
- Make a table with a row for each kind. We need a place to put the tally marks for each kind.Rows: 1, 2, 3, 4, 5, 6
- Go through the list one item at a time. Make one tally mark in the right row for each item. Cross off each item as you go, so you do not count it twice.3, 5, 1, 6, 2
4, 6, 3, 3, 5
2, 6, 1, 4, 5
6, 3, 2, 6, 4
1, 5, 6, 3 - Count the tally marks in each row. Count in fives, then add the single strokes. Write each total in the Frequency column.
Number rolled Tally Frequency 1 3 2 3 3 5 4 3 5 4 6 6 - Check the total. Every item in the list is in one row, so the frequencies must add up to 24.3 + 3 + 5 + 3 + 4 + 6 = 24, and the list has 24 items.
Check. The frequencies add up to 24, the same as the number of items in the list. ✓
Watch out. Cross off each item as you tally it. Then you will not miss one or count one twice.
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. Read every number, then find the biggest one.
- Count in fives. Each group of 4 strokes with a line across is 5 tally marks. Count the fives first, then the single strokes.Count: 5, 10, 15, 20 ...
- Read every number. We need these numbers for the calculation.1 = 3
2 = 3
3 = 5
4 = 3
5 = 4
6 = 6Number rolled Tally Frequency 1 3 2 3 3 5 4 3 5 4 6 6 - Compare the numbers. Look for the biggest number.The biggest number is 6.
- Write the answer. The question asks for the name, not the number.6
Check. No other number is bigger than 6. ✓
Watch out. The question asks which one, so write the name.
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. Find each number on the picture, then add.
- Count in fives. Each group of 4 strokes with a line across is 5 tally marks. Count the fives first, then the single strokes.Count: 5, 10, 15, 20 ...
- Read the numbers we need from the picture. We need these numbers for the calculation.2 = 3
4 = 3
6 = 6Number rolled Tally Frequency 1 3 2 3 3 5 4 3 5 4 6 6 - Add them. Together means add.3 + 3 + 6 = 12
- Write the answer. 12 rolls
Check. Subtract one number back: 12 − 3 = 9, which is the rest. ✓
Watch out. Make sure you read the right rows.
| Trip | Frequency |
|---|---|
| Zoo | 14 |
| Beach | 9 |
| Museum | 12 |
| Farm | 5 |
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. Look at the tally carefully and read off the number for Museum.
- Count in fives. Each group of 4 strokes with a line across is 5 tally marks. Count the fives first, then the single strokes.Count: 5, 10, 15, 20 ...
- Count the tally marks for Museum. Groups of five first, then the strokes left over.Museum: 2 groups of 5 = 10, and 2 more = 10 + 2 = 12
- Write the answer. Museum = 12 children
Trip Tally Frequency Zoo 14 Beach 9 Museum 12 Farm 5
Check. Look again at the picture: Museum is 12. ✓
Watch out. Count each crossed group as 5, not as 1. Then add the single marks.
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. Read each number from the picture, then add them all.
- Count in fives. Each group of 4 strokes with a line across is 5 tally marks. Count the fives first, then the single strokes.Count: 5, 10, 15, 20 ...
- Read every number. We need these numbers for the calculation.Zoo = 14
Beach = 9
Museum = 12
Farm = 5Trip Tally Frequency Zoo 14 Beach 9 Museum 12 Farm 5 - Add the numbers together. Altogether means add everything. Add one number at a time.14 + 9 + 12 + 5
14 + 9 = 23
23 + 12 = 35
35 + 5 = 40 - Write the answer. Total = 40 children
Check. Add in the opposite order: 5 + 12 + 9 + 14 = 40. ✓
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 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. To find “how many more”, read both numbers and then subtract the smaller from the bigger.
- Count in fives. Each group of 4 strokes with a line across is 5 tally marks. Count the fives first, then the single strokes.Count: 5, 10, 15, 20 ...
- Read the numbers we need from the picture. We need these numbers for the calculation.Zoo = 14
Farm = 5Trip Tally Frequency Zoo 14 Beach 9 Museum 12 Farm 5 - Find the difference. To find how many more (or fewer), subtract the smaller number from the bigger number.14 − 5 = 9
- Write the answer. 9 more
Check. Add back: 5 + 9 = 14. ✓
Watch out. Subtract: do not add. The question asks for the difference.
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. Find each number on the picture, then add.
- Count in fives. Each group of 4 strokes with a line across is 5 tally marks. Count the fives first, then the single strokes.Count: 5, 10, 15, 20 ...
- Read the numbers we need from the picture. We need these numbers for the calculation.Beach = 9
Farm = 5Trip Tally Frequency Zoo 14 Beach 9 Museum 12 Farm 5 - Add them. Together means add.9 + 5 = 14
- Write the answer. 14 children
Check. Subtract one number back: 14 − 9 = 5, which is the other number. ✓
Watch out. Make sure you read the right rows.
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.
Method. The numbers in the table must add up to the total. Add the numbers we know, then subtract from the total.
- Add the numbers we know. The missing number is the part of the total that is left.17 + 12 + 9 = 38
- Subtract from the total. Total minus the parts we know leaves the missing part.50 − 38 = 12
- Write the answer. Popcorn = 12
Check. Add them all: 17 + 12 + 9 + 12 = 50. ✓
Watch out. Use subtraction to find a missing part. Do not add the total.
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.
Method. The numbers in the table must add up to the total. Add the numbers we know, then subtract from the total.
- Add the numbers we know. The missing number is the part of the total that is left.16 + 9 + 11 = 36
- Subtract from the total. Total minus the parts we know leaves the missing part.40 − 36 = 4
- Write the answer. Cycle = 4
Check. Add them all: 16 + 9 + 11 + 4 = 40. ✓
Watch out. Use subtraction to find a missing part. Do not add the total.
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. Each group of five is worth 5, not 1. Count the groups in fives, then add the single strokes.
- Count the groups of five. Each group is worth 5.3 groups: 5, 10, 15
3 × 5 = 15 - Count the single strokes. There are 2 left over.2 strokes = 2
- Add them. 15 + 2 = 17
- Find Noah’s mistake. Noah counted each group as 1.3 groups + 2 strokes: 3 + 2 = 5 (this is wrong)
Check. Count in fives: 5, 10, 15, then 16, 17. ✓
Watch out. A group of five is worth 5, not 1.
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. Think about how we count. Counting groups of five is much quicker than counting every stroke.
- Look at the way a tally is drawn. Four strokes and a fifth across them make one neat group.
- Think about counting. We can count 5, 10, 15, 20 … for the groups instead of 1, 2, 3, 4 … for every stroke.Counting in fives is quicker, and there are fewer mistakes.
- Answer. Yes, Ella is right.
Check. 20 tally marks = 4 groups = 5, 10, 15, 20. ✓
Watch out. A good tally chart makes counting quick and easy.
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.
Method. Find the total for blue and green together, then share it so that blue is 4 more.
- Find blue and green together. The total is 25 and red is 9.25 − 9 = 16
- Take away the extra 4. Blue has 4 more than green. If we take 4 off blue, the two would be equal.16 − 4 = 12
- Share the rest equally. The two equal parts are the same size.12 ÷ 2 = 6, so green = 6
- Find blue. Blue is 4 more than green.6 + 4 = 10
Check. 9 + 10 + 6 = 25 and 10 is 4 more than 6. ✓
Watch out. Check your answers add to the total.