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Introduction
The Maths and Me Pupil’s Book consolidates learning by bringing the Primary Maths Curriculum (2023) to life through engaging, playful and interactive activities. It links maths to daily life through real-life pictures, problems and tasks, so children will appreciate the relevance and significance of maths in their everyday experiences.
The relatable Maths and Me characters, Lexi, Dara, Mia, Jay and Monty the Dog help children to understand that we are all mathematicians, and model a positive disposition to maths.
Pupil’s Book Features
Colour coding – Pages are colour-coded so you can see what the main strand is at a glance:
Number
Measures
Shape and space
Let’s talk! Let’s play!
Let’s investigate!
Maths eyes
Try this!
1
Data and chance
Algebra
Let’s play! – Incorporates playfulness into maths through engaging games and interactive activities, making maths a fun and enjoyable adventure for children.
Let’s talk! – Provides opportunities for children to share their strategies and ideas, helping them to reflect on their current knowledge and identify emerging concepts.
Let’s investigate! – Encourages children to develop creative strategies through active participation and exploration.
Maths eyes – Encourages children to look around them and recognise maths in the real world.
Try this! – Provides optional, cognitively challenging tasks that offer an enriching learning opportunity for children.
Self-assessment – Gives children an opportunity to reflect on their work and colour in up to three stars at the end of each page, depending on how they felt they performed on a certain task.
Additional resource icons – Indicates if a photocopiable is needed to complete an activity.
Digital resources – Allows easy access for teachers using the ebook to the extensive menu of interactive resources provided for each unit.
Clear signposting – Allows easy navigation across the programme through direct correlation of the Lesson Title and the footer information to the Teacher’s Planning Book and the digital resources.
Orange Blue Purple Green Red
PCM
Let’s talk!
Count in hundreds out loud from:
● 0 to 700
● 1,000 to 400.
What numbers did you say both times?
Write each amount as a number and/or in words.
What number do we say after nine hundred when counting in hundreds?
D Let’s talk!
Discuss as a class or in groups. Are these always, sometimes or never true? When counting in hundreds…
● the hundreds column changes
● the tens column changes
● all of the numbers will be even
● all of the numbers will be three-digit numbers.
Try this! 100 pegs can fit on this pegboard.
How many pegboards like this are needed for…
1. 400 pegs?
2. 700 pegs?
3. 1,000 pegs?
Let’s play!
Number of players: 2–6
Four Spins to 1,000
You will need: 0–9 spinner, place value counters
● Each player, in turn, spins the spinner and decides whether to collect that number of ones, tens or hudreds.
● For example, if you spin a 5, you can decide to collect 5 ones or 5 tens or 5 hundreds.
● Continue until each player has spun four times.
● The player with an amount closest to (above or below) 1,000 wins the game.
Representing Numbers
Let’s talk!
In pairs, discuss the amounts shown, make them using place value arrow cards, then write them using
Write each of these as a number using digits.
1. nine hundred and seventy
2. six hundred and seventy seven
3. five hundred and seven
4. eight hundred and seventeen
Write each of these as a number using digits.
Try this! Splat! Juice has been spilled on the page!
The numbers (not in order) are:
● four hundred and sixty
● six hundred and four
● four hundred and sixteen
● two hundred and ninety-six.
Write the number for each row using digits.
These are in word form.
These are in expanded form. Written as a number, 00 + 10 + 1 would be 11.
Place Value
Let’s talk!
In pairs, discuss the amounts shown and write each amount using a .
Let’s talk!
Make a three-digit number using place value arrow cards. Ask your partner:
● What digit is in the ones/hundreds/tens place?
Point at each digit in turn, and ask:
● How much is here?
Now repeat, but point at two digits this time.
Write the value of the underlined digit(s) in each number.
D In each group, write the number In each group, write the number in which 2 has the highest value. in which 8 has the lowest value.
267 592
Try this! The children were asked to sketch 316. Which pictures show 316? (3)
Representing Numbers on the Number Line
Are all the number lines going up by the same amount? How might we work it out?
Write each number marked by an arrow on the number line.
Write a reasonable estimate for each number marked by an arrow on the number line.
Answer these.
If you make a number line from… which number cannot be placed on it?
1. 0 to 1,000 200, 550, 700, 1,200, 890
2. 800 to 900 810, 908, 850, 802, 865, 881
3. 350 to 400 360, 390, 300, 375, 360, 399
D On your mini-whiteboard, use the open number line with markings to model and prove your answers to .
Comparing and Ordering Numbers
Look at sets A and B, and answer these.
1. Which number is greater, A or B?
2. If we move from A to B, which number will be greater?
Write <, > or = to make these true.
Write
Use place value arrow cards or materials to help you.
D Write the numbers in order from…
1. least to greatest: 196, 84, 302 2. greatest to least: 317, 731, 713
What number could go on each to make these true?
1. 923 is greater than 2.
Try this! Use
4.
Estimating and Rounding Numbers
Write the ten that is before and after these numbers. Draw an arrow from each number to its position on the number line. Ring the nearest ten.
Use the open number line on your mini-whiteboard to model these.
Write the hundred that is before and after these numbers. Draw an arrow from each number to its position on the number line. Ring the nearest hundred.
If the number is in the middle, we usually round to the larger option.
Answer these.
1. Round the numbers in the first table to the nearest ten and nearest hundred.
2. What do you notice about the numbers in Table 1? Can you suggest four other numbers like this? Write them in Table 2 and round them.
Number Nearest 10 Nearest 100
(a) 297
(b) 404
(c) 696
(d) 801
Number Nearest 10 Nearest 100
(e) 297
(f) 404
(g) 696
(h) 801
D Look at the number line and answer the questions.
xy z
1. Which of the numbers should be placed at x, y and z?
2. To what hundred should each of the numbers at x, y and z be rounded? x: y: z:
Let’s talk!
Look at the distances marked on the map. Do you agree with Jay? Explain why.
Estimate: the distance from Cork to Derry is…
● almost 400km?
● more than 400km?
● almost 500km?
● more than 500km?
When rounded to the nearest hundred, all these places are about 200km from Dublin.
Try this! Mystery numbers! For each clue, write the greatest and least number possible.
1. Lexi’s number, rounded to the nearest hundred, is 500.
2. Mia uses 7 place value counters to make a number. The number, rounded to the nearest hundred, is 400.
3. Dara’s number, rounded to the nearest ten, is 830. The number contains the digit 2.
Number Hunts
Maths eyes Car park number hunt
1. Choose a car. Write the reg. plate number:
2. What digit is in…
(a) the tens place?
(b) the hundreds place?
(c) the ones place?
3. Use three of the digits each time to make…
(a) the largest number possible
(b) the smallest number possible
4. Using the two numbers you made in question 3, find the… (a) (b) number before number after nearest 10 nearest 100
Choose a different car.
1. Write the reg. plate number:
2. Use the digits to make…
(a) four 3-digit numbers
(b) four 2-digit numbers
3. Order your numbers from the least to the greatest. < < < < < < <
Find and write the reg. plate number of the…
1. newest car in the car park
2. oldest car in the car park
Try this! What are the missing numbers on these reg. plates?
1. This number has three tens, two more ones than tens and four more hundreds than ones.
2. This number is the greatest possible odd number that rounded to the nearest ten is 920.
3 the right angles.
Not a right angle Right angle
Maths eyes
Find three right angles in the space around you.
Does it have an angle? 3 or 7. Ring the one that is a right angle.
D Answer these.
1. Is it less than (<) or greater than (>) a right angle? Write < or > for each.
2. In your copy, draw… (a) a right angle (b) an angle that is less than a right angle (c) an angle that is greater than a right angle.
3. Name a shape with no right angles.
Let’s talk!
Which of the mountain bikers is likely to go the fastest? Why do you think this?
Vertical, Horizontal and Perpendicular Lines
Maths eyes
Give two examples of something that has...
1. horizontal lines
2. vertical lines
Let’s talk!
Look at the soccer players. Why is one player horizontal?
Answer these.
1. Who is correct, Jay or Lexi?
The bookshelf is horizontal, but the books are vertical.
Any two lines that meet are perpendicular lines.
2. Which ones below are perpendicular lines? 3 or 7 (a) (b) (c) (d)
3. Find any perpendicular lines in your classroom.
D Does it have perpendicular lines? 3 or 7.
Try this!
What time might it be if the hands on the clock are perpendicular?
I think there are many possible answers to this.
Only lines that meet at a right angle are perpendicular lines.
Directions and Turns
Look at the picture and write the answers.
1. Write N, S, E or W.
(a) The ship is of the sailboat.
(b) The whale is of the plane.
(c) The submarine is of the helicopter.
(d) The lighthouse is of the whale.
2. What is N of the plane?
3. What is S of the helicopter?
4. What is E of the lighthouse?
5. What is W of the plane?
What will the arm of the crane be pointing to if it makes each turn below?
1. Half turn clockwise:
2. Full turn anti-clockwise:
3. Quarter turn clockwise:
4. Half turn to the left:
5. Quarter turn anti-clockwise:
6. Three quarter turn to the right:
Try this!
1. Look at the image. How many rotations (turns) does the frisbee make before Monty catches it? 3
2. Rotate this disc clockwise, 1 4 turn at a time.
3. How many right angles in a full turn?
Bricks
Lorry
Cement Timber
Grids
Write the missing grid letters and numbers in the grid. You could use your activity sheet (PCM 1).
Let’s talk!
Ask your partner.
Can you think of any board games that use a grid?
Look at the grid and answer these.
1. What colour is…
(a) A1? (b) B2?
(c) C3? (d) A4?
(e) B5? (f) C6?
2. Colour…
(a) D1 red (b) E2 purple
(c) F3 red (d) D4 green
(e) E5 yellow (f) F6 green.
D Look at the grid and write the length of each road. A = km B = km C = km D = km
Look at the grid.
1. How far did the bus travel? km
2. How long is the train line? km
Look at the treasure map and answer these.
1. Write the missing grid letters and numbers.
(a) The lighthouse is at A .
(b) The treasure (X) is at 1.
(c) The mine is at
(d) The ship is at .
(e) The haunted house is at
(f) The castle is at .
2. Place a counter at C3 and another at E4
Look at this map of train stations in a city.
1. station is West of Gallery.
2. station is East of Airport.
3. Name two stations South of Castle.
4. What direction will you travel from Zoo to Forest?
5. What direction will you travel from The Park to the Airport?
6. What directions will you travel from Forest to Gallery?
7. Add a station (make up a name) east of The Park.
8. (a) New is in A (b) Forest is in
9. Which station is in (a) E4 ? (b) A6 ?
Line Symmetry
Which shows a line of symmetry in each shape, A, B or C?
These are lines of symmetry.
Which image in each pair correctly shows a line of symmetry, A or B?
Let’s talk!
How many lines of symmetry can you find in each shape? Are they vertical or horizontal? (a) (b) (c) (d) (e)
D Let’s talk!
What do you notice about each picture?
Owl Fern leaf Custom’s House, Dublin
Can you name three other animals whose faces have a line of symmetry?
Do all leaves have a line of symmetry?
Would this building have a line of symmetry if there was no water?
Look at the shapes below and answer the questions.
1. Which shape does not have a line of symmetry?
2. Write how many lines of symmetry you can find in each other shape.
Use line symmetry to complete each design.
Try this!
1. Which capital letters have a line of symmetry? (Hint: There are 16!)
2. Find two letters that have both a vertical and a horizontal line of symmetry.
Transformations
What move? Write translate (slide), rotate (turn) or reflect (flip).
1. 2.
Let’s talk!
1. For the images in that were rotated, describe the rotation using the language right-angled turn(s) and clockwise / anti-clockwise.
2. For the images in that were reflected, were they reflected horizontally or vertically?
Answer these.
1. Rotate each shape in a clockwise direction around the thumbtack. Colour in. (a) 1 4 turn (b) 3 4 turn (c) 1 1 2 turns
2. Reflect each shape in the mirror (the line of symmetry). Colour in.
D Let’s talk!
To reach the purple square, the red circle translates (slides) 4 squares north.
How does the red circle reach the…
1. green square?
2. orange square?
3. blue square?
4. grey square? (Hint: two directions)
Rotational Symmetry
Look at the shapes and answer these. Mia wants to place each shape below in its space in the sand. 3 the ones that have rotational symmetry. 1. 2. 3. 4.5.
Let’s talk!
Which shapes below have rotational symmetry?
In your copy, draw a shape with… 1. rotational symmetry 2. no rotational symmetry.
Try this!
N O R Z E H I X S P J
Hint: rotate your book to see what letters look the same.
Which of these capital letters have rotational symmetry?
D These propellors need one more blade to have rotational symmetry. Add the missing blade to each propellor. 1. 2. 3. 4.
Adding and Subtracting Ones
Write the matching number sentence for each of these.
Let’s talk!
Take turns to estimate the answers for below as hundreds and something. Explain how you know.
This will be four hundred and twenty-something.
Write or draw the answers for these.
D Let’s talk!
Which answers in above were easier to calculate? Explain why. Check your answers. How did you do it?
Build it! Sketch it! Write it!
Using materials or in your copy, show three different ways to solve this: 352 + 9
Try this! Lexi added or subtracted ones counters to get the answer shown.
1. What might the calculation have been?
2. Can you find all the possible calculations?
Adding and Subtracting Tens
Write the matching number sentence for each of these.
Let’s talk!
Take turns to estimate the answers for below as hundreds and something. Explain how you know.
Write or draw the answers for these.
D Let’s talk!
Which answers in were easier to calculate? Explain why. Check your answers. How did you do it?
Build it! Sketch it! Write it!
Using materials or in your copy, show three different ways to solve this: 483 + 90
Explain how you did them.
Adding and Subtracting Hundreds
Look at each bar model. Complete the matching number sentence.
Let’s talk!
Take turns to estimate the answers for and D below as hundreds and something.
This will be six hundred and something.
Write or draw the answers for these.
D Write or draw the answers for these.
Try this!
1. A school raised €536. It was then given a donation of €400. How much has the school raised now?
2. A games console bundle costs €449. If the console is worth €300, what is the value of the rest of the bundle?
Adding and Subtracting without Renaming
Write the matching number sentence and solve each of these.
Let’s talk!
Take turns to estimate the answers for below as hundreds and something.
I have collected 546 cards. I have collected 233 more cards than Dara. I have collected 115 less cards than Dara.
Write two questions based on the story. Swap with a partner to solve. Then, check the answers.
Adding with Renaming
Let’s talk!
Take turns to estimate the answers for and below as hundreds and something. Explain how you know.
Write the matching number sentence and solve each of these without using the column method.
Use the column method to solve these.
Let’s talk!
Check your answers for above.
How did you do it?
Solve these.
1. If there are 159 boys and 173 girls in a school, what is the number of children in the school altogether?
2. Kayla has €286, Abbie has €349 and Mark has €453. How much money do they have altogether?
Try this!
1. Without solving the calculations, match each one to a suitable label.
(a) 736 + 196 A. No renaming
(b) 194 + 362 B. Renaming ones only
(c) 530 + 429 C. Renaming tens only
(d) 207 + 678 D. Renaming ones and tens
2. Write one more calculation to match to each label on the lines above.
Let’s play!
Number of players: 2–6
Chance Calculations Addition
You will need: mini-whiteboard and marker per player, 0–9 spinner, pencil and paper clip
● Each player should draw these boxes for a calculation on their mini-whiteboard.
● Each player, in turn, spins the 0–9 spinner and writes the digit in one of their empty boxes.
● When all the boxes are full, each player calculates their answer.
● The player with the greatest total (answer) scores a point.
● The player with the highest score when the time is up wins the game.
Variations
1. The player with the smallest total (answer) wins.
2. The player with the total (answer) closest to 800 wins.
3. Instead of spinning for one digit at a time, spin for all four digits and decide where to write them in the calculation boxes.
Let’s talk!
Subtracting with Renaming
Take turns to estimate the answers for and below as hundreds and something. Explain how you know.
Use the number line to help you find the difference for each.
482 – 346 =
Model and solve these without using the column method.
D Use the column method to solve these.
Let’s talk!
Check your answers for D above.
How did you do it?
Try this! Find the missing numbers and write a number story for each one.
Let’s play!
Number of players: 2–6
Chance Calculations Subtraction
You will need: mini-whiteboard and marker per player, 0–9 spinner, pencil and paper clip
● Each player should draw these boxes for a calculation on their mini-whiteboard.
● Each player, in turn, spins the 0–9 spinner six times and writes the digits in their empty boxes.
● When all the boxes are full, each player calculates their answer.
● The player with the greatest difference (answer) scores a point.
● The player with the highest score when the time is up wins the game
Variations
1. The player with the smallest difference (answer) wins.
2. The player with the difference (answer) closest to 500 wins.
Let’s talk!
Subtracting with Zeros
Look at the boxes below. The children are using different ways to subtract from a number with zeros. Do they work? Explain why. Can you think of any other ways? Which way(s) do you prefer?
Model and solve
Try this!
1. Mia has read 125 pages out of a total of 300. How many pages has she left to read?
2. Jay had €400 in his savings. He took out €209 to buy a bicycle. How much has he left? €
3. 500 collector cards can fit in a full album. After Lexi and Dara put in their cards, there were 284 spaces left.
(a) How many cards did they put in altogether?
(b) Suggest a possible number for how many cards Lexi and Dara had each.
Lexi: Dara:
Unit 3: Addition and Subtraction. Days and 10, Lesson x
4. A school’s fundraising target is €1,000. If they have already raised €833, how much more until they reach their target? €
Number of players: 2–6
Target 500
You will need: mini-whiteboard and marker per player, 0–9 spinner, pencil and paper clip
● Each player, in turn, spins the spinner twice, rearranges the digits spun to make the largest possible two-digit number, and records it on their mini-whiteboard. For example, if a player spins 5 and 6, they write down 65.
● On their next turn, each player adds the new two-digit number they have made to their previous two-digit number, as a running total on their mini-whiteboard. For example, if a player spins 2 and 8, they add 82 to 65.
● The first player to reach or pass 500 wins the game.
1. Aim for a higher target (e.g. 900).
Variations
2. Start with 500 (or 900), and subtract the two-digit number from this each time.
3. The first player to reach or pass 100 wins the game.
What’s the difference?
Number of players: 2–6
You will need: mini-whiteboard and marker per player, 0–9 spinner, pencil and paper clip
● Each player, in turn, spins the spinner four times and records the numbers spun. The highest number represents hundreds, and the player rearranges the other three numbers to make a three-digit number to be subtracted.
● For example, if a player spins 7, 6, 5 and 3, the 7 would become 700, and the other three numbers could become 653, 356 or 563, etc. This player then subtracts their three-digit number from 700 to calculate the difference (answer).
● The player who has the smallest difference (answer) wins the game.
Let’s talk!
Look at the block graph below. What do you think the title might be? Ask your partner some questions about the data in the graph.
Use these words in your questions: How many…? more than… fewer than most least in total
I think that a group of children were asked how they travelled to school that day.
What do you think? Explain why
I think that there might be some mistakes, some of these are not full blocks.
Complete the tally chart.
A group of children were asked their favourite kind of yoghurt. If the survey found that blueberry was the third most popular flavour, then how many people voted for blueberry?
Look at the pictogram and answer the questions below.
Title: Key:
Amount of books read in September
1. If Dara read 10 books, how many books did Lexi read?
2. How many books altogether did the children read in September?
D Look at the pictogram and fill in the blanks.
Title: Key: beech
oak hazel ash
Types of trees on the school grounds = books = 10 trees
1. There are half as many trees as trees.
2. There are 5 trees.
Try this!
A group of people were asked their favourite colour. These were their choices: blue, green, red, purple, yellow, blue, blue, green, red, green, blue, purple, red, purple, red, blue, yellow, green, purple, red, yellow, red, blue, red, blue
Organise this information and represent it in a chart.
Dara
Jay
Lexi Mia
Line Plots
Look at the line plot and answer the questions below.
A class did a survey to find out how many letters there were in the first name of each child in the class.
Number of letters in our names 6789 10 3 4 5
1. What was the mode?
2. How many children had names with less than 5 letters?
3. How many children had names with more than 5 letters?
Let’s talk!
Do you agree with Jay? Why or why not?
Use these words if you can:
The mode is the value that occurs the most.
I think that the most common length of name in every class would be 5 letters.
likely unlikely certain possible impossible
Look at the line plot and answer the questions.
1. What was the mode?
2. How many people had less than 2 pets?
3. How many people had more than 2 pets?
4. How many people were surveyed?
Try this! These were the test scores of the children in a class: 10, 8, 9, 6, 7, 10, 8, 9, 4, 5, 10, 8, 9, 2, 10, 6, 7, 8, 9, 8, 9, 10, 9
1. Draw a line plot to show the data above.
2. Write three questions about your line plot.
Bar Graphs
Look at the bar graph and answer the questions below.
Title: Favourite kind of fruit juice mango orange apple
1. Which juice was the most popular?
2. How many children chose apple juice?
3. How many more children chose orange juice than mango juice?
4. If there were 24 children in the class, how many did not vote?
Look at the bar graph and answer the questions below.
Title: Number of bottles collected
1. Which two classes collected 80 bottles each? Class and Class
2. Which class collected 42 bottles? Class
3. Estimate how many bottles 6th Class collected.
Try this!
1. Draw a bar graph to show the data in this tally chart.
2. Write three questions about your graph.
When making a bar graph, what must be included?
Let’s Look Back 1
1. What number comes next? 350, 550, 750,
2. I am facing north. I make a quarter turn anti-clockwise. What direction am I facing now?
3. Ring the number in which 4 has the least value: 643 874 499
4. 3 the flag without line symmetry.
5. How many marbles altogether in these jars?
6. Ring the correct answer: 612 – 90 = 702 603 522
7. Write a tally for the pets in the class: cat, dog, dog, bird, hamster, fish, cat, cat, dog, fish, fish, hamster, bird, cat, dog, dog, fish, bird, cat, dog, dog.
Dog: Cat: Fish: Hamster: Bird: 234 381
1. What number is represented here?
2. Ring the letter with perpendicular lines: V R H W
3. 453 – = 180 4. How many in this tally?
300 453 180
5. What is the place value of 4 in 947?
6. 3 the next picture in this pattern.
7. 865 – 230 =
8. If = 10, how many cakes does this represent?
1.
2. Round this number to the nearest ten: 404
3. Write <, > or = to make this true.
What should I take away from this number to make 253? This angle a right angle.
4. There are 254 pages in one book, 86 in another and 152 in a third book. How many pages altogether?
5. How many books if = 5?
6. Write a capital letter that has a horizontal line.
7. Write this number in digits: six hundred and nine.
Try this!
1. (a) What is the grid reference of the house?
(b) What is the grid reference of the tree?
(c) If there was a pond 2 squares north and 1 square west of the tree, what would its grid reference be?
Title: Ice creams sold today banana caramel cherry vanilla lemon mint
(a) How many more vanilla than mint ice creams were sold?
(b) How many ice creams were sold altogether?
(c) Twice as many as ice creams were sold.
2. A B C 40 30 20 10 0
I think there might be more than one correct answer for (c).
3. 3 the one that shows what the first shape will look like when rotated clockwise through 2 right angles.
A Trip to the Shopping Centre
The children have taken a trip to the shopping centre. Look at the image and answer the questions below.
1. Match these. Mia is facing the escalators. Mia will be facing… …if she turns the furniture shop 1 right angle to the left the coffee shop table 2 right angles anti-clockwise the information stand 3 right angles to the left
2. Find three examples of right angles. (a) (b) (c)
3. The pillars are… (3) horizontal vertical
4. Find an example of line symmetry.
5. Find an example of rotational symmetry.
6. The person moving on the escalator is an example of… (3) sliding rotating reflecting
7. The motion of the fan is an example of… (3) translating (sliding) rotating reflecting
8. The person seen in the mirror is an example of (3) translating rotating reflecting
9. (a) The person in the Sushi Bar is facing... (3) north south east west (b) Lexi is facing… (3) north south east west
Answer these.
1. The children bought these items in the toy shop. What number does each of these represent? Then, complete the table.
(a) (b) (c) (d)
Number Nearest 10 Nearest 100
(a) crayons
(b) paper stars
(c) pom-poms
(d) beads
2. Order the numbers above from the least to the greatest.
3. Who bought more items: Mia and Dara or Jay and Lexi?
4. What is the difference between their amounts?
Let’s investigate!
Class shopping centre survey
What are the favorite shopping centres of the people in our class? Use the PPDAC cycle and your activity sheet (PCM 2) to carry out the survey.
D Bar graph
1. Below are the numbers of cones sold at the ice cream stand each day for a week. In your copy, draw a bar graph to show this data. Monday 10; Tuesday 12; Wednesday 14; Thursday 18; Friday 20; Saturday 24; Sunday 22
2. On which day were…
(a) the most cones sold?
(b) the fewest cones sold?
Remember to include a title and labels.
Multiples of 2, 10 and 5
Multiples are numbers that go up in jumps of a given number.
What is missing?
Count in multiples to work out the value of the money in each.
Let’s talk!
Discuss as a class or in groups: Are these always, sometimes or never true?
● Multiples of 2 are even numbers.
● Multiples of 5 are odd numbers.
● Multiples of 5 end in a 5.
● Multiples of 2 are also multiples of 10.
Try this!
Can you find an example to prove or disprove each one?
The library will be open from Monday to Saturday every week in November. Mia plans to go on all the dates that are multiples of 2, Dara plans to go on all the dates that are multiples of 5, and Lexi plans to go on all the dates that are multiples of 10.
1. Who will go to the library…
(a) the most?
(b) the least?
2. On what dates will all three of them go to the library?
Multiplication as Repeated Addition
Let’s talk!
Describe the images below in different ways.
The first one could be 10 + 10 + 10, or three groups of 10, or 3 times 10, or 3 tens. For , the first one will be: 3 × 10 = 30
Write and solve the matching multiplication sentence for each of the images in above.
Write the symbol for greater than (>), less than (<) or equals (=) to make these true.
Try this! Look at the images. Use Build it! Sketch it! Write it! to model these.
1. Mia has 80 crayons. How many packs is that?
2. Dara has 35 pens. How many packs is that?
3. Lexi has 4 packs of crayons and 3 packs of pens. How many items altogether?
4. Jay has 45 crayons and pens in total. What packs might he have?
Arrays
Maths eyes
Arrays are items arranged in rows and columns.
Write the matching multiplication sentence for each array.
Model these and write the matching number sentences.
1. 9 rows of cars with 10 in each row
2. 8 rows of children with 2 in each row
3. 6 rows of pictures with 5 in each row
4. 7 rows of counters with 2 in each row
5. 9 rows of playing cards with 5 in each row
Let’s play!
Number of players: 2
Capture the Area
You will need: 1 sheet of squared paper, a marker/ pencil/crayon of a different colour per player, 0–9 spinner, 2/5/10 spinner, pencil and paper clip
● Each player, in turn, spins the two spinners, and then draws a rectangle according to the numbers spun, and writes the total number of square units inside it. For example, if a player spins a 2 and a 9, they draw a rectangle that is 9 squares by 2 squares and write 18 inside it.
● If there is not enough space on the paper for a player to draw their rectangle, the player misses a turn.
● Play continues until time is up or there is no more space left on the paper.
2 0 1 8 3 6 72 9 4 5 5 10
● The player with the greatest number of square units overall wins the game.
Try this! Headline story! 30 playing cards were arranged as an array.
What maths questions could you ask?
How could you model and solve the questions?
Strategies for Multiplying by 2, 10 and 5
Use doubling to solve these.
1. 2 × 3 = double =
2. 2 × 8 = double =
3. 2 × 4 = double =
4. 2 × 9 = double =
5. 2 × 6 = double =
6. 2 × 7 = double =
Move the digits to solve these.
1. 10 × 8 =
2. 10 × 3 =
3. 10 × 9 =
4. 10 × 4 =
5. 10 × 1 =
6. 10 × 6 =
Use ‘half the 10 times’ to solve these.
1. 10 × 8 = , so 5 × 8 =
2. 10 × 4 = , so 5 × 4 =
3. 10 × 10 = , so 5 × 10 =
4. 10 × 6 = , so 5 × 6 =
5. 10 × 2 = , so 5 × 2 =
6. 10 × 5 = , so 5 × 5 =
D Solve these.
To multiply by 5, get half of 10 times the number. 2 × 5 =
When multiplying by 2, think doubling.
Try this! Use models or strategies to solve these. 1. 2 × 15 = 2.
=
×
= 3
To multiply by 10, move the digits one place to the left.
= 5. 10 × 16 = 6. 5 × 20 = 7.
× 19 =
Division as Sharing Equally
Build it! Sketch it! Write it! Use materials and sketches to represent these. Write the matching division sentence for each. Share these equally among…
Model and solve these.
Let’s talk!
Think of a story to match some of the number sentences in .
Try this! Use models and division sentences to help you solve these.
1. 20 scones were divided evenly into 5 bags. How many scones were there in each bag?
2. There were 18 girls and 12 boys in a class. The teacher divided them all into 10 equal groups. How many were there in each group?
Division as Repeated Subtraction
Build it! Sketch it! Write it! Use materials and sketches to represent these. Write the matching division sentence for each.
For how many days will the apples last, if 2 are eaten every day?
If 5 yoghurts are eaten every day, for how many days will they last?
If Mia puts 10 stars on every card she makes, how many cards is that?
How many pairs of socks can be made from these?
How many sticks of 10 can be made from 80 cubes?
Drawing bar models
For how many weeks will this bottle last, if 5 washes are done every week?
This bar model represents question 1 in above. Draw bar models to match two other questions in
Let’s talk!
Make up new repeated subtraction stories for each bar model that you drew in .
Try this! Dara got €30 for his birthday.
1. If he spends €5 every week, for how many weeks will the money last?
2. If he spends €10 every week, for how many weeks will the money last?
Multiplication and Division as Inverse
Write a matching multiplication and division sentence for each of these.
Write a matching multiplication and division sentence for each of these bar models.
Are these correct? 3 or 7.
What strategies did you use to check the answers in above?
Try this! Draw a bar model and write a matching number sentence to show each of these.
1. Mia has €18, which she divides equally between Jay and Dara. How much does each get?
What is the same and what is different about your bar models? Explain why.
2. Lexi has €18 in €2 coins. How many coins does she have?
Try this! Use models or strategies to solve these. 1. 24 ÷ 2 =
=
= 12 ÷ 2 = 6
Match and fill in the missing dates.
29th of February today 17th of March Christmas Day
31st of October my birthday 25th of December Halloween St Patrick's Day
Look at the calendar and answer the questions.
1. Which day of the week is the 24th of May?
2. How many Tuesdays are there in this month?
3. Jay’s library books were due back on the last Thursday in May. What date was this?
4. Jay went to the library when his books were 4 days overdue (late). On what date did he go?
5. Jay’s birthday fell on the second Thursday of this month. What is the date of his birthday?
6. Jay goes training every Wednesday and Saturday. How many times did he go training this month?
Try this!
1. Look at the calendar in . On what the day of the week will the 8th of June fall?
2. On what day did the 28th of April fall?
3. How many days in each month? Complete the table.
Seconds, Minutes, Hours
Let’s investigate!
Estimate how long each activity will take. Then, time it.
1. Write the names of 8 Irish counties without using a map.
2. Touch your toes and straighten up 10 times.
3. Say the tongue twister ‘A Big Black Bear’ 10 times.
4. Count in 5s from 5 to 100.
Change hours and minutes to minutes. 1.
Estimate Time
2. (a) 1 hr and 5 mins = mins (b) 1 hr and 15 mins = mins (c) 1 hr and 25 mins = mins (d) 2 hrs and 15 mins = mins (e) 2 hrs and 25 mins = mins (f) 2 hrs and 35 mins = mins
Change minutes to hours and minutes.
2. (a) 70 mins = (b) 80 mins = (c) 119 mins = (d) 120 mins = (e) 145 mins = (f) 160 mins =
D Let’s talk!
99 minutes. 60 + 40 = 100 60 + 50 1hr 50 mins
Look at the children. Who was fastest? Who was slowest? Did the marathon begin a.m. or p.m.? What time might it be now at the finish line? 65 1 hr 10 mins I ran it in 11/2 hours. You? 1 hour and 40
Analogue and Digital Clocks
Write the missing times.
Write or draw the missing times.
2. 3. 4.5.
25 past 8 5 to 6
Which time comes 20 minutes after… (3)
1. 10 past 6? (a) 10 to 6 (b) half past 6 (c) 20 past 6
2. half past 9? (a) 10 to 10 (b) 10 past 9 (c) 20 to 10
3. quarter to 11? (a) 5 past 11 (b) 10 past 11 (c) 5 past 10
4. 5 to 1? (a) 5 past 1 (b) 10 past 1 (c) quarter past 1
D Let’s talk!
Look at Dara.
What is the latest time he should leave his house? I need to be at the swimming pool by 6 o’clock. The journey takes 25 minutes, and I want to stop at the shop on the way
Calculating Time
If it is 2 o’clock now, what time will it be in…
1. 30 minutes? 2. 50 minutes?
3. 1 1 4 hours? 4. 2 hrs 40 mins?
Look at the bus timetable and answer the questions.
Destination Leaves at
1:55 p.m.
2:05 p.m.
1. Dara arrives at the bus station at 2 o’clock. (a) Which bus is next to leave?
(b) How long does he have to wait for the bus to Sligo?
(c) Which bus leaves in just under 3 hours?
2. Mia arrives at the bus station at a quarter to 3. How long does she have to wait for the bus to Westport?
Look at the cinema timetable and answer the questions.
1. Which film is the longest?
2. Which film begins earliest?
3. Which film is last to start?
4. Which film is last to end?
5. If Jay watched Robot Rooster, would he have enough time to visit a nearby café before going to watch Captured?
6. Which two films end at the same time? and
7. If Lexi arrived to watch Lost on Mars at 6:50
how much of the film did she see?
Spending and Saving
Let’s talk!
Look at the photos. How does each customer pay?
Which amount would you rather save? (3)
1. (a) €2 a week for 4 weeks or (b) €3 a week for 3 weeks
2. (a) €4 a week for 3 weeks or (b) €2 a week for 5 weeks
3. (a) €6 a week for 3 weeks or (b) €5 a week for 4 weeks
4. (a) €10 a week for 5 weeks or (b) €5 a week for 12 weeks
5. (a) €20 a week for 4 weeks or (b) €10 a week for 7
Estimate the price. Place the needle to show how much you
ks
Notes and Coins
Let’s talk
!
Look at the bags of money. Do you agree with Lexi? Explain why.
How many…
I’d choose the bigger bag. It definitely holds more!
make ?
How much altogether, if you have…
D Which is the greater amount in each row? (3)
How many €5 notes are worth the same amount of money as… 1. 15 ? 2 25 ? 3. 10 ? 4. 15 ? 5. 20 ?
1. (a) or (b)
2. (a) or (b)
Try this! How can you make…
1. 65c using as few coins as possible?
2. €1.45 using as few coins as possible?
3. €1 using one 20c and 9 other coins?
4. €2 using one 50c and 9 other coins?
Put these amounts of money in order, beginning with the lowest.
In front-end estimation we add only the euros. With front-end estimation, the estimate will always be less than the actual total.
D The sports shop is giving a free gift to customers who spend at least €25. Estimate who will get a free gift if they buy these items. (3)
I
Calculating Change
What change will each child get?
1. The pen costs 75c.
2. The book costs €3 70.
Mia’s change from €1 will be c.
Dara’s change from €5 will be € .
What change will you get from €1 if you spend… 1.
What change will you get from €5 if you spend…
D Subtract.
1.
What strategies can we use to subtract across zeros? See page 32.
Try this!
1. Use the clues to work out the amounts missing from Jay’s shopping receipt.
(a) The cereal was twice the price of the milk.
(b) The juice cost 60c more than the teabags.
(c) The price of the apples was exactly halfway between the prices of the bananas and the milk
2. If Jay paid with €20, what was his change? €
Till receipt
Bananas €1.10
Milk €1 20
Teabags €1.50
Cereal € ___ Juice € ___ Apples € ___ Total: € ___
Multiples of 4 and 8
What is missing?
Let’s talk
!
Discuss as a class or in groups: Are these always, sometimes or never true?
● Multiples of 4 are also multiples of 8.
● Multiples of 2 are also multiples of 4 and 8.
Can you find an example to prove or disprove each one?
● Numbers ending in 0, 2, 4, 6 or 8 are multiples of 4
● Multiples of 8 are also multiples of 4.
● Multiples of 8 are odd numbers.
● If you add a multiple of 8 to a multiple of 4, the answer is a multiple of 4.
Count in 4s or 8s. How many…
legs?
arms?
pencils?
Try this!
1. In a collection of squares and octagons, Jay counts 32 sides. How many of each shape might there be? (a) squares: (b) octagons:
An octagon has 8 sides.
2. What is the lowest possible number of each shape there could be? (a) squares: (b) octagons:
Multiplication as Repeated Addition
Let’s talk!
Describe the images below in different ways.
The first one could be 4 + 4 + 4, or 3 times 4, or three 4s.
Write and solve the matching multiplication sentence for each of the images in above.
Write <, > or = to make these true.
Try this! Look at the images. Use Build it! Sketch it! Write it! to model this.
Jay has 4 packs of pencils with six in each. Lexi has 7 packs of pencils with four in each. Who has more pencils?
Arrays
Maths eyes
Write matching addition and multiplication sentences in your copy for each array.
How many in total? Model each of these and write the matching number sentences.
1. 7 rows of counters with 4 in each row
2. 9 rows of playing cards with 8 in each row
3. 8 rows of bottles with 4 in each row
4. 5 rows of stamps with 8 in each row
5. 10 rows of children with 4 in each row
6. 6 rows of pictures with 8 in each row
Strategies for Multiplying by 4 and 8
To multiply by 4, double and double again. To multiply by 8, double, double and double again.
Complete these bar models.
Use doubling to help you solve these.
Try this! Use models or strategies to solve these.
Division as Sharing Equally
Build it! Sketch it! Write it! Use materials and sketches to represent these. Write the matching division sentence for each. Share these equally among…
This bar model represents question 1 in above. Draw bar models in your copy to match two of the other questions in . Model and solve these.
D Let’s talk!
Think of a story to match some of the number sentences in .
Try this! Use models and division sentences to help you solve these. There are 19 green apples and 13 red apples in a box.
1. If the apples are divided evenly among 4 bags, how many will there be in each?
2. If the apples are divided evenly among 8 bags, how many will there be in each?
1.
Division as Repeated Subtraction
Build it! Sketch it! Write it! Use materials and sketches to represent these. Write the matching subtraction and division sentences for each.
If Lexi puts 4 buttons on every card she makes, how many cards is that?
Dara has 40 matchsticks. How many octagons
For how many weeks will these last, if 8 are used every week?
For how many days will the oranges last, if 4 are eaten every day?
This bar model matches question 1 in above. Draw bar models in your copy to match two of the other questions. Let’s talk! Think of a story to match some of the number sentences in .
Strategies for Dividing by 4 and 8
Complete these bar models.
Solve these.
Let’s talk!
Check your answers to . What strategies did you use to check your answers?
Try this! Use models or strategies to solve these.
Multiplication and Division with 1 and 0
Write the matching multiplication sentence for each.
Write a matching division sentence for each one in if it is possible.
Write the answer for each of these. If it is not possible to answer it, write 7 as the answer.
D Find the missing factors.
Times Snap
Number of players: 3–4
You will need: deck of playing cards with picture cards removed
● Create two piles of cards: pile A has all the 2s, 5s, 10s, 4s and 8s; pile B has all the remaining cards (without picture cards). Place both stacks of cards face down beside each other.
● The dealer turns over the top card in both piles in full view of the other players.
● The player who first calls out the product of the two cards wins the card turned in pile B. The card from pile A is not claimed but returned to the bottom of that pile.
● Play continues until all the cards in pile B are gone.
● The player with the most cards at the end wins the round, and becomes the dealer for the next round.
Capture the Area
Number of players: 2–3
You will need: deck of playing cards with picture cards removed, 1 sheet of squared paper, crayon/marker/pencil of a different colour per player
● Organise the stacks of cards as before.
● Each player turns over two cards, then draws a rectangle according to the cards turned, and writes the total number of square units inside it. For example, if a player turns a 2 and a 9, they draw a rectangle that is 9 squares by 2 squares and write 18 inside it.
● If there is not enough space on the paper for a player to draw their rectangle, the player misses a turn.
● Play continues until time is up or there is no more space left on the paper.
● The player with the greatest number of square units overall wins the game.
1. (a) Write the time shown. (b) What time will it be 1 1 2 hours later? (c) What time was it 30 minutes ago?
2. 7 × 5 =
3. Write using digits and the correct symbols: four euro and seventy cent
4. 40 – 5 – 5 – 5 =
5. This watch has 2 hands. How many hands do 7 such watches have?
6. What is the difference between €1 20 and 75c? (3) (a) €1 95 (b) €0 55 (c) €0.45 (d) €0.50
7. How many hours are there in 2 days?
1. How many hours and minutes are there in 155 minutes? hrs mins
2. 80 ÷ 8 = 3.
8. How many cows are there in a field if there are 32 legs? € 8.00 – € 4 65 + __2.40
4. Jay went to see a rugby match. The match started at 2:45 p.m., but Jay arrived 25 minutes late. At what time did he arrive?
23 4 2:45
5. 32 ÷ 4 =
6. How many groups of 5 can I make from 30 cubes?
7. How many people are there in the room if there are 60 toes?
8. Estimate how much money you would need to buy a new hurley at a sports shop. (3)
(a) €0–€10 (b) €10–€50 (c) €50–€100 (d) €100–€150
1. Write a multiplication sentence and a division sentence for this array. × 4 = ÷ 4 =
2. How many days are there altogether in May, June and July?
3. Write using digits and the correct symbols: six cent more than six euro
5. If it is 3:15 p.m. now, what time will it be in 1 hour and 20 minutes?
6. Write a multiplication sentence and a division sentence for this array. × = ÷ =
7. How many candles are in 9 boxes if each box holds 10 candles?
8. How many €2 coins are there in this piggy bank if it contains one €1 coin and one €5 note only?
4. What total does this bar model show? ? 5555555 €18
Try this!
1. If Mia had 20c more, she could buy a carton of juice for €1.15. How much money does she have? c
2. In a classroom, there are 48 legs. How many chairs and children might there be? chairs and children
3. If the 31st of May is a Saturday, what day and date will it be… (a) 10 days later?
(b) two weeks later?
4. Lexi has €2.60. Dara has €1.20 less than Lexi. Jay has 90c more than Lexi.
(a) How much money does Dara have? €
(b) How much money does Jay have? €
(c) How much money do the children have altogether? €
5. (a) Write 2 multiples of 2 that are not multiples of 5 or 10. (b) Write 2 multiples of 5 that are not multiples of 10. (c) Write 2 multiples of 5 that are also multiples of 10.
6. In a pet shop there are 76 legs in the glass cases. How many spiders and lizards might there be? spiders and lizards
Let’s talk!
A Trip to the Cinema
Look at the table below. What do you notice? What do you wonder? What could be written after each time to make the information clearer?
Look at the table in above and answer the questions.
Mia and Jay went to see Pirates! straight after school on Tuesday.
1. What was the date?
2. At what time do you think the film started?
3. (a) Pirates! lasted 115 minutes. What is this in hours and minutes? hrs mins
(b) At what time did Pirates! end?
Answer these.
Mia got more sweets, but my sweets cost more! Why is that?
1. How much did Mia’s sweets cost?
2. What was the total cost for both children’s sweets? €
D Look at the table below and answer the questions.
Adult €10 50 €14 50
Child €7.50 €10.00
Senior €8.00 €10.50
Family (2 adults, 2 children) €30.00 €45.00
Why are there different prices on different days?
1. How much would it cost for Lexi’s family to go to the cinema on Tuesday if…
(a) they bought five tickets separately? €
(b) they bought a family ticket and another ticket? €
2. How much would they save by choosing the cheaper option above? €
3. How much would it cost for Lexi’s family to go to the cinema on Friday if…
(a) they bought five tickets separately? €
(b) they bought a family ticket and another ticket? €
Look at the image and answer the questions.
One full row of seats
1. How many seats are there in…
(a) 4 side groups?
(c) 8 side groups?
(b) 7 side groups?
(d) 3 middle groups?
(e) 6 middle groups? (f) 9 middle groups?
2. (a) If there are 10 full rows, how many seats are there altogether?
(b) If 65 people come to watch a film, how many seats would be empty?
Try this! Use the clues to work out which person in Lexi’s family sat in each seat.
● They sat in this order: male, female, male, female, male.
● Lexi’s mum sat between her husband and her son.
● Lexi did not sit beside her brother.
● The eldest person sat in the first seat.
Halves, Quarters and Eighths
What fraction of each shape is red?
In , what fraction of each shape is yellow?
What fraction does each number line show?
D Let’s talk!
Try this! Draw three shapes the same as the one that Dara coloured. Use Dara’s way of colouring to show 1. 1 half, 2. 1 quarter and 3. 1 eighth. This is what I coloured.
Do any of the models in or C show more than one fraction? Which ones? Explain how.
Dara was asked to colour in 3 quarters of this shape red. Is he correct?
Tenths and Fifths
What fraction of each shape is red?
In , what fraction of each shape is yellow?
What fraction does each number line show?
D Let’s talk!
Do any of the models in or show more than one fraction? Which ones? Explain how.
Try this!
1. Four people each had a slice of this pizza. What fraction of the whole pizza was left?
2. The remaining slice was cut into two equal pieces and one of these was eaten. What fraction of the whole pizza was left then?
Equivalent Fractions
What are the missing equivalent fractions?
Model and solve these.
What fractions could each letter stand for? Write at least two equivalent fractions for each.
D Let’s talk!
Write down two equivalent fractions.
Look carefully at these equivalent fractions. Look at the numerators and the denominators. What patterns do you spot?
Write down two other equivalent fractions. Do they also have patterns?
Numerator
Denominator
Comparing and Ordering Fractions
Use these bar models or other models to help you answer the questions.
Let’s talk!
Look at the coloured parts above.
What fraction name can be given to each?
Which unit fraction is the smallest?
Which unit fraction is the largest?
What word is missing?
As the number of parts gets bigger, each part gets
Write >, < or = to make these true.
Put each group of fractions in order, starting with the smallest.
D What fraction could be missing in each of these?
I am thinking of a fraction that is
Try this!
1. Look at Jay. What fraction could he be thinking of? Can you work out three possible answers?
2. Make up a similar clue for your partner to solve.
Fractions Greater than 1
Express each amount shown below as an improper fraction and a mixed number.
8 = proper fraction
= improper fraction
=
= 3. =
Complete these branching bonds. Sketch matching images.
Show each amount in using a branching bond.
D Write the value of each letter as both an improper fraction and a mixed number.
Try this!
1. Dara and Lexi are counting in fifths.
Dara starts at 2 1 5 and counts forwards.
Lexi starts at 4 1 5 and counts backwards.
What fraction will they say at the same time?
2. Jay and Mia are counting in eighths. Jay starts at 5 3 8 and counts backwards.
Mia starts at 3 3 8 and counts forwards.
What fraction will they say at the same time?
Adding and Subtracting Fractions
Write the fraction that is missing in each branching bond.
Let’s talk!
Look at Monty. Is he correct? Explain why.
I think the answer to question 1 in is 4 10.
Write and solve the matching addition or subtraction sentence for each of these.
D Draw or use models to help you solve these.
Try this! Look at the children. What maths questions could you ask about these images? How could you model and solve the questions?
Finding a Fraction of a Whole Amount
Find these fractions.
1. What fraction of the pens are… (a) blue? (b) red?
2. What fraction of the apples are… (a) green? (b) red?
Model and solve these.
Model and solve these.
1. 1 eighth of the 80 trees in the park are oak trees. How many oak trees is that?
2. Jay cut this ribbon into quarters. What length was each quarter? cm
3. A box of 25 strawberries was shared equally among 5 children. How many did they each get?
Try this! Below are the results of two class surveys. If there are 30 children in the whole class, how many children voted for each of the options?
How many strawberries did each child have at the start? They have each drawn a bar model as a clue.
1. Mia has 1 4 left.
2. Jay has 1 8 left.
Total at the start =
3. Lexi has 1 5 left.
Total at the start =
4. Dara has 1 10 left.
Total at the start =
Total at the start =
Each paper strip has had a fraction cut off it. What was the length of each paper strip at the start?
1. 1 4 of strip = Length at the start: cm
2. 1 10 of strip = Length at the start: cm
3. 1 8 of strip = Length at the start: cm
4. 1 5 of strip = Length at the start: cm
Try this! Look at the children. How much money do they have altogether? €
I have €12. I have twice as much money as Jay I have 1 quarter of the amount that Lexi has. I think bar models could help.
Pizza Party – Eighths
Number of players: 2
You will need: mini-whiteboard and marker per player, eighths spinner, pencil and paper clip
● To start, on their mini-whiteboard, each player draws three circles divided into eighths to represent pizzas.
● Each player, in turn, spins the spinner and shades out the fraction spun of one of their pizzas to show that this amount has been eaten.
● The first player to eat (shade out) all their three pizzas wins the game.
Variations
● Pizza Party –Tenths: Play as above, but use the tenths spinner, and to start, each player draws three circles divided into tenths.
Who has more? – Eighths
Number of players: 2
You will need: mini-whiteboard and marker per player, eighths spinner, pencil and paper clip
● Each player, in turn, spins the spinner and writes the fraction spun on their miniwhiteboard.
● The player who thinks that they have the larger fraction in that round must prove it by using models. If they are correct, they score a point. (Tip: Use tally marks to record the points.)
● The player with the most points after five rounds wins the game.
Variations
● Who has more? –Tenths: Play as above, but use the tenths spinner.
● Who has more? –Eighths and Tenths: Use both spinners.
● Option 1: One player spins the tenths spinner and the other spins the eighths spinner throughout the game.
● Option 2: The players swap spinners each round. (Tip: Play both options to see which one the players prefer.)
Let’s talk!
Mia wants to measure the height of the classroom door. Which piece of measuring equipment below do you think she should use? Give reasons for your choice. Is there any piece of equipment that would not work?
Let’s investigate!
Estimate and measure in metres…
1. the height of the door
2. your height
3. the length of your table
4. the width of the window
Estimate: m Measure: m
Maths eyes
Estimate: m Measure: m
Estimate: m Measure: m
Estimate: m Measure: m
You can make your own metre strip to help you!
Find and draw things with these lengths. 1. Less than 1 4 metre
About 1 4 metre
Greater than 1 4 metre, but less than 1 metre
Let’s investigate!
Centimetres
Estimate and measure in centimetres…
1. the width of your table
2. the length of your copy
3. the length of your Pupil’s Book
Estimate: cm
Measure: cm
Estimate: cm
Measure: cm
Estimate: cm
Measure: cm
Estimate the length/width of the dashed line and measure with a ruler.
Estimate: cm
Measure: cm
Estimate: cm Measure: cm
Estimate: cm Measure: cm
Estimate: cm Measure: cm
Estimate: cm Measure: cm
Try this! In your copy, draw a picture of an object in your classroom that measures 10cm.
Estimate: cm Measure: cm
This is called a benchmark, which means that it helps you to remember what 10cm looks like.
Measuring Metres and Centimetres
Let’s talk!
Mia wants to measure the height of the goalposts in the school yard, but her metre stick is broken. It only shows from 25cm to 75cm:
Who do you agree with, Jay or Lexi? Why?
Let’s investigate!
I don’t think she can measure it, because the metre stick is too small. I think she can still measure it. 1m = 100cm
In pairs, estimate and measure in centimetres…
1. the length of your standing stretch
2. the length of your step stretch
Estimate:
Estimate: cm
Rename these lengths in m and cm and then mark their position on the measuring tape.
Try this! If you added the total length of the four legs of your chair, what would this be? cm or m cm
Comparing and Ordering Lengths
Playground posts
Look at the picture. Lexi was designing an obstacle course, but she mixed up the posts.
1. Redraw the posts in the correct order from smallest to tallest.
2. Rewrite the lengths in centimetres in the correct order from tallest to smallest. cm, cm, cm, cm, cm
Let’s investigate!
Lexi designed 5 paper planes and wanted to test which one flew the longest distance. Her notebook shows the results.
1. Write the distances in order from shortest to longest.
2. What was the difference between the longest distance and the shortest distance? m cm
3. Dara designed a plane that flew 80cm farther than Lexi’s plane C. What distance did Dara’s plane fly? m cm
3 the shortest length in each set.
1.
Try this! Look at the sets in again. Work out the difference between the longest and the shortest length in each set in cm.
Tenths as Decimals
What fraction of each shape is yellow? Write each answer as (a) a fraction and (b) a decimal.
(a) (b) 4. (a) (b)
(a) (b)
In , what fraction of each shape is white? Write the answer as (a) a fraction and (b) a decimal.
(a) (b)
. (a) (b)
(a) (b)
(a) (b)
Write each amount as (a) a fraction and (b) a decimal.
D Write the decimal number that is located at each letter.
A: B: C: D: E: Let’s talk!
Who is correct, Dara or Mia? 10cm is 1 tenth of a metre. 10cm is 0.1 metres.
1. (a) (b)
(a) (b)
Let’s talk!
Look at the sections 1, 2 and 3 below. Where have you seen information like this? What does each section tell us?
D Model these. Order them from least to greatest.
1. 0 6, 0 2, 0 7 2. 1 4, 2, 1 1
3. 0.6, 3 10 , 0.4 4. 4.5, 5, 4.8
5. 6, 5 6, 6 5 6. 0 7, 1 2 , 0 3
Look at the table and answer the questions.
1. Who is the tallest?
2. Who is the shortest?
3. Who is exactly 1.5 metres tall?
4. Who is closest to 1 metre?
Look at Monty and the table, and answer the questions.
The magnitude or strength of an earthquake is measured on a scale of 0 to 10. The higher the number, the stronger the earthquake.
1. Where did the strongest earthquake occur?
2. Where did the weakest earthquake occur?
Try this! Dara used 5 of these coins to show a decimal number on the place value grid. Write four possible numbers he could have made, and order them from least to greatest. least greatest Ot .
Calculations with Decimals
For each model, write the matching number sentence using decimal numbers, and solve.
Write the decimal number that is missing in each branching bond.
Draw or use models to help you solve these.
Try this! Model and solve these.
(a) What is the difference in capacity between the greatest and the least? l
(b) What is the total capacity of all three containers? l 2.
(a) What is the difference in weight between the heaviest and the lightest? kg
(b) What is the total weight of all three cases? kg
Draw one straight line to make 2 right-angled triangles. Draw one straight line to make 1 triangle and 1 four-sided shape. Draw two straight lines to form 3 triangles. Join A to B, B to C, C to D, and D to A. What shape have you made? A B C D
Tessellations
Let’s talk!
Look at the images below. Do you agree with Jay? Which image(s) do you think show tessellation?
I think that just one of these show tessellation.
7 the one that is not a tessellation.
What tells you that it is not a tessellation?
3 the shapes that tessellate.
D Complete the pattern on each ribbon.
Maths eyes
Can you think of places where you have seen tessellations like these?
Tessellating and Transforming
What move is needed to make the missing piece fit? (3)
Translate Rotate Reflect
Translate Rotate Reflect
Rotate and translate Rotate and reflect
Translate Rotate Reflect
Which piece will complete each pattern? (3)
Answer these.
1. How many more tiles are needed to cover each area?
Translate Rotate Reflect
2. What shape are the red tiles in (e)?
3-D Shapes – Pyramids and Prisms
Match the 3-D shapes to the frames below. cube cuboid square pyramid triangular pyramid triangular prism
What 2-D shapes could we make by pressing these 3-D shapes into sand?
1. Square pyramid:
2. Triangular pyramid:
3. Triangular prism:
4. Cuboid:
Let’s investigate!
I made a circle using a cylinder.
Using materials, investigate whether these statements are always, sometimes or never true.
1. A cuboid has 8 faces.
2. The faces of a cube are squares.
3. A pyramid has 5 vertices.
4. A pyramid is pointed at one end and flat at the other end.
5. A prism has 5 faces.
6. Every face of a prism is a triangle.
D Maths eyes
Properties of 3-D Shapes
Complete the table. How many…
Name curved surfaces? flat faces? curved edges? straight edges? vertices?
Let’s talk!
Choose a 3-D shape from above. Your partner closes their eyes and you describe your shape. Can your partner work out what shape it is?
Mia has sorted the 3-D shapes below. Help her to complete the labels.
My shapes has 6 flat faces, 6 straight edges...
Constructing and Deconstructing 3-D Shapes
Match each 3-D shape to its net.
The shapes are 3-D, but the nets are 2-D
Cut out the nets on your activity sheet (see PCM 3) and fold each along the dotted lines. Stick the faces together using sticky tape to construct 3-D shapes.
Let’s Look Back 3
1. What value is shown by the 2. How many quarters are coloured arrow? in the circle?
3. What must I add to 75cm to make 1 metre? cm
4. Write as centimetres: 1m 2cm = cm
5. Jay ate 3 4 of his strawberries and he had 5 left. How many did he have at the start?
6. How many flat faces does a cylinder have?
7. Put these fractions in order, starting with the smallest: 2 10 , 7 8 , 4 8
8. Name each shape. Is it regular or irregular? (3) A
1. Put these numbers in order, starting with the largest: 5 5 10 , 0.4, 2.3
2. 3 the shapes that have no triangular faces: cone triangular prism cuboid square pyramid
3. Write as m and cm: 245cm = m cm
4. What fraction goes in each box?
5. What am I? I am a 3-D shape. I have 5 vertices and 5 flat faces. Four of my faces are triangles and one is a square.
6. Write 2 5 10 as a decimal.
7. Put these lengths in order from shortest to longest: 1 2 m, 45cm, 1m 20cm, 94cm, 3 4 m
8. 1 2 = 4 = 8 = 10
1. Insert the correct symbol (<, > or =): 6 10 1 2
2. Measure the total length of this line with your ruler. cm
3. Name two shapes you see around you that can tessellate.
4. 7.8 – 4.4 =
5. Mia’s scarf is 146cm long. Dara’s scarf is 190cm long. How much longer is Dara’s scarf? cm
6. Which shape below is the odd one 7. How long is the paper clip? out, A, B or C? cm Why?
AB C
8. Which would you prefer, 1 8 of your favourite cake or 0.6 of it?
Try this!
1. Make this equation true: 2 5 < < 8 10
2. AB CD E
(a) What is the weight of D if it weighs twice as much as B? kg
(b) What is the weight of E if it weighs half as much as A? kg
(c) Which two cases weigh 7kg together? and (d) How much less than 10kg does each weigh?
3. What is the length of this pencil? cm
5. The teacher put a 3-D shape on her desk and it rolled off. What shape might it have been?
6. In the long jump, Lexi jumped 1m 75 cm. Dara jumped 15cm more than Lexi. Jay jumped 20cm less than Lexi. Who jumped closest to 2m?
4. 30 children in a class were surveyed about their favourite pets. What decimal fraction preferred… dogs? cats? fish? birds?
Let’s talk!
The Sitting Room
Look at the image below. What do you notice? What do you wonder?
Look at the image above and answer the questions.
1. What shape is…
(a) the mirror on the wall?
(b) the picture frame on the wall?
2. True or false?
(a) Some of the shapes on the mat are parallelograms.
(b) The shapes on the mat do not tessellate.
3. Complete the table for shapes A–E.
How many…
Name flat faces? curved surfaces? curved edges? straight edges? vertices?
4. Choose any 3-D shape and draw its net in your copy.
Look at the sizes of the shelving units below and answer the questions.
Units F and H: length 77cm, height 184cm
1. True or false?
(a) Unit H is more than 2m high.
Unit G: length 147cm, height 77cm
(b) The height of unit G is closer to 1m than 1 2 a metre.
(c) The length of unit G is more than 1 5m.
(d) The length of unit F is close to 3 4 of a metre.
2. What is the total width of the green wall in metres and centimetres? m cm
3. What is the difference in height between units F and G in metres and centimetres? m cm
4. Which of these is the most likely size of the TV? (3) (a) 160cm by 92cm (b) 110cm by 62 cm (c) 60cm by 32cm
D Look at the image and solve.
When all the brown boxes are in place, what fraction of the shelves in unit G have brown boxes?
Look at the image and complete the table.
Express the number as…
(a) a fraction in its simplest form (b) a decimal fraction
1. The number of sections in unit F that have doors
2. The number of sections in unit F that have books
3. The number of sections in unit H that have books
4. The number of sections in unit H that are empty
Try this!
Of all of the books on the shelves, 9 10 are fiction and the rest are non-fiction. If there are 8 non-fiction books, how many books are there in total?
What is missing?
Multiples of 3, 6 and 9
Let’s talk!
Discuss as a class or in groups: Are these always, sometimes or never true?
● Multiples of 3 are also multiples of 6.
● Multiples of 6 are even numbers.
● Numbers ending in 0, 2, 4, 6 or 8 are multiples of 6.
● Multiples of 6 are also multiples of 9.
● Multiples of 9 are odd numbers.
Can you find an example to prove or disprove each one?
● If you add a multiple of 3 to a multiple of 6, the answer is a multiple of 9.
Count in 3s, 6s, or 9s. How many… 1. scones?
D Let’s investigate!
If you add the digits in a multiple of 3, the total is always a multiple of 3.
Arrays of 3, 6 and 9
Let’s talk!
Look at the images in below. Describe the images in different ways.
Maths eyes
The first one could be 3 + 3 + 3 + 3, or 4 rows of 3, or 3 columns of 4, or 4 times 3, or four 3s.
Write matching multiplication sentences for each array.
Try this! Can you work out how many counters Mia has in the bag? Read the clues carefully. She has counters.
I have more than 30, but less than 60. I can make an array with equal rows of 9, but not with equal rows of 6. 4 3 x x 3 4
Scaling and Comparison Bar Models
Write and solve the matching multiplication number sentences.
1. Mia has six toy cars. Dara has three times as many cars as Mia. How many cars does Dara have?
2. Jay has €4 in his piggy bank Lexi has six times as much money as Jay. How much money does Lexi have?
3. A pair of football socks costs €5. A pair of football boots is nine times as expensive as a pair of socks. How much are the football boots?
Match each multiplication sentence to a suitable bar model and then solve.
1. 9 × 8 = (a)
2. 3 × 4 = (b)
3. 6 × 8 = (c)
Let’s talk!
Make up a story to match each of the bar models and number sentences in .
D Model and solve these.
1. The width of a garden is 5m. How long is the garden if its length is 3 times the width? m
2. Jay has 5 pencils. Dara has 9 times that amount. How many pencils does Dara have?
3. A pencil is 10cm long. The desk is 6 times as long as the pencil. What length is the desk? cm
Try this! A computer game costs 6 times as much as a book
1. If the computer game costs €48, how much for…
(a) the book? €
(b) the book and the game? €
2. If you bought both, how much change would you get from €70? €
Let’s play!
Number of players: 3–5
Domino Draw
You will need: set of dominoes
● The set of dominoes should be placed face down on a table.
● Each player, in turn, draws a domino. Taking the dots on either side to represent the factors, they call out the product. For example, if a 2 and a 6 is drawn, the player calls out 12, because 2 times 6 is 12.
What if I don’t have a set of dominoes? Could I still play this game?
● If calculated correctly, the player keeps the domino. If not, the domino is returned, face down, to the table.
● The player with the most dominoes at the end wins the game.
Strategies for Multiplying by 3, 6 and 9
To multiply by 9, treble and treble again.
To multiply by 6, treble and double.
Write the matching number sentences for the bar models. Use trebling and doubling to solve them.
Use one set less to solve these.
In above, I think trebling could have been used.
In above, I think one set more could have been used.
D Use related facts to solve these. 1. 10 × 5 = so 9 × 5 = 2. 5 × 6 = so 6 × 6 = 3. 3 × 10 = so 6 × 10 = 4. 10 × 9 = so 9 × 9 = 5. 2 × 5 = so 3 × 5 = 6. 3 ×
=
Solve these.
Try this! Use models or strategies to solve these.
You will need: deck of playing cards with picture cards removed
● Create two piles of cards: pile A has all the 3s, 6s and 9s; pile B has all the remaining cards (without picture cards).
The dealer turns over the top card in both piles in full view of the other players.
Can you think of a different strategy to use for each?
3s, 6s and 9s go here.
AB
● The player who first calls out the product of the two cards wins the card turned in pile B. The card from pile A is not claimed but returned to the bottom of that pile.
● Play continues until all the cards in pile B are gone.
● The player with the most cards at the end wins the round, and becomes the dealer for the next round.
Variation
● Put the whole deck of cards together and turn over the top two cards from the deck each time.
● The first player to call out the product of the two cards wins both cards.
Modeling Division with 3, 6 and 9
Build it! Sketch it! Write it! Use materials and sketches to represent these. Write the matching division sentence for each. Share these equally among…
This bar model matches question 1 in above. Draw bar models to match two of the other questions in . Model and solve these.
is another way to write division calculations.
D Let’s talk!
Think of a story to match some of the number sentences in above.
Try this! Use models and division sentences to help you solve these. There are 14 boys and 16 girls in a class.
1. If the children are divided evenly into 3 teams, how many will there be on each team?
2. How many would be in each team if 6 teams were made?
Remainders
Let’s talk!
Look at below. Predict which ones will have a remainder and which will not.
The remainder is the amount left over after dividing a number.
Build it! Sketch it! Write it! Use materials and sketches to represent these. Write the matching division sentence for each.
14 plums divided into groups of 3
D Let’s talk!
Look at Jay. Is he correct? Explain why.
Try this!
The remainder should always be less than the divisor.
1. Grandad had 20 €1 coins to share equally among his three grandchildren.
(a) How much money did each child get? € (b) Were there any coins left over? If so, how many? R
2. This car transporter can carry 9 cars at a time.
(a) How many transporters are needed for 45 cars?
(b) How many transporters are needed for 80 cars?
Multiplying and Dividing with 7
What is missing?
Write matching multiplication and division sentences for each.
Model and solve these.
strategies will you use?
Try this! Use models or strategies to solve these.
1. Mary’s age is a multiple of 7 and a multiple of 10. How old is she?
2. Jamie is Mary’s grandson. This year, his age is a multiple of 7. Next year, it will be a multiple of 5. How old is he?
3. Beth is Jamie’s mother. This year, her age is a multiple of 8. Next year, it will be a multiple of 7. How old is she?
Exploring Maths Symbols
Use a and . Write the missing numbers and symbols.
Write an amount to make each number sentence true. Check your answers, using the and .
2 Truths and 1 Lie! 7 the number sentence in each set that is a lie.
Try this!
2. Write
Maths Picture Puzzles
Solve the number sentences to work out what number goes on the answer line.
Numberless Word Problems
Solve these.
1. Lexi had stickers. Jay gave her more stickers.
Which one of these can tell us how many stickers Lexi had then? 3
2. There are chairs. The chairs are organised into equal rows.
Which one of these can tell us how many chairs there are in each row? 3
3. There are boxes. There are apples in each box.
Which one of these can tell us how many apples there are altogether? 3
4. Jack is years old. He is years older than Anna.
Which one of these can tell us Anna’s age? 3
5. There were loaves of bread in a shop. of these were sold. more loaves were delivered.
Which one of these can tell us how many loaves there were then? 3
6. Dara had collector cards. He collected more. He gave cards to Mia.
Which one of these can tell us how many cards Dara had then? 3
Pair work
(a) ÷
(b) –(c) + (d) ×
(a) × (b) ÷
(c) –(d) +
(a) + (b) –
(c) × (d) ÷
(a) –(b) + (c) –(d) ×
(a) – + (b) + –
(c) + –
(d) – +
(a) – –
(b) + +
(c) + –
(d) – +
For each of the word problems in , give each shape a reasonable value. Then, swap with a partner, who can model and solve each problem.
Inputs, Outputs and Rules
What are the missing outputs?
Use a calculator to check your answers to above.
What are the missing inputs?
D Use a calculator to check your answers to above. Work out the rule for these by comparing the inputs and outputs. Then, work out the missing input and output. The first one is done.
Repeating Patterns
Let’s talk!
What is the core of these repeating patterns? Say the colours aloud to help you. 1.
Use letters to represent the core of each of the patterns in above.
For example, in 1, the core of the pattern is AB.
What is the core of each of these patterns?
Try this! Model and solve these.
1. Dara started this pattern using counters: If he continues the pattern, what will the colour be of the… (a) 10th counter? (b) 15th counter?
2. Lexi made a pattern with 20 cubes, which started like this:
(a) What colour was the final cube?
(b) How many red cubes did she use?
6.
Growing or Shrinking Patterns
Model each pattern and complete the matching T-chart.
Try this!
1. For each of the patterns in , describe the rule using words and/or numbers to a partner.
2. For each of the patterns in , with a partner, work out what would be the 20th term.
3. In the image, there are 7 blue matchsticks. Without counting them, work out how many yellow matchsticks there are.
(a) If there were 15 blue, how many yellow would there be?
(b) If there were 25 blue, how many yellow would there be?
(c) If there were 75 blue, how many yellow would there be?
Number Patterns
Let’s talk!
For each of the patterns in below, say whether they are growing or shrinking patterns. Then, work out the rule of each pattern.
1. Jay is skip counting in 6s. Which of the following numbers should he not say: 72, 84, 98, 114?
3. A snail is at the bottom of an 11m wall. Each night it crawls up 3m, but during the day, it slips down 1m. On what night does the snail reach the top of the wall?
2. The temperature at 7 a.m. was 12 °C. If it increased by 2 °C every hour, what was the temperature at 11 a.m.? °C
4. Look at the sign below. If this pattern continues, what is the start time for the 4th show? p.m.
ShowStart time
1st 2:00 p.m.
2nd 3:30 p.m.
3rd 5:00 p.m. 4th ? 6, 12, 18, 24
5. The paddling pool is leaking!
At 2 p.m., there are 12 litres of water left.
At 3 p.m., there are 10 1 2 litres left.
At 4 p.m., there are 9 litres left.
(a) How many litres will be left at 6 p.m.? l
(b) At what time will the pool be empty? p.m.
Square Metres
Let’s investigate!
1. How many copies fit in 1 square metre?
2 How many playing cards fit in 1 square metre?
3. How many Pupil’s Books fit in 1 2 a square metre?
Estimate Count
Look at the map of the school garden and write the answers.
1. What is the area of both flower beds? sq m
2. What is the area of the ? sq m
3. What is the area of the path? sq m
4. What is the area taken up by all of the ? sq m
Let’s create!
Design a map of a school garden that is different to the one in . Your garden must have flower beds, benches and a path.
m 1 square = 1 sq m
Let’s create!
Look at Jay.
Let’s make a square centimetre.
How will you do this? What will you need to use?
Estimate and measure the area of each item.
Hello from Ireland
Estimate: sq cm
Measure: sq cm
Estimate: sq cm
Measure: sq cm
Estimate: sq cm
Measure: sq cm
Estimate: sq cm
Measure: sq cm
What strategy did you use to measure these? Did you count every square?
If no, what strategy did you use instead?
Estimate: sq cm
Measure: sq cm
Maths eyes
Find and draw an item with an area that is…
1. 20 sq cm 2. greater than 20 sq cm 3. less than 20 sq cm
D Broken 100 square! Write the answers. 3 4 67 910 11 13 15 18 20 23
1. What is the area of this broken 100 square? sq cm
Each square measures 1 square centimetre.
2. What is the area of the squares with missing numbers? sq cm
3. What is the area of the squares with a 3 in the ones place? sq cm
4. What is the area of the squares showing a multiple of 3? sq cm
Colour in some of the broken 100 square in D using one colour, and ask your partner to work out the area of the coloured part.
Let’s investigate! Area Hunt
Go on an area hunt in your classroom. Estimate and measure the areas of rectangular and square objects. What units of measurement will you use?
Try this!
1. Mia has drawn her dream adventure park. Write the area of the…
(a) football pitch sq cm
(b) swimming pool sq cm
2. How much empty space is left in the adventure park? sq cm
Area of Shapes
Look at the geoboard shapes and answer the questions.
1. What is the area of shape A? sq cm
2. What is the difference between the area of shapes B and C? sq cm
3. Which shapes have the same area?
4. How could you find the area of shape D?
Let’s create!
Draw a shape with an area of 24 square centimetres in the grid.
Estimate and measure the area of each shape below in square centimetres.
What shape will you choose?
How can you check the area?
You can use centimetre-squared paper to help you measure the area of each shape. Estimate: sq cm
Area Estimate
Number of players: 2
You will need: mini-whiteboard and marker per player, items to estimate (e.g. pencil case, book and school bag), items to measure with (e.g. playing cards, cubes or envelopes)
● The players agree on what unit of measurement is being used (e.g. playing cards, cubes or envelopes) and these are left to the side.
● Player 1 selects an item (e.g. a school bag). Each player estimates the number of units (e.g. playing cards) that are equal to its area and records this on their miniwhiteboard.
● Working together, they measure the area of the item.
● The player whose estimate was closest to the actual result, scores a point, which they record on their mini-whiteboard.
● Player 2, then, selects a new item to measure and repeats the game. Each player gets to pick a new item on their turn until the time is up.
● When the time is up, the player with the most points wins the game.
Variation
● Each player calculates the difference between their estimate and the actual result, and records this on their mini-whiteboard. For example: If they estimated that the area was 10 playing cards and the actual area was 10 playing cards, they record 0 on their mini-whiteboard.
● When the time is up, the player with the lowest score wins the game.
1. The area of this large red rug is sq m.
2. Insert the correct symbol (<, > or =): 17 + 4 27
3. If a pack of football cards costs €3, how much will 6 packs cost? €
4. If 60 = + + , then =
5. Share 24 oranges equally among six people. Each gets
6. Continue this pattern: 710, 700, 690, , , The rule is:
7. What is the area of the stamp in sq cm? sq cm
= 1 sq m = 1 sq cm
1. What is the remainder if you divide these counters into groups of 9? R
2. Make this number sentence true: 23 + < 39
3. Create your own pattern: 65, , , , , The rule is:
4. Mia’s holiday is 50 days away. How many full weeks is that?
5. 3 the shape with the greater area. 6. How many paints are there? Write a number sentence for this. =
7. 30 ÷ 6 =
8. True or false: area is measured in grams?
1. 24 – 3 – 3 – 3 =
2. Make this number sentence true: 49 > 52 –
3. Write a division sentence to 4. What is the total area of the purple match this array. shape? sq cm
oranges
5. Continue this pattern: 502, 504, 503, 505, 504, 506, , , The rule is:
6. Dara saw 4 ants on a leaf Each ant had 6 legs. How many legs did Dara count altogether?
7. Divide 36 pencils into 6 equal groups. ÷ 6 =
Try this!
1. Make this number sentence true: 9 + (2 × 3) ≠ (3 + ) + 7
2. Lexi shared 3 equally among 5 friends and herself How many pieces did Lexi get?
3. There were 102 swans on a lake. 25 flew away, and 34 more arrived. Write a number sentence to show how many swans are there now.
4. (a) Write two multiples of 9 that are also multiples of 6. (b) Write two multiples of 6 that are not multiples of 9.
(c) True or false: The answers to (a) and (b) are also multiples of 3?
5. This is a diagram of a garden with a path around it. (a) What is the area of this garden? sq m
(b) What area of the garden is not covered by grass? sq m
The Café
Work out the area in square units of the items on the table.
Answer these.
1. Without counting them all, work out how many flapjacks there are on the tray.
2. A bag of coffee beans weighs 9kg. Annie, the café owner, ordered 8 bags. How many kilograms of coffee beans did she order in
3. There are 11 tables in the café, and each table has 6 chairs.
(a) How many chairs are there in total?
(b) If only 5 chairs were empty at lunchtime, how many chairs were filled?
Answer these.
Annie baked 40 scones this morning. 27 were sold, and then she baked 24 more.
1. Write the matching number sentence.
2. Solve this: How many scones did she have then?
D Below is a section of the wallpaper in the café. Which piece will complete the pattern? (3)
Complete this pattern.
What number is missing from this pattern?
Scones sales at the café last week Mon Tue Wed Thu Fri Sat 61 64 67 73 76
Solve this.
Annie has baked 50 brownies. These will be packed in boxes of 6. How many boxes will be filled? How many brownies will be left over? Write a number sentence to show this.
Try this! The café sometimes has a special offer for customers on Saturday.
Saturday, 14th of January
€5 off every bill of €20 or more! Write the missing input and outputs to show this.
Saturday, 21st of January
Look at the input and outputs to work out the special offer (the rule).
Multiplying 2-digit Numbers by 0, 1 and 10
Write and solve the matching number sentences.
Write a matching number sentence to show how each starting number has been multiplied.
Write and solve the matching number sentences.
1. After the cake sale, there were 15 plates with zero buns on each. How many buns were left?
2. Twelve children each won a €10 prize in a competition. How much money was given out in prizes? € = €
D Let’s talk! Is each calculation true or false? Explain why.
Multiplying 2-digit Numbers using Materials
Write and solve the matching number sentences.
Use base ten materials to model and solve each of these.
Build it! Sketch it! Write it! Model and solve these using your preferred method.
1. There are 26 seats on a minibus. How many people can four minibuses carry?
2. Some larger buses have 52 seats. How many people can three of these buses carry?
3. There are 29 children in each class in a school. How many children are there altogether in four classes?
4. There are 28 dominoes in a set. How many dominoes are there altogether in three sets?
5. How many days altogether are there in January, March and May?
6. There are 24 hours in a day. How many hours are there in four days?
D Let’s talk!
Could you work out any of the answers to or (a) without using concrete materials or (b) mentally? Explain how.
Multiplying 2-digit Numbers using Sketches
Write and solve the matching number sentences.
Multiplying 2-digit Numbers using Calculations
Let’s talk!
Take turns to estimate the answers to and below. Explain how you arrived at your estimate.
Do you think the answer will be thirty-something, fortysomething, fifty-something ?
Partition the 2-digit number and use separate calculations to model and solve these.
Use the column method to model and solve these.
Let’s talk!
Work out the errors in each of these. What advice would you give?
Try this!
1. How many hours in a full week?
2. Ava is 18 years old. Her gran is 4 times her age. What age is her gran?
Multiplying Three Numbers
Write and solve the matching number sentence. How many seats in total in…
1. 3 carriages, with 4 rows of 2 seats in each carriage?
2. 4 carriages, with 5 rows of 2 seats in each carriage?
How many small cubes in each of these cuboids? Write and solve the matching multiplication sentence.
Let’s talk!
Compare with your partner: How did you each do and ?
Did you get the same answers?
Which two numbers did you each multiply first and why?
Try this! Lexi will make a cuboid using 48 cubes. What might her cuboid look like?
What might the matching multiplication sentence be?
Dividing Bigger Numbers using Materials and Sketches
Write and solve the matching division sentence.
Model and solve these.
Let’s talk!
How could you check that your answers in are correct?
Let’s play!
Play ‘Chance Calculations – Division’ on page 138.
Division
Calculations
For each of these, break up each dividend into friendlier numbers and divide to solve.
Solve these related calculations. 1. (a) 50 ÷ 5 = (b) 25 ÷ 5 = (c) 75
Model and solve these using the column method.
D Let’s talk!
Check your answers to above using a different strategy. Explain to your partner how you did this.
A dividend is the number that is to be divided into smaller groups: dividend ÷ divisor = quotient.
Solve these.
1. €96 euro was divided evenly among 4 people. How much did they each get? €
2. Dara cut a ribbon measuring 72cm long into 2 equal pieces. What was the length of each piece? cm
3. The calf’s weight is 4 times Monty’s weight. If the calf weighs 60kg, how much does Monty weigh? kg
4. A packet of 48 cherries was shared equally among three children.
(a) How many cherries did each child get?
(b) How many were left over?
5. 5 pairs of football shorts cost €85. How much would 4 pairs cost? €
Try this! Write the matching division sentence and answer for each of these.
Chance Calculations – Multiplication
Number of players: 2–6
You will need: mini-whiteboard and marker per player, 0–9 spinner, pencil and paper clip
● To start, on their mini-whiteboard, each player draws a blank 1-digit × 1-digit multiplication calculation.
● Each player, in turn, spins the spinner and writes the number spun into one of their boxes.
● When all of the boxes are full, the players calculate the product.
● The player with the highest product wins the game.
Variations
● Play as above, but draw a blank 2-digit × 1-digit multiplication calculation.
● Play as above, but draw a blank 1-digit × 1-digit × 1-digit multiplication calculation, and use a 1–6 spinner.
Chance Calculations – Division
Number of players: 2–6
You will need: mini-whiteboard and marker per player, 0–9 spinner, pencil and paper clip
● To start, on their mini-whiteboard, each player draws a blank 2-digit ÷ 1-digit division calculation.
● Each player, in turn, spins the spinner three times, and arranges the numbers spun into their boxes.
● The player with the highest answer wins the game. (Ignore any remainders.)
Let’s talk!
Look at Jay. Which instrument would be best for weighing the flour? Why?
Can you think of any other instruments for measuring weight?
Let’s investigate!
How many of the following would be needed to weigh 1kg? How will you find out? Estimate first and then measure.
Estimate Measure
Maths eyes
Is the weight closer to 1kg, 2kg or 3kg? Estimate first and then measure.
Estimate – closer to 1kg, 2kg or 3kg?
Measure – closer to 1kg, 2kg or 3kg?
1. Handfuls of pasta
2. Glue sticks
3. Copies
1. Clock
2. Maths book
3. Three full paint bottles
4. Tennis ball
Grams
Let’s talk!
Look at the balance. What do you notice? What do you wonder?
Let’s investigate!
How many of each item would be needed to reach the target weight? Estimate first and then measure.
Another way to say 1kg is 1,000g.
How many… Target weight Estimate Measure
1. paper clips? 12g
2. pens? 100g
3. rulers? 250g
4. maths books? 1,000g
Estimate and measure the weight of the following items. Choose something else for the last row.
What is the weight of…Estimate (g) Measure (g)
1. one pair of scissors?
2. three spoons?
3. five glue sticks?
4. Let’s create!
Make a monster from recyclable materials that meets the following criteria. It must...
● be at least 10cm tall
● be able to stand on its own
● weigh between 25g and 100g.
Measuring Kilograms and Grams
Let’s talk
!
Look at Mia. How could she balance the two sides?
Can you think of any other ways to balance the two sides?
Write the weight of the red boxes and answer the questions.
1. What is the combined weight of boxes B and C?
2. What is the difference in weight between boxes A and C?
3. In your copy, draw a different combination of weights that could be used to balance each of the three scales.
Write the weight for each of these.
Try this! Use the number line to work out the weight of the butter in these.
Litres
Maths eyes
1. Which containers do you think hold less than 1 litre? (3) (a) (b) (c) (d) (e) (f)
2. Which containers do you think hold more than 1 litre? (3)
Let’s investigate!
1. Choose three containers in the classroom. Is the capacity of each container closer to 1 4 litre, 1 2 litre or 1 litre? Estimate first and then measure.
Container
Estimate –closer to 1 4 litre, 1 2 litre or 1 litre?
Measure –closer to 1 4 litre, 1 2 litre or 1 litre?
2. Which container has the greatest capacity?
3. What is the total capacity of the three containers combined?
4. Now, choose two larger containers than the ones you used above. Estimate first and then measure the capacity of each in litres.
Container
Estimate (l)
Measure (l)
Maths eyes
Millilitres
There are 1,000 millilitres (ml) in 1 litre (l).
Look at each container. Do you think its capacity would be measured in litres or millilitres?
Complete the number lines.
1.
2. Use the interval markings to help you work out the amount of liquid.
Try this! Write the amount of liquid in millilitres.
Measuring
Litres
and Millilitres
Let’s talk!
Look at these jugs. What do you notice?
What do you wonder?
Let’s investigate!
Estimate and then measure the capacity of each item below. Work out the difference between your estimate and the actual capacity.
Some containers have interval markings to help us measure.
Compare with a partner to see who had the closest estimates.
Look at the table in above and answer the questions.
1. Which container had the smallest capacity?
2. What was the difference between your closest estimate and the actual capacity? ml
3. Roughly how many beakers of water would be needed to fill a 2-litre bottle?
Estimate (ml) Measure (ml) Difference (ml)
1. Lunch box
2. Mug
3. Beaker
Using Units of Measure
Let’s talk!
Which instrument would you use to weigh the items on the right? Explain why.
Kitchen weighing scale Bathroom weighing scale
Weighbridge Hanging scale
Write the correct unit of measurement for the weight of each toy. Is it kg or g?
Write the correct unit of measurement for the capacity of each container. Is it l or ml?
Try this! Mia has a pet terrapin, Frankie.
1. If Frankie weighs 100g more than the playing cards in , then how much does he weigh?
2. The capacity of Frankie’s tank is four times bigger than the fish tank in , what is the capacity of Frankie’s tank?
Comparing and Ordering Measures
Match the weights of equal value.
Match the
Let’s talk!
Would you rather…
I’d rather 600g because ...
● 1 2 kg of strawberries or 600g of strawberries?
● 1 4 kg of popcorn or 500g of popcorn?
● 1 2 kg of grapes or 290g of grapes?
● 1 4 kg of blueberries or 500g of blueberries?
D Write the weights of Jay’s parcels in order from lightest to heaviest. < < < lightest heaviest
Receipt
Post Office: 1847 Position: 1 Date: 14-March-2026 Time: 09:01:52
Parcel 1: 4kg @ 50c per 100g =
Parcel 2: 300g @ 50c per 100g =
Parcel 3: 2kg @ 50c per 100g =
Parcel 4: 100g @ 50c per 100g =
Parcel Post Total = Tracking number: IE 789 27385 28394 B
Try this! Look at Jay’s parcels in D above. How much will it cost him to post them all if he has to pay 50c per 100g of weight? €
Look at each group and answer these. A 1 can = 330ml BC 1 spoon = 5ml D
1. Which group contains the most liquid?
2. Order the groups from least to most liquid. < < <
Operations Using Measures
What is the capacity What is the weight of each fruit? of bottle C? C = ml
A B C
Look at Jay’s recipe and answer the questions.
Here’s what you need to make 8 pancakes with apple sauce:
1. If a teaspoon holds 5ml, how much olive oil does Jay use in total? ml
2. If a tablespoon holds 15ml, how much apple sauce does Jay use in total? ml
125g flour
300ml milk
2 medium eggs (55 grams each)
2 teaspoons olive oil
3 tablespoons apple sauce
3. What is the total weight of the eggs? g
4. What is the difference in weight between the eggs and the flour? g
5. How much flour would Jay need to make 16 pancakes? g
Try this! The total amount of oil in the four tanks is 494l.
Look at the bar model to help you with this question.
1. How much oil is in tank D? l
2. If the worker takes 21l of oil from each tank…
(a) How much does she take in total? l
(b) How much is left in the tanks in total? l
How Likely Is it?
Which chance word best matches each sentence below? Write the first letter for each.
1. A pig will fly.
3. You will brush your teeth this evening.
5. A rainbow will be seen after the rain.
2. You will see the moon tonight.
4. You will have homework this evening.
6. You will grow taller than your mother.
7. The sun will rise tomorrow.
9. You will walk home from school.
8. It will snow in July.
10. You will read a book today.
11. It will rain tomorrow.
13. You will see a real horse today.
Write one event that… 1. will happen today 2. will not happen today 3. might happen today.
12. You will go to bed to sleep tonight.
14. You will watch TV tonight.
Possible Outcomes
Complete the branching to work out the different possible two-course meals that can be ordered.
On your mini-whiteboard, use branching to work out all of the possible combinations that can be made.
Build your own kite!
How many different kites can be made in total?
On your mini-whiteboard, use branching to work out all of the possible combinations that can be made.
Bob’s Bread Bites Menu
Choose your bread:
How many different combinations can be made in total?
Try this! In a game, 3 bean bags must be tossed one at a time at this target to score points. Assuming that the 3 bean bags always hit some part of the target, work out all of the possible scores.
Chance Investigations
Let’s talk!
For each of the investigations below, discuss and agree on the following with your group:
● How will you do it? How will you make sure it is fair?
● How many times for each person?
● How will you record your results?
● How will you share your findings?
Let’s investigate! Coin Toss
You will need: mini-whiteboard and marker per person, one coin
1. Beforehand, predict the possible outcomes: The tossed coin could be
2. Write chance words. How likely is it that you will toss…
(a) either a head or a tail?
(b) a head?
(c) a tail?
(d) a head and a tail at the same time?
Let’s investigate! Cards
You will need: mini-whiteboard and marker per person, King, Queen and Jack from a deck of cards placed face down on a table
1. Beforehand, predict the possible outcomes: The card picked could be
2. Write chance words. How likely is it that you will pick
(a) a King?
(b) an ace?
(c) a picture card? (King, Queen, Jack)
D Let’s investigate! Colours
You will need: mini-whiteboard and marker per person, 12 cubes or counters – 4 red and 8 blue, non-transparent bag
1. Beforehand, predict the possible outcomes: The colour pulled could be .
2. Write chance words. How likely is it that you will pull…
(a) red?
(b) green?
(c) blue?
Let’s talk!
After each investigation, discuss the following with your group: How did you do it?
How did you make sure it was fair? What were your findings?
Were you surprised by your findings? Explain why
Try this! Dara put these shapes into a bag and then pulled one out without looking.
1. Which shape was least likely?
2. Which shape was most likely?
3. Do we know for certain that he pulled the shape in question 2?
1. Which unit would be used to measure the weight of a fridge? (3) (a) kilograms (b) kilometres (c) grams
2. How much money?
Write a number sentence: c × = c
3. (13 + 5) × 10 = 4. 64 ÷ 8 =
5. How much would 3 boxes 6. How much more does of tea weigh? g the larger container hold than the smaller one? ml
7. There are 12 bags of apples. Each bag has 7 apples. How many apples in total?
8. You will see a unicorn today. (3) (a) possible (b) impossible (c) certain
1. Dara is baking scones. He needs 250ml of milk. 2. Which instrument should he use to measure the correct amount? (3)
3. A bird will fly past your classroom window. (3) (a) likely (b) unlikely (c) possible (d) certain
4. Jay is posting a package weighing 5kg to his cousin in Australia. How much will the postage cost if the charge for 1kg is €40? €
5. Put these amounts in order, starting with the smallest: 3 4 l, 1l, 250ml, 0.5l
6. There are 72 markers in a box. The teacher will divide them equally among 6 pots. How many will there be in each pot? Write a number sentence: =
7. When you get up tomorrow, you will eat breakfast. (3) (a) likely (b) unlikely (c) possible (d) certain
8. 56 ÷ 7 =
1. I bought 14l of milk in 2l containers. How many containers did I buy?
3.
2. Christmas Day will take place on the 25th of December next year. (3)
(a) possible (b) impossible
(c) certain (d) likely
4. Can you work out what digit goes in the box? 1 × 6
5. I have a box of raspberries weighing 125g and a net of oranges weighing 750g.
(a) How much less do the raspberries weigh than the oranges? g (b) How much do the two objects weigh altogether? g
6. There are 7 jars of marbles on a shelf Each jar contains 48 marbles. How many marbles are there on the shelf altogether?
7. 1.5l = ml
8. A chair has 4 legs. How many legs do 24 chairs have? 896
Try this!
1. The code to open a safe is a 3-digit number made up from the 3 digits missing from the keypad. How many possible combinations are there? (Hint: Use branching.)
2. Solve these. (Hint: You 3. Lexi drinks about 1 2 l of could use the previous water every day. How much answers to help each time. water does she drink in…
(a) 7 × 1 = (a) 2 days? l
(b) 7 × 5 = (b) 4 days? l
(c) 7 × 10 = (c) 1 week? l
(d) 7 × 15 = (d) 2 weeks? l
(e) 7 × 30 =
(f) 7 × 35 =
4. How can I buy 2kg of flour in… (a) the least number of bags?
(b) the greatest number of bags?
(c) some of both types of bag?
5. The teacher has 5 pencil pots and he wants to put 32 pencils in each. If he is 5 pencils short, how many pencils does he have?
The Garden Centre
Match each item to its most likely weight.
Match each item to its most likely capacity.
Which chance word best matches each sentence below? Write the first letter for each. impossible unlikely possible likely certain
1. The President will visit the garden centre.
2. A snowman will visit the garden centre.
3. A child will visit the garden centre.
4. A person will visit the garden centre.
D Answer these.
1. A packet of bird food weighs 3.5kg. Express this as kg and g. kg g
2. A plant feeder holds 40ml of water. If 5ml is used every week, how many weeks will it last?
3. A bottle contains 1 1 2 litres of plant food. If 1 4 litre is used every month, how many months will it last?
4. What is the total capacity of a water butt if 1 5 is 50 litres? l
Solve this.
Dara’s purchases weigh 5kg. If the compost weighs 2 1 2 kg and the plant food weighs 1 1 4 kg, what is the weight of the bulbs? kg
Answer these.
1. Without counting them all, work out how many sections...
(a) in this planting tray
(b) in 5 such planting trays
(c) in 10 such planting trays
(d) in 15 such planting trays
2. If 40 customers are served in an hour, roughly how many customers are served in (a) 15 minutes? (b) 4 hours?
3. In a basket, there is an assortment of seed packets: 15 carrot seeds, 25 cabbage seeds, 10 onion seeds and 10 cucumber seeds. If I pull out a packet without looking, what type of seeds am I most likely to get?
The children are ordering sandwiches in the café. Complete the branching to work out the different possible combinations that can be made.
Garden Centre Café Menu
or or
Try this! The children can also add a drink to their orders in the café: milk or juice. Use branching or another strategy to work out the total number of possible combinations now. Choose your bread: Choose your filling:
End-of-year Challenge
Use Build it! Sketch it! Write it! to show at least one way to do this. Afterwards:
● Explain why you did it this way.
● Compare your plan with that of others.
● Prove why you think your plan is the best one.
cards
red card is worth 2 yellow cards 2 red cards are worth 3 blue cards
Dara has 8 red cards to trade.
How many yellow cards could he get?
How many blue cards could he get?
Lexi has 10 red cards to trade.
She wants to trade for as many cards as possible. What colour cards should she trade for?
How many of those cards could she get?
Mia has 4 yellow cards to trade.
How many red cards could she get?
How many blue cards could she get?
Jay has 15 blue cards to trade.
How many red cards could he get?
How many yellow cards could he get?
I think a T-chart might help me work these out.
Try this! Make up your own Trading Challenge! Swap with another and solve it.
STEM Exploring
Use your STEM eyes!
Which one doesn’t belong?
Same but different! What is the same? What is different?
Let’s talk!
How does a sand timer work?
I think it’s to do with the shape of this part where the top and bottom bulbs meet.
I think the amount of time it lasts depends on the size of the hole.
I think the more sand it contains the longer it lasts.
What do you think?
STEM Challenges and Investigations
Design and Make Cycle
1. Explore Think about what you could design and make as a solution.
● What do you need to do?
● Look at the available materials. What will you use?
● How will you do it?
2. Plan Plan and design your solution.
● Draw it out.
● Write a list of what will be needed.
● Discuss it with your group and explain your reasons.
3. Make Using the plan and criteria, make or build your solution.
4. Evaluate Test your solution.
● Does it satisfy the criteria?
● How well does it work?
● How could it be improved?
Design and make a flying frisbee.
Criteria: The frisbee must fly for more than 5 seconds before touching the ground. It must travel a distance greater than 2 metres. It must be made from recyclable materials.
Let’s investigate!
How does the shape of the frisbee affect how far it travels?
Can you think of a fair test to investigate this question? Use the Investigation Planning Sheet (PCM 4) to help you.
1. Explore 2. Plan 3. Make 4. Evaluate
Design and make a paper plate obstacle course for a marble.
Criteria: The paper plate needs to hold structures such as arches that allow a marble to pass through. The obstacle course must have a start and an end point. There needs to be a clear scoring system.
1. Explore 2. Plan 3. Make 4. Evaluate
Scoring system
Marble through blue arch = 2 points
Marble falls off the plate = –2 points
Marble through green arch = 5 points
D Design and make a windmill with rotational symmetry.
Criteria: The blades must turn freely. It must have rotational symmetry.
1. Explore 2. Plan 3. Make 4. Evaluate
Let’s investigate!
How could you simulate wind in the classroom?
How does the wind speed affect how fast the blades turn?
Can you think of a fair test to investigate this question? Use the Investigation Planning Sheet (PCM 4) to help you.
Design and make a one-minute timer using dry sand or salt.
Criteria: It must measure one minute of time exactly.
1. Explore 2. Plan 3. Make 4. Evaluate
6 5 4 3 2 I
Location Grid and Spinners
Number of players: 2–6
Capture the Counters
You will need: location grid, 1–6 spinner, A–F spinner, 36 counters, paper clip and pencil
● Lay a counter on each space in the grid.
● Each player in turn spins both spinners and uses the letter and number spun to take a counter from that square in the grid. If the counter has already been taken, the player misses a go.
● Continue playing until time is up or all the counters have been taken.
● The player with the most counters at the end wins the game.
Variation
● The first player to get 10 counters wins the game.
Deepen
● Capture the Coins: Place 36 assorted coins on the grid. The player with the most money (in cents) at the end wins the game.
Number of players: 2
You will need: location grid, 1–6 spinner, A–F spinner, counters (a different colour for each player), paper clip and pencil
● Each player in turn spins both spinners and uses the letter and number spun to place one of their counters on that square in the grid. If a counter has already been placed there, the player misses a go.
● The first player to get 4 counters in a straight line wins the game.
Variation
● Shape ’em Up: Play as above, but the first player to make a square using their counters in a 2 × 2 formation wins the game.
Deepen
● Shape ’em Up: The first player to make a shape with an area of 6 squares wins the game.
Line ’em Up!
Number of players: 2
Fair Play
You will need: mini-whiteboard and marker per player, 1–6 spinner, pencil and paper clip, 18 counters (or other items)
● Before the game, one player is named Odd and the other is named Even. (The player whose birthday is next can choose first.)
● Each player starts with nine counters. One of the players spins the spinner.
● If the number spun is even, the player named Even takes that number of counters from the other player.
● If the number spun is odd, the player named Odd takes that number of counters from the other player.
● Continue spinning until one player has all of the counters. This player wins the round.
● Play a number of times and record what is happening.
Move 4 or Not!
You could use calculations to record what is happening.
Number of players: 2
You will need: 100 square (see PCM 5), 1–6 spinner, pencil and paper clip, two counters of different colours (or other items)
● Before the game, one player is named Player 1 and the other is named Player 2. (The player whose birthday was most recent can choose first.)
● Each player places their counter on 1 on the 100 square.
● On each of their goes, Player 1 spins the spinner and moves forwards that number of places.
● Player 2 does not spin the spinner, but moves forwards 4 places on each of their goes.
● The player who passes 50 (or 100) first wins the game.
Let’s talk!
Are the games fair? Describe and explain what is happening. Use some of these words to help you: more chance less chance impossible unlikely
Number of players: 2
Squares
You will need: dot grid (or squared copy), a marker/crayon of a different colour per player
● To start, draw a 10 × 10 square border on the dot grid (or squared copy page). Play takes place inside this border.
● Each player, in turn, joins two neighbouring dots (or two intersections on a squared copy page) vertically or horizontally to draw a ‘side’ for a square. On their go, a player can add another side to a square or start a new square.
● The player who closes a square claims that square and fills it with their colour.
● Play continues until time is up or there is no more space to draw a new side.
● The player who has claimed the most squares wins the game.
2-D Shape Headbands
Number of players: 2–6
You will need: 2-D shape cards (PCM 6), paper headbands
● Each player takes a 2-D shape card and puts it on their headband without looking at it (players can also work in pairs to do this).
● Each player, in turn, asks a yes/no question, such as: ‘Do I have 3 sides?’, ‘Do I have any curved sides?’, etc. As long as they are getting ‘yes’ answers they can continue asking. If they get a ‘no’, the next player starts asking their questions.
● Play continues until every player knows their shape.
Variations
Do I have 6 vertices?
No, my turn! Do I have 4 sides?
● Each player writes a 2-D shape name on a piece of paper and uses sticky tape to stick it to the forehead of the player to their left.
● 3-D Shape Headbands: Play as above, but using 3-D Shape Cards (PCM 7).
Strengthen
● Use the 2-D Shape Reference Guide (PCM 8) or 3-D Shape Reference Guide (PCM 9).
Deepen
● Play with both 2-D shape cards and 3-D shape cards.
Glossary
Analogue clock: A clock with a circular face and at least two rotating hands
Angle: The measure of turn; wherever two or more straight lines meet angles are formed
Anti-clockwise: Turning in the opposite direction to the way hands on the clock go
Array: Shapes or objects arranged in rows and columns
Bar graph: A graph that uses bars to show information
Benchmark: A standard or point of reference against which things can be compared (e.g. width of little finger is roughly 1 cm, standard bag of sugar is 1 kg)
Block graph: A graph that uses blocks to show information
Calendar: A table showing all, or sections, of a year broken up into months, weeks and days
Centimetre (cm): Unit of measurement used to measure length that is one
a metre, 1m = 100cm
Certain: Will definitely happen
Chance: The likelihood that a particular outcome will happen
Clockwise: Turning in the same direction as the way hands on the clock go
Combinations: Arrangements of groups of items in various ways
Commutative: Multiplication and addition are this, because the total/product is the same regardless of order
3 + 4 = 4 + 3 = 7
3 × 4 = 4 × 3 = 12
Core: The shortest part of a repeating pattern
Data: A collection of information
Decimal fraction: An amount (e.g. tenths) that is written using a decimal point (e.g. 0 6)
Decimal point: A dot that is written to separate whole numbers and decimal fractions (e.g. 0 6)
Digital clock: A clock that uses digits and a colon (not hands) to show the time
Dividend: The number that is to be divided into smaller groups:
divisor dividend or dividend ÷ divisor = quotient quotient
Division sentence: A number sentence that includes the division symbol (e.g. 4 ÷ 2 = 2)
Double: The result of adding a number to itself (e.g. 24 = 12 + 12)
Eighth:
One part when the whole is divided into 8 equal parts
Equal groups: Groups that have the same amount in each
Equilateral triangle: A triangle with equal sides and equal angles
Equivalent fractions: Fractions with the same value (e.g. 1 2 = 2 4 )
Factors:
Fifth:
Numbers that are multiplied by each other to get a product
One part when the whole is divided into 5 equal parts
Fraction: When a whole is divided into equal parts/amounts (e.g. 1 5 )
Fraction form: When we say or write fractions using their fraction names (e.g. one fifth)
Gram (g):
Unit of measurement used to measure weight that is one thousandth of a kilogram, 1kg = 1000g
Growing pattern: A pattern (or sequence) in which the values are increasing
Half:
One part when the whole is divided into 2 equal parts
Horizontal: Going straight across, or sideways, like the horizon. For example, a line that goes straight across from left to right, or right to left, is horizontal
Identity property: In multiplication, any number multiplied by 1 is the number itself: (e.g. 9 × 1 = 9)
Impossible: Will definitely not happen
Improper fraction: A fraction equivalent to or larger than one whole; the numerator is larger than or equal to the denominator (e.g. 3 2 )
Interval markings: A space between two marked points, that represents a measure or a value. For example, each interval below represents 100
1,000
Inverse: To do the reverse/opposite calculation
Kilogram (kg): Unit of measurement used to measure weight in the metric system
Likely: Will probably happen
Line (dot) plot: A graph that uses marks (usually dots or crosses) arranged above a number line to show information (frequency)
10 3 4 5
Line symmetry: A shape or object has line symmetry/ is symmetrical when one half is a mirror image of the other half
Litre (l): Unit of measurement used to measure capacity in the metric system
Maths symbols: Symbols used in maths to represent operations (e.g. +, –, ×, ÷) or relationships (e.g. <, >, =, ≠)
Measuring instrument: An item or object used for measuring
Metre (m): Unit of measurement used to measure length in the metric system
Millilitre (ml): Unit of measurement used to measure capacity that is one thousandth of a litre, 1l = 1000ml
Mixed fraction: Mixed number; a number written as a whole number with a fraction (e.g. 1 1 2 )
Mode: The value that occurs the most often in a data set
Multiples: Numbers that go up in jumps of a given number (e.g. some multiples of 5 are 5, 10, 15, 20, 25, etc.)
Multiplication sentence: A number sentence that includes multiplication (e.g. 5 × 2 = 10)
Octagon: A polygon with 8 straight sides and 8 angles
Pentagon: A polygon with 5 straight sides and 5 angles
Perpendicular: Meeting at a right angle. For example, these perpendicular lines meet to form at least 1 right angle
Pictogram: A graph that uses pictures to show information
Polygon: Any 2-D shape with straight sides
Possible: May or may not happen
Prism: A 3-D shape with two identical polygon shapes on opposite ends
Product: The result of multiplying numbers by each other (e.g. 5 × 2 = 10)
Proper fraction: A fraction smaller than one whole; the numerator is smaller than the denominator (e.g. 1 2 )
Pyramid: A 3-D shape with a polygon base and triangular faces that meet at a point
Quarter: One part when the whole is divided into 4 equal parts
Reflection: Also called a flip. A type of transformation which creates a mirror image; where a shape is flipped over a mirror line to face the opposite direction
Regular polygon: A polygon with sides and angles of equal measure/length
Remainder: The amount left over after dividing a number (e.g. 5 ÷ 2 = 4 R 1)
Repeating pattern: A pattern in which the elements are repeated
Right angle: Also called a square corner. An angle measuring 90 degrees. For example, wherever perpendicular lines meet, at least 1 right angle is formed
Right-angled triangle: A triangle with one right angle, and two perpendicular sides
Rotation: Also called a turn. A type of transformation where a shape or object is turned around a centre point
Rotational symmetry: A shape or object has rotational symmetry if, when turned less than a full turn around its centre point, it can match its original outline
Shrinking pattern: A pattern (or sequence) in which the values are decreasing
Slide: Movement that involves direction and distance
Square centimetre: A unit of measurement equal to a square measuring 1cm × 1cm
Square metre (sq m): Unit of measurement used to measure area in the metric system, 1m × 1m = 1 sq m
Survey: A way to collect data by asking people questions
Tally chart: A table that uses tally marks to show information (frequency)
1 sq m1m
Favourite ice cream Tally butterscotch
Tenth: One part when the whole is divided into 10 equal parts
Tessellation: A repeating pattern of shapes that fit together, with no gaps or overlaps
Timetable: A chart showing events organised according to a time schedule; often used to display lesson times, TV programs or transport times
Transformation: A change in size or in position for a shape. It can include reflection (flip), translation (slide) and rotation (turn)
Treble: Three times the same amount (e.g. treble 5 = 3 × 5 = 5 + 5 + 5)
Unlikely: Will probably not happen
Whole: All, everything, all of the parts or the full amount
Vertex (vertices): Also called a corner. Where 2 sides of a polygon meet on a 2-D shape, or where 3 or more edges meet on a 3-D shape
Vertical: Going straight up and down, at right angles to the horizon. For example, a line that goes straight up and down, not sideways, is vertical
Zero property: In multiplication, any number multiplied by 0 is 0
