Place value everyday - media.openlearning.com

| NSW Department of Education

education.nsw.gov.au

Place value everyday This resource has been designed to support students’ development and understanding of place value. Tasks in this resource can be used as 5 – 10-minute daily tasks with your students. Each task card outlines what’s some of the key mathematical goals, required resources, instructions and prompts to support students in thinking and talking like mathematicians.

Key aspects of place value Each task card has been coded to emphasise the key aspects of place value.

Naming and recording Reading and writing or recording a number in words and symbols. This should also include naming the same quantity in equivalent ways. For example, we can name a half as one half, five tenths or fifty hundredths. We can also name it as four eighths, 0.5 and ½.

Making and representing Making and representing quantities that are proportional, non-proportional, canonical and non-canonical.

Calculating Applying knowledge and understanding of the place value system when operating with numbers using with multiplication, division, addition and subtraction.

Counting with understanding The process of matching number word sequence to items to answer the question ‘how many?’

Renaming Renaming involves talking about numbers in multiple ways without the use of representations, both canonical. For example, 67 is 6 tens and 7 ones and non-canonical 67 is 5 tens and 17 ones.

© NSW Department of Education, Jul-21 1

Comparing and ordering We can make comparisons between quantities and different collections. When comparing we look at the different ways numbers are composed and their relationships. Ordering involves placing numbers in order from smallest to largest or largest to smallest without attending to proportionality.

Task stage overview

Task name Early Stage 1 Stage 1 Stage 2 Stage 3 Stage 4

10 or bust

101 you’re out

3 tens in a row

Building towers

Capture ten

Decimats

Dicey addition

Garbage

Gone missing

Handfuls

Hit it!

Mastermind

Minute to win it

More, less or the same

Number busting

Numbers on rope

Order! Order!

2 Place value everyday

Task name Early Stage 1 Stage 1 Stage 2 Stage 3 Stage 4

Part whole bingo

Pattern block triangles

Place value game

Rekenrek duel

Tiled area questions

Place value key idea overview

Task name

Ren

amin

g (R

)

Com

parin

g an

d or

derin

g (C

/O)

Cou

ntin

g w

ith

unde

rsta

ndin

g (C

WU

)

Nam

ing

and

reco

rdin

g (N

/R)

Mak

ing

and

repr

esen

ting

(M/R

)

Cal

cula

ting

(C)

10 or bust

101 you’re out

3 tens in a row

Building towers

Capture ten Decimats

Dicey addition

Garbage

Gone missing

© NSW Department of Education, Jul-21 3

Task name

Ren

amin

g (R

)

Com

parin

g an

d or

derin

g (C

/O)

Cou

ntin

g w

ith

unde

rsta

ndin

g (C

WU

)

Nam

ing

and

reco

rdin

g (N

/R)

Mak

ing

and

repr

esen

ting

(M/R

)

Cal

cula

ting

(C)

Handfuls

Hit it!

Mastermind

Minute to win it

More, less or the same

Number busting

Numbers on rope

Order! Order!

Part whole bingo

Pattern block triangles

Place value game

Rekenrek duel

Tiled area questions

v

What’s (some of) the maths? • 10 can be composed in many different ways.• When we compose a quantity, we can use 2 or more ‘chunks’ (or

parts, or collections).

Collect resources • A game board (a number track, a

ten-frame, a drawing of 10 fingers, adrawing of a known numbercombination to 10)

• Counters• A dice, spinner or numeral cards

from 1-6• Pencils or markers.

Let’s play! • Have 3 turns each to roll the dice and place the matching number of

counters on your game board

• You can choose to miss one turn, but it cannot be your last roll• If you go over 10, you have ‘busted’ and are out of the game• The player closest to 10 after 3 rolls each is the winner• Players can play best out of 3, playing by making up to 10 as well as

backwards to zero.

10 or bust


Watch the video to learn how to play Let’s think and talk like mathematicians…

• How could we change the game to make itmore/less challenging?

• Did you work out a way to play this game sothat you didn’t lose?

| NSWMS PL Team V.1.2021

What’s (some of) the maths? • The position of a digit in a number determines its value.• In our number system, every time we collect 10 of something,

we regroup and rename it.

Collect resources • Paper• Markers or pen• 6-sided dice.

Let’s play! • Make a game board by drawing a 6 x 4 table• Label the first column as ‘tens’, th e second column as ‘ones’, the

third column as 'number' and forth column as 'total'• Each time you roll the dice, you have to decide whether the number

is representing ‘ones’ or ‘tens’. For example, if I roll a 3, I could use it as 3 ones (3) or 3 tens (which we rename as 30). If you choose to use your 3 as 3 ones, record the number in the ones column. If you choose to use your 3 as 3 tens (30), record your number in the left column

• Continue to play for 6 rolls• Once you write a number, you can’t change it• The winner is the player with the sum that is closest to 100 without

going over!

101 you’re out From Marylin Burns


Watch the video to learn how to play

Let’s think and talk like mathematicians… • How could you use your original game board

to get closer to 100 than you did in your firstgame?


What’s (some of) the maths? • Knowing numbers that nest inside other numbers (having part-

part-whole number knowledge) is helpful when solving problems.• There are many ways of combining quantities to find the total.

Collect resources • 2 different coloured markers• Paper or your workbook• A 0-9 dice (a spinner or playing

cards A-9).

Let’s play! • Draw a 3x3 grid as a game board (like noughts and crosses game

board)• Players take turns to roll the dice and write the number in one of

their boxes• The goal is to be able to write two numbers in each box that

combine to make 10• Players continue taking turns until a player has been the first to

make 3 tens in a row.

3 tens in row


Let’s think and talk like mathematicians… • How did you use what you know to help you

solve what you don’t know?• Did you work out a way to play this game so

that you didn’t lose?



What’s (some of) the maths? • Numbers are made up of smaller numbers (part-part whole).• We can use knowledge of part-part whole relationships to

determine ‘how many more’. For example, because we know thatinside of 7 is 5 and 2, we also know that 7 is 2 more than 5.

Collect resources • Some blocks or LEGO• A dice, numeral cards 1-6 or

spinner• Pencils or markers.

Let’s play! • Choose 4 numbers to build as your towers (for example, 5, 7, 11 and 3)• Take turns to roll a dice and use the number of bricks to build up

your towers• Towers can be built up in any way you choose• Take turns to build up your towers until one player gets the exact roll

to complete the last tower• You can also play this in reverse.

Building towers


Watch the video to learn how to play.

Let’s think and talk like mathematicians… • Can you determine who has more/less blocks and

who is closest to the target number? How do youknow?

• If you were to play the game again tomorrow, whatis one thing you would do differently? Why?


Collect resources

•• Paper • Markers or pencils

What’s (some of) the maths? • Using the ‘make ten’ (also sometimes called ‘bridging to ten’ or

‘using landmark numbers’) helps me to solve problems flexibly.For example, when I see 6 and 9, I can adjust the numbers to 5and 10.

Let’s play! • Shuffle your cards• Turn over 2 cards• Work out: Can you capture a ten? If you can, record your cards in

the appropriate column before you put them at the bottom of thepile. Then, have another turn

• If you can't capture a ten, put your cards at the bottom of the pileand take 2 more cards.

Capture 10 From Cathy Fosnot and Antonia Cameron


Watch this video to learn how to play

Let’s think and talk like mathematicians… • Is there more than one way we can visualise

dots moving to capture ten?• Is your strategy the same or different as

someone else’s?

Collect resources • A deck of cards A-10, ten-frame and

dot cards 1 – 10 • A marker • Gameboard.


What’s (some of) the maths? • In our number system, every time we collect 10 of something, we

regroup and rename it, for example, we rename 10 tenths as onewhole.

Collect resources • Decimat board game• Coloured pencils• 1x 0-6 sided dice• 1x dice labelled 1/10, 1/100, 1/100, 1/ 1000,

1/1000, 1/1000. (you can use masking tape to cover a regular 6-sided dice.

Let’s play! • Players take it in turns to roll the 0 -9 sided dice as well as the tenths,

hundredths or thousandths dice or spinner. For example, if a you roll a 5 and hundredths, you create 5 hundredths or 5/100

• Players then record what they have rolled as a fraction, a decimal and colour in 5 hundredths of the game board using the same colour

• As the game progresses each player calculates their cumulative total on their game board

• A new colour is chosen for each roll• You can further divide you game board if required• The first player to reach one or closest to one after an agreed amount of

time is the winner.

Decimats From Anne Roche


Read about and find download resources in this article by Anne Roche.

Let’s think and talk like mathematicians… • How can you strategise to improve your

chances of winning the game?• What strategies did you use to keep track of the

cumulative total?


What’s (some of) the maths? • The position of a digit in a number determines its value.• Mathematicians can use their mathematical reasoning to

strategise to improve their chances of winning a game.

Collect resources • A 0-9 dice or 0-9

spinner• Some paper• Pencils or markers.

Let’s play! • Find a partner and a 0-9 dice or spinner• Draw your gameboard so you each have the same one. (We used

this one to start with: _ _ _ + _ _ _ + _ _ _ = ________ You can startwith something different if you like)

• Each player takes a turn to spin the spinner and decide where toplay that digit in your number sentence (equation)

• Spin the spinner 9 times each• The person whose sum is closest to 1000 is the winner!

Dicey additionFrom NRICH Maths



Let’s think and talk like mathematicians… • Why did you decide to place that number there and give

it a value of ___?• What is the ideal number to roll for each place value

position?


What’s (some of) the maths? • When we count, number words always have the same order.• We can use knowledge of the counting sequence to determine

the number before and the number after.

Collect resources • Playing cards A-10.

Let’s play! • Using a full deck of playing cards, deal 10 cards face down in front of

each player, making a row of ten. The rest of the cards are then placed in the middle as a draw pile

• Player one draws a card, let's say it’s a 6. They find their sixth card in the row, remove it and place the 6 they drew. This is now located in the sixth position in the counting sequence as you count by ones, starting from zero

• Player one then determines whether they can place their card in their row

o if they can go, they place the card and draw another one.o if they can’t go because the number has already been placed or

they draw a picture card, their turn is over• The first person who fills in their entire set of 10 cards is the winner.

Garbage


Let’s think and talk like mathematicians… • Can you describe the position of one of your

cards using before, after, more or less? For example, 6 is 2 less than 8 and 2 after 4.


What’s (some of) the maths? • There are a few patterns in place value, for example, in each

period, there is a ‘ones’, ‘tens’ and ‘hundreds’ place.• Mathematicians can use what they know to help them solve what

they don’t know.

Collect resources • A hundreds chart puzzle with

an identified unknown piece.• Piece of paper• Markers or pencil.

Let’s play Using the unknown puzzle piece, can

you investigate and

answer the following questions? • What numbers might be on the unknown piece?

o Can you find one possible solution?o Can you find some solutions?o How will you know if you’ve found all the possible

solutions?• What can’t the numbers on the piece be?• What if the piece had to be in a particular orientation? What

might the numbers be then?• What if a number, such as 65, has to be in a particular location?

What might the numbers be then?

Gone missing Developed by Peter Sullivan (2017)


Let’s think and talk like mathematicians… • How did you determine what the unknown

pieces were?• What can’t the numbers on the piece be?


What’s (some of) the maths? • We can use familiar structures such as ten frames, to help us

determine how many, by looking and thinking.• Collections can be quantified in many ways.

Collect resources • Items such as counters, lima

beans or pasta• Pencils or markers• Paper.

Let’s play! • Take a handful of counters (or lima beans or pasta)• Hold the objects in your hand and imagine how many you have• Record your estimate• Describe what that collection might look like by visualising and

imagining• Organise your collection so that someone can determine how

many items there are by looking and thinking.

Handfuls Adapted from Ann Gervasoni, Monash University. Published on reSolve - Counting handfuls


Watch the video to learn how to play. Let’s think and talk like mathematicians…

• Compare the different ways you can arrange thecollections:

o Write down 3 things that are the same anddifferent about the way you organised yourcollections.


Collect resources • Dot cards • Approximately 40 counters• Paper• Markers or pencils

What’s (some of) the maths? • We can use familiar structures such as ten frames, to help us

determine how many, by looking and thinking.• Collections can be quantified in many ways.

Two Handfuls Adapted from Ann Gervasoni, Monash University. Published on reSolve - Counting handfuls


Let’s play! • Take two handfuls of counters (or lima beans or pasta)• Hold the objects in your hands and imagine how many you have• Record your estimate• Organise your collection so that someone can determine how

many items there are by looking and thinking• Is there any other ways you can arrange your collection so we can

tell how many by looking and thinking?

Let’s think and talk like mathematicians… • Compare the different ways you can arrange

the collections:o Write down 3 things that are the same

and different about the way youorganised your collections.

Collect resources • A large collection of

counters.

Watch the video to learn how to play..


What’s (some of) the maths? • We can use our place value knowledge to determine which

landmark number is closest to any given number.• We can use a range of flexible strategies to determine the

difference between two numbers.

Collect resources • 2 markers• Some paper• A 0-9 dice (you can also

use playing cards A-9 ornumeral cards).

Let’s play! • Draw up your game board (in this game, we were working with 3-

digit numbers but you can use larger or smaller numbers if you like)• Select a multiple of hundred between 100 and 900 to be your target

number

• The person with the most letters in their surname goes first• Take it in turns to roll the dice and use the digit somewhere in your

number• Once the digits are full, players read their number and determine

how far they are away from the target number. The player who isclosest to the target number wins a point.

Hit it!From Mike Askew


Let’s think and talk like mathematicians… • What strategies did you use to hit your target

number?• How did your strategy differ from your partners?



What’s (some of) the maths? • The position of a digit determines its value.• Mathematicians can use their mathematical reasoning to

strategise to improve their chances of winning a game.

Collect resources • A pencil• Paper.

Let’s play! • Each player writes down a 3-digit number (with no repeating digits.• Each player draws up their game board (a table with 3 columns:

'guess', 'digits', 'places')

• Players take turns to guess a 3-digit numbero Their opponent tells them how many digits are correct and how

many are in the correct placeo Players record their guess, the number of digits that are correct

and the number of digits that are in the right place. Players then use this information to refine their guesses

• The first player to correctly guess their opponents' number is the winner!

• You can choose to play using 4, 5 and 6-digit numbers.

Mastermind From Mike Askew



Let’s think and talk like mathematicians… • What are some of the strategies you used to

determine your next guess?


Collect resources • Dot cards • Approximately 40 counters• Paper • Markers or pencils

What’s (some of) the maths? • Collections can be quantified in many ways.• You can use familiar structures to help you count in multiples.• Mathematicians use a range of representations to communicate

ideas.

Let’s play! • Teams are made up of two players, one rolling the die and the other

collecting the chosen materials for example, counters

• Set a timer for one minute• Once the time commences, work together rolling the die and

collecting materials. This continues until the your minute is up• Teams then organise their collection to prove how many they have

just by looking and thinking.

Minute to win it From Doug Clarke and Anne Roche



Let’s think and talk like mathematicians… • Visualise what the collection would look if you

had 1 ten more? What would that look like?Describe the mental picture you’ve made to aclassmate and ask them to draw/make it.

Collect resources • A large collection of

counters • One dot dice per team• A timing device.


What’s (some of) the maths? • Knowing how numbers relate to other numbers helps us to solve

problems.• Knowing one more than, 2 more than, one less than and 2 less than

helps us with things like:○ identifying the number before and after○ counting forwards and backwards.

Collect resources • More or less cards (4 or 5 sets)• Number cards (2 sets)• Counters• Cup or bowl.

Let’s play! • Player one takes a number card, places it face up and puts that

number of counters in the cup• Player 2 takes one of the more-or-less cards and places it next to

the number card. If it is a more card, counters are added to the cup, if it is a less card, counters are removed

• Both players predict how many counters are in the cup• The counters are then emptied and counted.

More, less or the same From Van de Walle, Karp, Bay-Williams, Brass and Bentley


Scan this link to access resources

Let’s think and talk like mathematicians… • What are some ways that we could record our thinking

that shows the total number of counters in the cup?


Number busting From Professor Dianne Siemon

What’s (some of) the maths? • You can work out how many there are in a collection (you can

quantify a collection) in different ways.• Mathematicians can see the same collection in different ways.

Collect resources • A number of the same items

(for example, pasta pieces,counters, pencils or LEGO)

• Pencils or markers andpaper.



Let’s play • Choose a number such as 7 (or you may wish to bust 27)• Get the amount of items for that number. (for example pasta

pieces, counters or pencils)• Organise your items• Describe your collection• What other ways you can organise your items?• Describe your other ways• You may like to use a mathematical structure such as a ten-frame

to help you.

Let’s think and talk like mathematicians… • Were you surprised by all the different you

could organise your collection?• What did your structure help you notice? (For

example, ten-frame, dice pattern).


What’s (some of) the maths? • We can use our knowledge of place value to order and sequence

numbers.• We can compare different collections by looking at the different

ways numbers are composed.

Collect resources • Rope• Numeral cards or

sticky notes• Pegs.

Let’s play! • Determine the numbers you wis h to have at the start and end of

your rope. This can include any range of numbers, includingdecimals and negative numbers

• Using sticky notes, write 5 numbers that range between yoursmallest and largest number

• Order and sequence the sticky notes along the length of rope.Sequencing requires you to order numbers in relation toproportion of rope as well as relative to other numbers. Use pegsto hold sticky notes or numeral card in place.

Numbers on a rope From Professor Dianne Siemon


Let’s think and talk like mathematicians… • What knowledge and thinking did you use to

sequence your numbers on the rope?• How can we check that the numbers are sequenced?


What’s (some of) the maths? • We can use a range of flexible strategies to determine the

difference between two numbers.• We can use our knowledge of place value to order numbers from

smallest to largest and largest to smallest.

Collect resources • Sticky notes (or blank number cards)• Markers• 0-9 dice (you could also use playing

cards, a spinner or numeral cards).

Let’s play! • Roll the dice and create and record a 2-digit number on the

sticky note. (This game can also b e played using 3, 4 and 5-digitnumbers)

• The sticky notes are to begin in the order that the numbers wererolled

• Repeat until you have 4 numbers• Order them from smallest to largest, and largest to smallest in

the fewest moves possible, moving adjacent cards only.

Order! Order! From Mike Askew


Watch the videos to learn how to play Order! Order!

Let’s think and talk like mathematicians… • What knowledge and thinking did you use to

order your numbers?• How do you know the numbers are ordered in

increasing or decreasing value?


What’s (some of) the maths? • Numbers can be broken up into smaller parts (part-part-whole).• Different representations of quantities can help us to see different

ways of partitioning.

Collect resources • Part-whole bingo game boards• Part-whole bingo spinners• Pencil• Counters.

Let’s play! • Spin the spinner two times• Find the total of your two spins• Place this total number of counters on the game board• The counters can be placed on one column or they can be shared

between columns, however, a column must be completely covered (for example, if a player spins a total of 6, they can completely fill a column with 4 spaces available and a column with 2 spaces available)

• Take turns and work as a team to cover all the columns on the game boards.

Part-whole bingoFrom Cathy Fosnot and Antonia Cameron


Let’s think and talk like mathematicians… • Can you explain why you can or cannot place

your amount in a particular space on the gameboard?


What’s (some of) the maths? • Numbers can be broken up into smaller parts (part-part-whole).• Different representations of quantities can help us to see different

ways of partitioning.

Collect resources • Pattern blocks (minus

the narrow rhombusesand squares)

• Pencils or markers.

Let’s play! How many blocks you can use to build a triangle from pattern blocks?

• Write a list of numbers from 1 - 20• Using pattern blocks, can you build a triangle for each of the

numbers to 20?• When you create a triangle, write an equation for that number

and add it to your list. For example, if you make a triangle using 6 blocks, you could write 3 triangles plus 3 trapezoids equals 6 or 3+3=6.

Pattern block trianglesFrom Math for Love


Let’s think and talk like mathematicians… • Were there some target numbers that were

harder to make triangles for than others? Why or why not?


Scan link to view Math for Love website

What’s (some of) the maths? • The position of a digit determines its value.• We can use our place value knowledge to compare and order

numbers.

Collect resources • Place value game

board (link below)• Dice• Marker or pencil.

Let’s play! • Each player has a game sheet and takes it in turns to throw 2 ten-

sided dice• The numbers are used to create 2-digit numbers, for example, a 5

and a 2 could be recorded as 25 or 52• Players record their numbers in the most appropriate position

between zero and 100• If numbers cannot be placed, the player misses his/her turn.• The winner is the first to fill all places.

Place value gameFrom Professor Dianne Siemon


Let’s think and talk like mathematicians… • Can you explain why you decided which number to

rename tens and which to rename ones?• If you were to replay your game again, are there any

moves you would change and why?


Scan link to view download the game board

What’s (some of) the maths? • Tools such as rekenreks can help us see important relationships

such as the way smaller numbers nest inside bigger numbers.• Mathematicians use what they know about numbers to solve

problems in multiple ways.

Collect resources • A rekenrek each• A set of numeral cards (0-20)• Some paper• Markers or pencils.

Let’s play! • Shuffle the number cards and place them in a pile,

number side face down

• One player turns over a card• Players then take turns in making the number using the

Rekenrek in one or 2 slides• Each player records their thinking on the same piece of

paper• The winner is the last player who was able to make a move

that has not already been recorded.

Rekenrek duel



You can learn how to make a Rekenrek here.

Let’s think and talk like mathematicians… • How can you use colour and the structure of

the rekenrek to help you make a move?


What’s (some of) the maths? • We can compose and decompose numbers in many different

ways.• Different representations of quantities can help us to see

different relationships between numbers.

Tiled area questions From Steve Wyborney


Scan this link to access resources


Asking effective questions Asking effective questions plays a vital role in engaging students in inquiry and prompting them to construct explanations to help find solutions to tasks. The Asking effective questions article provides examples of questions that can be used when engaging students to think and talk like mathematicians. (Ontario Ministry of Education, 2011.)

Variations and considerations • Use varying representations of this stimulus for future number

talks. Further resources can be found using the link above.• This task can be adapted by changing the value each coloured

square represents.

Scan this to read the 'Asking effective questions' article

Let’s talk If the blue square equals ¼ what is the area of the shape?

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