CAMBRIDGE PRIMAR PRIMARY Y
Mathematics Teacher’s Resource
with
CD-ROM
Cherri Moseley and Janet Rees
1A
1 Counting to ten
Quick reference Core activity 1.1: Recognising and saying numbers up to ten (Learner’s Book pxx) Learners use number songs, rhymes and stories to say the numbers from one to ten, recognise the associated numerals and understand the meaning of counting.
Core activity 1.2: Counting to ten (Learner’s Book pxx) Learners accurately count to ten in a wide variety of situations.
Prior learning •
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Objectives 1A: Numbers and the number system 1Nn1 – Recite numbers in order (forwards from 1 to 100, backwards from 20 to 0). 1Nn2 – Read and write numerals from 0 to 20. 1Nn3 – Count objects up to 20, recognising conservation of number. number.
Learners must have recognition recognition of some spoken words for number. Playing at counting. Say the numbers numbers one to one to five (not 10 – this section extends them to 10) in order.
Vocabulary Voca bulary one two three four five six seven eight nine ten amount number how many? count •
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Cambridge Primary Mathematics 1 © Cambridge University Press 2014
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Core activity 1.1: Recognising and saying numbers up to ten
LB: pxx
rhymes for examples (CD-ROM)). Counting resources such as counters, straws, balls, Resources: Number stories, rhymes and songs (see Maths rhymes for sticks, beads and cubes. Materials for creating a washing line such as string and clothes pegs. Materials for practising writing numerals such as sand trays, foam, paint, chalk, pens, dough etc. Numeral practice photocopy photocopy master (CD-ROM); materials for practice photocopy master (pxx). (Optional: Shirts Shirts photocopy decorating and/or printing such as scrap paper and card, corks, buttons, bottle tops, and paint; large paper or card; empty plastic drinks bottles and coloured sticky tape/paper.)
Saying numbers to ten To say the numbers from one to ten correctly in the right order, learners need plenty of experience of hearing and saying the numbers. Read number stories, and sing or say number rhymes modelling actions for the learners to copy. Learners often have favourite number songs from their local culture that they request to hear and sing again and again. This repetition helps them to remember the numbers used and what they represent.
Understanding the meaning of counting Learners need to become fluent at counting to five initially, then to ten. At first, learners might simply copy the sounds so meaning needs to be added through lots of practical counting activities.
Opportunities for display Depending on the age ranges in your class, create an ‘Age display’. Display colourful numerals and pictures of the children around a sentence such as ‘We are 4!’; ‘We are 5!’ and/or ‘We are 6!’ You could make a border from birthday cards contributed by the learners after their special day. When a learner has a birthday, make sure they move from one display to another.
Use a range of counting resources such as counters, straws, balls, sticks, beads and cubes. There should be many counting rhymes and songs from the local culture; use these if the learners are familiar with them from pre-school clubs. Useful early ones often include finger actions, for example One One,, Tw Two o, Three Three,, Four Four,, Five Five,, Once I Caught a Fish Alive. Many rhymes count backwards. Ensure that counting forwards is secure before attempting to count backwards. Check learners are ready by doing the counting that the rhyme demands together first (e.g. counting the five little ducks or counting the currant buns in our example rhymes) before singing or saying a rhyme that counts backwards (in this case, Five Little Ducks Went Swimming One Day and Day and Five Currant Buns in a Baker’s Shop). Shop). If you have pictures of the items you sing about, peg these on a washing line and give learners the opportunity to peg them in order themselves and to add or remove them as the song is sung.
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Example: pegging on a washing line.
Model counting behaviour as you share the song/rhyme, sometimes using counting resources and sometimes using the learners themselves. If the numeral in the story is written on the page, then draw attention to it. As the learners become familiar with the shape of the numeral practise writing it in the air. Learners will copy your actions, so make sure that you write the numeral in the air back to front so that they see it the right way round and learn the shape correctly. Move on to writing numerals in wet and dry sand, then writing them using foam, paint, chalk and chunky pens and/or modelling them in dough and in many other ways before asking the learners to record on paper. If necessary, use the Numeral practice photocopy master when they are ready to write the numerals.
Example: writing the number ‘3’ in the air. Teacher view Learner view whilst whilst writing. teacher is writing.
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Learners who reverse numerals when writing, for example writing 3 more like a capital ‘E’; or learners who get confused between the appearances of two similar-looking numbers, for example 5 and 3 are commonly mistaken for each other by learners. Show them how to write it correctly, or count to identify the correct number. Learners who might know some larger numbers, for example the age of a sibling or a door number. Support them to find this number on a number line and to write it if they wish.
Summary •
Learners are able to recite the numbers one to ten in order and begin to recognise the matching numeral.
Notes on the Learner’s book Numbers (px): point to the numerals and say their name in order together. Learners might like to refer back to this page later to remind them of the numbers one to ten. Up to 10 (px): count the items and look at the shape of the matching numeral.
Check up! •
Sing a familiar song or rhyme together, allowing the learners to take the lead and supporting only when necessary.
Core activity 1.1: Recognising and saying numbers up to ten
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More activities Use the Shirts photocopy master to encourage learners to count or sing along the line, and to fill in the missing numbers.
My number (individuals) You will need materials for decorating/printing, such as scrap paper and card, corks, buttons and bottle tops, and paint. Learners readily recognise and say their age. Learners cut-out large numerals of their age and decorate it. Learners could print on their numeral using corks and other shapes dipped in paint. When a learner has a birthday, make sure they decorate a new number.
Order (groups) You will need paper or card for making large 1 to 10 number cards and resources for making a washing line, such as string and pegs. Make large number cards, with the number on both sides so learners can always see which number they are holding. Ten learners each hold a number card and move themselves into the correct order (from one to ten) in time with a chosen number song, which is being sung by the rest of the class. Ask each learner to give their card to a friend who doesn’t have one, then repeat the activity using a different song or rhyme. Start with songs and rhymes up to 5 first. These number cards could also be pegged on a washing line as the learners sing a counting song. They can also be removed one at a time when counting back from ten to one.
Number rockets (groups) You will need empty plastic drinks bottles and coloured sticky tape or coloured paper. Learners put a different number on each differently coloured rocket. Learners line up the rockets in order, with 1 at the far right-hand side of the line. Learners will enjoy counting back along the line of rockets and shouting ‘blast off’ after saying 1.
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1 Counting to ten
Core activity 1.2: Counting to ten
LB: pxx
Resources: (Optional: counting materials such as counters, straws, balls, sticks, beads, cubes, feathers, stones, beans, small b ells, pompoms, mini cars, assorted buttons, bottle tops as well as commercial sets; assorted containers for learners to count into, such as small bowls, empty boxes and cartons; number tracks; number cards for learners to label their counts with; a set of ten containers, each labelled with a different number. Provide equipment such as pens, paper and sticky labels for learners to make their own labels. Materials for decoration, such as paint, coloured paper, glue, pictures cut from magazines, pens and pencils; sheets of A4 paper and a stapler.)
Learners need lots of experience of counting to understand what a number really means, for example to understand ‘the threeness of three’. Songs, rhymes and stories help learners to get the words in the right order, but unless they count items one by one and realise that the last number said is the total, learners cannot really count. Stories often use contexts that the learners enjoy and this helps to give the counting a real purpose. Stories such as Goldilocks and The Three Bears, The Three Billy Goats Gruff and others provide lots of opportunity to count to three. You might be counting bowls of porridge, bears or goats. This helps the learners to recognise that anything can be counted. Each country will have its own familiar traditional stories. Some counting stories will lead to activities that the learners can carry out to practise counting. If a story uses ten black spots in a large variety of pictures, learners can then make their own pictures with a particular number of coloured spots. Stories which focus on counting legs could be followed up by learners creating their own creature with a particular number of legs. And so on. Actions and sounds can also be counted. Learners could tap drums, shake tambourines, clap or jump a particular number of times. They also need to count things they cannot touch, such as clouds or things that are simply out of reach. Opportunities for counting are all around us and learners will be happy to join in, even if the numbers go beyond the range they understand.
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Learners who frequently miscount and need more practice at touching and moving each object as it is counted. Encourage them to slow down and exaggerate their movements so they ca n be sure of what has been counted and what still needs to be counted . Learners who can confidently count objects up to ten. Challenge them with questions such as “What if there was one more? ”
Summary •
Learners are able to accurately count to ten in a wide variety of situations.
Notes on the Learner’s book How many? (px): ask learners how many shells there are in each group. They could then draw a group of shells for a counting number they know, or for a number that is missing from the learner’s book page.
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Show the learners a small handful of items and invite them to count them with you. Alternatively, begin to count as you clap and encourage learners to join in then take over.
More activities Counting box (individuals, groups or class) You will need counting materials such as counters, straws, balls, sticks, beads, cubes, feathers, stones, beans, small bells, pompoms, mini cars, assort ed buttons, bottle tops as well as commercial sets; assorted containers for learners to count into, such as small bowls, empty boxes and cartons; number tracks; number cards for learners to label their counts with; a set of ten containers, each labelled with a different number; pens, paper and sticky tlabels for learners to make their own labels. Create a counting box for the learners to explore when they have completed an activity or during free time. Make the box interesting and enticing by decorating it as a treasure chest or something else that will appeal to the learners. Add sets of counting materials in assorted containers and some number tracks. Make sure the sets are of interest and change them regularly to ensure the learners are curious enough to revisit the box. Provide small bowls, boxes or containers for the learners to count into and number cards for learners to label their counts with. You could also provide a set of ten containers, each labelled with a number. Provide equipment such as pens, paper and sticky labels for learners to make their own labels.
Number street (class)
Opportunities for display You will need empty boxes and materials for decoration. Make a street of houses from empty boxes and other materials. Learners can complete the houses according to the house number. So house number one has one window, one door, one of anything the learners would like to include (tree, bush etc.). Arrange the houses into a street.
Display the houses made for ‘Number street’ along a drawn road. Make matching gardens too. Ask questions such as “Who might live here? How can you tell which number this house is? ”
Core activity 1.2: Counting to ten
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Counting books (individuals or pairs) You will n eed sheets of A4 paper, a stapler, glue, pictures and d rawing materials. Fold three sheets of paper in half and staple in the middle to form a book. Start with a large number 1 on the inside front cover and continue to number 10 on the inside back cover. You could draw these numerals and photocopy the sheets before stapling together. Learners then draw or stick th e matching number of items on each page. Books could be themed: toys, bugs, animals and so on. Place the completed books in the book area for everyone to share. Alternatively, pair up the learners so that they interview one another to find out their interests, then illustrate the book according to those interests. When the learners deliver the counting books, make sure there is time for each pair to share the book together. Put the books in your reading area so that everyone can enjoy them.
Games book (ISBN 9781107646407) Race to school (pxx) is a game for up to four players. It reinforces accurate counting of small numbers. Dice grid (pxx) is a game for two players. It helps the learners to match their count and the numeral.
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1 Counting to ten
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1A
2 Playing with ten
Quick reference Core activity 2.1: Make ten (Learner’s Book pxx) Learners use a ten frame to practise finding number pairs to ten. Core activity 2.2: Ten take away (Learner’s Book pxx) Learners use a ten frame to practise finding ‘take away’ facts for ten using number pairs to ten.
Core activity 2.3: Doubles (Learner’s Book pxx) Learners use a ten frame to practise finding double 1, 2, 3, 4 and 5.
Prior learning •
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Count in ones to ten and beyond. Read and write numbers to ten and beyond.
Objectives 1A: Numbers and the number system 1Nn1 – Recite numbers in order (forwards from 1 to 100, backwards from 20 to 0). 1Nn2 – Read and write numerals from 0 to 20. 1Nn3 – Count objects up to 20, recognising conservation of number. strategies ) 1A: Calculation mental ( 1Nc1 – Know all number pairs to 10 and record the related addition/subtraction facts. 1Nc5 – Know doubles to at least double 5. and subtraction ) 1A: Calculation Addition ( 1Nc8 – Understand addition as counting on and combining two sets; record related addition sentences. 1Nc9 – Understand subtraction as counting back and ‘take away’; record related subtraction sentences. 1Nc11 – Add/subtract a single-digit number by counting on/back.
Vocabulary ten frame number pair (or bond) add equals take away double •
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Cambridge Primary Mathematics 1 © Cambridge University Press 2014
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Unit 1A
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Core activity 2.1: Make ten
LB: pxx
Resources: Packaging from, not for ten it ems (e.g. biscuits, pencils, egg carton). Ten frames photocopy master (pxx). Resources for counting: counters, cubes or other count ing objects in two different colours. 0–10 Number cards (CD-ROM). (Optional: a set of ten objects and a container that will hold the ten objects; a set of ten pictures or the Monsters hunt photocopy master (CD-ROM); a hole punch or scissors and string. Mystery number pair to 10 photocopy master (CD-ROM).)
Count with the learners how many fingers they have. Explain that ten is a very important number in our number system. We count in tens and use ten all the time, perhaps because we have ten fingers. You could show the learners some food or other packaging which contained ten items, to show that lots of things come in tens.
number pair to ten: two numbers that add together to make ten, for example 7 + 3 = 10.
Finding number pairs to ten
equals: has the same amount or value as; the sign is =.
Explain that because ten is a very useful number, we need to get to know it really well. Give each learner one ten frame from the Tens frame photocopy master. Count the squares with them. Give the learners ten counters (or cubes or other counting objects) in one colour and ten in another colour. Ask them to put a counter of the same colour on each square of their ten frame.
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“How many counters do you need of the other colour to fill the ten frame? ” The learners will tell you that there is no more room to add ot her counters. Tell them, “You are right: ten and 0 makes ten.” Swap one counter at the right-hand end for the other colour. “Now how many are there of the first colour? ” (Answer: nine) “How many of the second colour? ” (Answer: one). Say the number sentence, “Nine and one makes ten.” Continue in this way until all the cou nters have been swapped for the second colour. You could ask learners to record the number pairs on a sheet of ten frames by colouring in the squares, or by recording the number sentences. For example:10 and 0 makes 10; 10 + 0 makes 10; 10 + 0 = 10 or in some other way. Explain that our number pairs for ten are an example of combining two sets of objects together and this is known as addition. Repeat the number sentence, this time using ‘add’ or ‘plus’. For example, ‘7 plus 3 is 10’.
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Vocabulary
Unit 1A
2 Playing with ten
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Learners who make mistakes when counting the counters. Check that they are pointing to each counter and not missing one out or counting one twice. Provide further opportunities to practise counting . Learners who can predict the second number to make ten or recognise a pattern. Challenge them to find all the number pairs for 20.
Call out a number less than 10 and ask the learners to count on to 10. Explain that counting on from a starting number to a target number is another way of adding. Repeat this activity for other numbers less than 10 so that the learners gain confidence in counting on. Then extend the activity by calling out a number and asking them to call out the corresponding number pair without counting on. They can always return to using their ten frames and counters for the number pairs that they struggle to remember. Make use of the fact that we have ten fingers by practising quick additions to ten using fingers.
Opportunities for display Display a coloured set of ten frames showing all the number pairs to ten with the matching number sentences.
You will need to decide whether to continue the activity by matching the number pairs that are simply reversals, for example 3 and 7 or 7 and 3, or whether this is better left until the learners are more confident.
Summary •
Learners have begun to know the number pairs to ten and have learnt useful strategies to find out the number pairs that they cannot recall.
Notes on the Learner’s book Make 10 (px): learners use the ten frame and counters of two different colours to practise finding two numbers to make ten. They could then explore using three numbers to make ten, using counters of three different colours.
Check up! “Here is a set of number cards from zero to ten.” “Make ten with two cards.” “Which card do you have left over? ” “You need more cards to make all the number pairs for 10. Which numbers do you need (5 and 10)? ” “I have three blue counters. How many green ones do I need to make ten altogether? ” • • •
More activities Peek-a-boo (class) You will need the Tens frame photocopy master, a set of ten objects, a container that will hold the ten objects. Count a set of ten objects onto a ten frame with the learners. Tip the objects out into a container, making sure the learners know that there are still ten. The learners close their eyes and you remove some of the objects, holding them in your fist so learners cannot see them. When learners have opened their eyes they guess or work out how many objects you are holding. Show them how to count what is left onto a ten frame and count the empty spaces to find out how many objects you are holding. Verbalise what the learners found out, for example, “Seven in the pot and three in my hand makes ten altogether.” Play the same game with different numbers of objects, making sure that learners understand how many you are working with each time.
Core activity 2.1: Make ten
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Ten memory game (pairs) You will need a set of cards from the 0 – 10 number cards photocopy master, with one additiona l ‘5’ card. Shuffle the cards and place them face down in a four by three grid. Learners take it in turns to turn over two cards. If the two cards make ten, they can keep them; if not, they must return them face down in their original positions. The learner who collects the most cards is the winner.
Ten snap (pairs or groups) You will need two sets cards from the 0 – 10 number cards photocopy master with two additional ‘5’ cards. (Use one set of cards per player.) Shuffle the two sets of cards. Deal all the cards out to the players, face down. Players take it in turns to turn over their top card and place it in the middle of the table. Players call out ‘Snap’ when two consecutive cards make a number pair to ten.
Monster hunt (class) You will need a set of ten pictures that reflect learners’ interests or the Monster hunt photocopy master; a hole punch or scissors and string. Label the ten pictures from 1 to 10. Punch a hole near the top of each picture and tie a loop of string through the hole. Hang up the pictures in various places around the classroom/school and challenge learners to find them all. During the day, frequently check with the learners which pictures have been found and which are still hiding, by ordering the numbers from one to ten. You could extend beyond ten.
Mystery number pair to ten (class) You will n eed the Mystery number pair to 10 photocopy master. Read aloud the clues on the photocopy master to help learners find the mystery number pair to ten.
Games book (ISBN 9781107646407) Playing with 10(1): Making 10 (pxx) is a game for two players. It can be used to help learners recognise the different ways of making ten.
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2 Playing with ten
Core activity 2.2: Ten take away
LB: pxx
Resources: Resources for counting: counters, cubes or other counting objects. Ten frames photocopy master (pxx). (Optional: 0–10 Number cards photocopy master (CD-ROM); Mystery 10 take away photocopy master (CD-ROM).)
Explain to the learners that this is another activity to help us get to know the number ten better. Count from 0 to ten, forwards and back, as a class..
Finding number pairs for subtraction to ten Give each learner one ten frame from the Tens frame photocopy master. Count the squares with them. Give each learner ten counters (or cubes or other counting objects) and ask them to place one counter in each square. “ Can you see just by looking how many counters you have? ”
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Ask each learner to take one counter off the ten frame, from the right-hand end. Explain that we had 10 and we have ‘taken away’ 1. “How many do we have left? ” 1 9
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You could ask the learners to record this on a sheet of ten frames by colouring in the squares, or by writing down: 10 → 1 leaves 9; 10 − 1 leaves 9; 10 − 1 = 9, or in some other way. Tell learners, “Put the counter back where it was on the frame. Now take away two count ers. How many do we have left? ” If you wish to record, continue as before: 10 → 2 leaves 8; 10 – 2 leaves 8; 10 – 2 = 8 Continue like this until you have taken away all ten counters. You could also take away zero counters. Explain that ‘take away’ is another term for subtraction. A sk the learners to place 10 counters on their ten frame again. This time, tell them that we are going to take away 4 by counting back. Start at 10, then as you say ‘9’ remove one counter, then as you say ‘8’ remove another and so on until you have removed 4 counters and in doing so have counted back 4. Explain that this is another way they can subtract a number from 10.
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Learners who make mistakes when counting the counters. Check that they are pointing to each counter and not missing one out or counting one twice. Provide further opportunities to practise counting . Learners who can predict the next take away pair because they have recognised a pattern. Challenge them to find all the take away pairs for another number.
Example: using a ten frame to show 10 – 2 = 8. 2 8
Practise by calling out ten take away [insert a number less than or equal to 10], asking the learners to take away the number you say and tell you how many are left. Show the learners how to use their fingers to help. You may need to revisit or repeat this activity to enable all the learners to feel confident in taking away.
Summary •
Learners have begun to know the subtraction pairs for ten and have learnt a useful strategy to find out the subtraction pairs that they cannot recall.
Notes on the Learner’s book 10 take away (px): learners use the ten frame to practise finding number pairs for subtraction from ten.
Check up! “Show me ten fingers.” “Fold three fingers away; ten take away three leaves? ” “What if you folded four fingers away? ” “How many fingers do you need to fold away to leave six? ” Encourage learners to say the complete number sentence aloud. • • •
More activities Ten take away memory game (pairs) You will need a set of cards from the 0 – 10 Number cards photocopy master with an additional ‘5’ card. Shuffle the cards and place them face down in a 4 by 3 grid. Learners take turns to turn over two cards. If the two cards make ten, they can keep them; if not, they must return them face down in their original positions. The learner who collects the most cards is the winner. When the learners find pairs of cards to make ten, they must say the corresponding number sentence in order to keep the cards. For example, ‘10 take away 3 leaves 7’ or ‘10 take away 7 leaves 3’ to keep the cards.
Mystery ten take away (class) You will need the Mystery 10 take away photocopy master. Read aloud the clues on the photocopy master to help learners find the mystery take away number pair to ten.
Games book (ISBN 9781107646407) Playing with 10(2) : Take away from 10 (pxx) is a game for two players. It will help learners to recognise the different ways of making ten.
Core activity 2.2: Ten take away
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Core activity 2.3: Doubles
LB: pxx
Resources: Ten frames photocopy master (pxx). A piece of string or a stick to place across the ten frame. Ten cubes: five of one colour, five of another colour. (Optional: 0–10 Number cards (CD-ROM); different coloured dice and counters; Dominoes (CD-ROM).)
Remind learners that they have been finding out all about ten. Say “There was one number that we needed two of to make ten. What was that number? ” Learners should be able to tell you that this was five. Show learners a ten frame and place a piece of string or a stick, horizontally across the middle cubes. Put five counters of the same colour along the top row and five of a different colour along the bottom row. Remind learners of the number sentence “ five and five makes ten”. Now stack the five counters from the top row and then the five counters from the second row separately, away from the ten frame and say “Double five makes ten. What do you think ‘double’ means? ” Elicit that it means ‘two lots of, the same amount twice and multiply by 2’. You could talk about how sometimes people say they are ‘seeing double’, meaning they saw two of something. People might also say that they have a ‘double’, someone who looks exactly the same as they do, like an identical twin. Ask the learners if they think there is another number they could double to make ten. From their experience with the first two core activities, they should be able to say that only five will work. Continue to work in the same way to find double 1, 2, 3 and 4. You could also extend this to finding doubles to ten using two ten frames.
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Learners who are not sure what ‘double’ means. Make a tower of between two and five cubes and ask the learner to make another that is the same as yours. Explain “Now we have double the number of cubes because we have two lots that are the same.” Count the cubes in both towers and say, for example, “Double three is six.” Learners who are comfortable working with higher numbers. Challenge them to find out doubles to double ten.
Opportunities for display Display several towers made from cubes with a sign inviting learners to find doubles, and label them.
Summary •
Learners understand what double means and are able to find doubles of the numbers one to five.
Notes on the Learner’s book Doubles (px): learners can use the ten frame to practise finding doubles, up to double five.
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Check up! “How many cubes will you need to make two t owers that each have three cubes? ” (Answer: six) Learners say their answer and then make the towers to see if they were right. Repeat for other numbers from one to five.
More activities Finger doubles (class) Use the fingers on each hand to make doubles. For double 1, show a finger on each hand and bring them together saying “ Double one is two”. Continue for all the numbers to double 5, modelling the actions and words for the learners until they can do this for themselves.
Doubles memory game (pairs) You will need the 0–10 Number cards photocopy master to make two sets of 1 to 5 number cards. Shuffle the cards and place them face down in a 2 by 5 grid. Learners take turns to turn over two cards. If the two cards are the same that have to say the corresponding number sentence in order to keep the ca rds. For example, ‘Double four makes eight’ to keep the ca rds. If the cards are not identical, they must return them face down to their original positions. The learner who collects the most cards is the winner.
Double snap (two or more players) You will need two sets of cards from the 0 – 10 Number cards photocopy master. (Use one set of cards per player.) Shuffle two sets of the cards. Deal all the cards out to the players, face down. Learners take it in turns to turn over their top card and place it in the middle of the table. They call out ‘Snap’ for identical cards. To keep the cards the learner must then say the corresponding number sentence, for example, ‘Double three is six’ or the cards must be returned to the middle of the table and play continues.
Dice snap (two or more players) You will need a different coloured dice for each player and some counters. Learners each roll their dice. If both dice show the same number, the first player to say ‘double’ claims a count er. When all the counters have been taken, the learner with the most is the winner. Alternatively, the learner who first says the corresponding number sentence ‘Double three is six’ when the dice show 3, gets the counter.
Domino hunt (groups) You will need the Dominoes photocopy master. Spread out a set of dominoes face down. Learners take turns to pick up two dominoes. They discard all the non-doubles and keep the doubles. Who has collected the most doubles by the end of the game? Use the spots to find out the totals for double 0 (blank) 1, 2, 3, 4, 5 and 6.
Core activity 2.3: Doubles
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Ten frames
Original Material © Cambridge University Press, 2014
1A
3 Length
Quick reference Core activity 3.1: Measuring length (Learner’s Book pxx) Learners make observations and comparisons about length. They then put different lengths into order. Learners begin to understand that height is a length from top to bottom.
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Objectives 1C: Measure ( Length, mass and capacity ) 1MI1 – Compare lengths and weights by direct comparison, then by using uniform non-standard units. 1MI3 – Use comparative language, e.g. longer, shorter, heavier, lighter. 1C: Problem solving ( Using techniques and skills in solving mathematical problems ) 1Pt1 – Choose appropriate strategies to carry out calculations, explaining working out. 1Pt9 – Make a sensible estimate of a calculation, and consider whether an answer is reasonable.
Comparing and ordering measures (length). Using the language of measure (length). Comparing two lengths by direct comparison.
Vocabulary measure size compare guess estimate about the same as just over just under roughly length width height long short tall longer shorter taller longest shortest tallest •
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Core activity 3.1: Measuring length
LB: pxx
Resources: Giant footprints made from A2 paper (make sure they are all the same width and length as each other). Materials for learners to make their own paper feet: sheets of A4 paper, pencils and scissors. Non-standard measuring devices: paper, interlocking cubes, string or ribbon. 15 cm and/ or 30 cm rulers. (Optional: Stepping stones photocopy master (CD-ROM); 1–20 tracks from the Number tracks (chapter 4, pxx) for class display.)
We are aware that activities and discussions involving bare feet is no t always appropriate. If necessary, adapt this session to ensure all footprints are made with shoes kept on, or changed to hand prints.
Comparing and measuring lengths Show learners the giant footprints. Remind them what is mea nt by ‘length’ by indicating the straight line distance from heel to toe; and the ‘width’ by indicating the straight line from one side to the other at the widest part of the footprint. Discuss the length of the footprints. “What do you think could make a footprint this long? ” Accept all the answers given. “Why do you think that? Does it look like your foot? Is it the same as your foot? What is the same? What is different? Encourage use of vocabulary such as ‘longer’, ‘shorter’, ‘wider’, ‘less wide’, ‘more wide’. Ask:
“How can we find out what is the same and what is different about our footprints and the giant footprints? ”
Draw out that we need to compare the length, width and shape of the footprints. We can do this by measuring or direct comparison. Give pairs of learners a pencil and scissors and inform them that they are going to make their own footprints. Learners help their partner to draw round one foot and cut out their footprint. Ask learners to write their name on their own paper footprint
Learners compare the length of their footprint with the length of the giant footprints. They need to decide if they are going to use direct comparison (laying one on top of the other) or if they are going to use a non-standard measure. Show learners the non-standard units of measure and explain how they can be used: if we were using interlocking cubes for example, we would keep interlocking one cube to the next
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Vocabulary length: is the straight line distance from one end of an object to the other end. width: is the straight line distance across an object from one side to the other side.
length
width
height: is the straight line distance of an object from top to bottom. estimation: making a sensible guess based on previous knowledge.
until it matched the length of a giant footprint. We would then do the same with a different set of cubes for your own footprint and compare how many cubes made up each length. The learners should choose their own method and what the measure will be. Learners can draw pictures or make jottings to record their findings. Encourage them to explain their choices. “What do you notice about the length of your footprint against the length of the giant footprints? What do you notice about the width of your foot and the width of the giant footprints? (Encourage vocabulary such as ‘smaller’, ‘shorter’, ‘less wide’, ‘longer’, ‘wider’, ‘bigger’, ‘larger’ and so on.) Find out as much as you can about your footprint and the giant footprints. What do we need to think about? How can you record what you find out? ”
Look out for! •
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Once everyone has made and measured their footprints against the giant footprints, introduce the task of ordering all the footprints by length, including the giant footprint. This reinforces the idea of comparing lengths relative to one another. Encourage the use of vocabulary such as ‘longest’, ‘shortest’, ‘longer’ and ‘shorter’.
Estimating lengths Make sure learners understand what is meant by ‘estimating’ and encourage them to make estimates by asking questions such as: “How many of these footprints do you think will fit into this one? ” Ask them to explain their reasoning, then get them to check if they are correct by measuring. Discuss the results.
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Length and height Explain that height is a type of length. It measures from the top to the bottom of an object. Invite a learner to the front of the class and demonstrate their height. Ask learners if they think the giant who made the footprints is taller or shorter than the learner.
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Ask pairs of learners to measure the height of their partner and to record it. They can use whatever
Learners who find it difficult to estimate length with reasonable accuracy. Provide more opportunities that allow them to practise this skill. For example, the length of a pencil, a book, their table, their stride. Learners who have difficulty ordering two or more items according to their length. Check why learners are making mistakes. “Do you think we need to have the ends of the items at the same place? Is that an important thing to remember? ” Demonstrate with the ends of some items at the same place and then with the ends at different starting places. “Is there a difference? Which do you think will give the best result? Why? ” Learners who have difficulty measuring lengths. Allow more time for the skill of measuring to develop. Start with shorter items and provide different resources to measure with. For example, rigid cardboard strips with points marked might be more effective than ribbon or string that moves easily. Learners who have difficulty choosing appropriate strategies for measuring. Use the strategies of other learners in the class as a teaching point.
equipment they like. Ask learners to line up from shortest to tallest, discussing it as a class as
they do it. (Be aware of any personal issues regarding height.) Encourage use of vocabulary such as ‘tall’, ‘tallest’, ‘taller’, ‘short’, ‘shorter’ and ‘shortest’.
Opportunity for display •
End the session with further questions. “What have you found out about your footprint and the giant footprints? What did you do to find out? Did anyone do anything differently? What equipment did you use? How did you record what you found out? Did you use any new words today? Show or tell me what they mean.”
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Display the learners’ footprints in order of size. Use the giant footprints to create a ‘giant walk’ around the classroom or school.
Core activity 3.1: Measuring length
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Summary • • •
Learners are able to compare and order lengths (and heights) using comparative language. They can measure lengths using direct comparison and using non-standard measures. They begin to understand estimating.
Notes on the Learner’s book Giant footprints (px): provides a visual reference for the Core activity. The vocabulary ‘longer’ and ‘shorter’ is explained using diagrams. Height (px): use the pictures as a basis for discussion. Make sure learners understand the concept of height as a length.
Check up! •
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“Order the lengths of these pencils/books/ribbon from longest to shortest.” “Order the lengths of this range of objects.” (e.g. pencils, books, ribbons, string.) “Who is taller? [learner 1] or [learner 2]? ” “Who is the shortest person in the class? ” “Who has the biggest feet in the class? ”
More activities Stepping stones (class) You will n eed the Stepping stones photocopy master. Give each pair of learners one giant’s footprint, one Jack’s Mother’s footprint and one Jack’s footprint from page 2 of the photocopy master (there are multiple copies of each to reduce the amount of photocopying required). Explain that each one represents a footprint but do not tell them yet who each footprint belongs to. Ask the following questions to the class: “Which footprint is the longest? Which is the shortest? ” (Learners lift the bits of paper in the air in response to these questions). “One of these belongs to a giant, the other to Jack, who is 10 years old, and the other to his Mother. ” Show each footprint one at time and ask “Who does this footprint belong to? Why do you think that? ” Learners should be able to recognise that the longest, widest and largest footprint will belong to the giant and the shortest, narrowest and smallest footprint will belong to Jack. Display the stepping stone path for the whole class to see (learners should also have their own copy between pairs). Explain “The giant’s footprint is four stones long. Each time the giant takes a step, he moves forward four stones. ” Demonstrate that after two steps he has moved 8 stones along the path, and that as his footprint is 4 stones long, this is one ‘step’ for the giant. Ask: “ How many steps does it take the giant to reach Jack’s house? ” Give time for discussion in pairs and for the learners to move the giant’s footprint along the path, matching 4 stones of the footprint to the next four stones on the paths, and then take responses. Accept all answers and reasoning. (Answer: 9 steps) “How long is Jack’s footprint? How long is his Mother’s? Who will take more steps to reach Jack’s house, Jack or his Mother? Why? ” Learners discuss their ideas in pairs and then share their answers with the class. Learners should reason that as Jack’s Mother’s footprints are longer than Jacks, she will take less steps to get back home.
All in order (groups) Ask groups of learners to arrange themselves by height starting from shortest to tallest, or tallest to shortest. (Be aware of any personal issues regarding height.)
Games book (ISBN 9781107646407) Shoes and feet(1)–(3) (pxx) is a series of games for pairs, threes and the whole class. They can be used to practise length comparison and vocabulary, and to encourage discussion and reasoning.
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1A
4 Counting over ten
Quick reference Core activity 4.1: Number pairs less than ten (Learner’s Book pxx) Learners practise finding number pairs for numbers less than ten. Core activity 4.2: Ten and a bit more (Learner’s Book pxx) Learners are introduced to all the teen numbers using two ten frames and counters. They understand that teen numbers are ‘10 and a bit more’. They move on to order the numbers 1 to 20.
Prior learning •
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Count in ones to ten and beyond. Read and write numbers to ten and beyond.
Objectives 1Nn1 1Nn2 1Nn3 1Nn6 1Nn8 1Nn9 1Nc1 1Nc2 1Nc8 1Nc9 1Nc11
1A: Numbers and the number system Recite numbers in order (forwards from 1 to 100, backwards from 20 to 0). Read and write numerals from 0 to 20. Count objects up to 20, recognising conservation of number. Begin partitioning two-digit numbers into tens and ones and reverse. Use more or less to compare two numbers, and give a number which lies between them. Order numbers to at least 20, positioning on a number track; use ordinal numbers. 1A: Calculation ( Mental strategies ) – Know all number pairs to 10 and record the related addition/subtraction facts. – Begin to know number pairs to 6, 7, 8, 9 and 10. and subtraction ) 1A: Calculation Addition ( – Understand addition as counting on and combining two sets; record related addition sentences. – Understand subtraction as counting back and ‘take away’; record related subtraction sentences. – Add/subtract a single-digit number by counting on/back. – – – – – –
Cambridge Primary Mathematics 1 © Cambridge University Press 2014
Unit 1A
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Core activity 4.1: Number pairs less than ten
LB: pXX
Resources: Ten frames photocopy master (Chapter 2, pxx). Number pair frames photocopy master (CD-ROM). Resources for counting: counters, cubes or other counting objects in two different colours. (Optional: 0–10 Number cards photocopy master (CD-ROM); 1–9 dice (if not available use the 1–9 dice net photocopy master (CD-ROM); Target 5 – Target 10 photocopy masters (CD-ROM).)
Begin by counting to ten and back with the learners. Remind them of the importance of ten. Explain that we use all the numbers up to ten a great deal and it is useful to be able to spot these numbers when they a re split into two parts. Tell them you will be looking at number pairs to numbers less than ten. Show the learners a blank ten frame and ask them to write in the numbers as shown:
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Recognising number pairs to ten, and number pairs for targets below ten, is a good way to generate some simple addition and subtraction facts that will be useful for mental methods. It is also a good practical activity to reinforce addition as counting on and as combining two sets, and subtraction as counting back and taking away.
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Choose a focus number, such as five. Show the learners how to cut off all the numbers higher than five to create a five frame. Alternatively, use the Number pair frames photocopy master.
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Give the learners five counters (or cubes or other counting objects) in one colour and five in another colour. Ask them to put the same coloured counter on each square of the five frame. “How many counters do you need of the other colour to fill the five frame? ” The learners will tell you that there is no more room to add other counters. Tell them that they are right, “ five and 0 makes five”. Swap one counter at one end for the other colour. “How many are there of the first colour? ” (Answer: four) “How many of the second colour? ” (Answer: one). With the learners, say the resulting number sentence, “4 and 1 makes 5”. Continue in this way until all the counters have been swapped for the second colour. Accept number pairs which are simply
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4 Counting over ten
number pair (or number bond): two numbers that add together to make a particular number, e.g. 7 and 2 are a number pair for 9.
Look out for! Learners who find the numbers on the ten frame confusing. Replace their ten frame with a blank one of the appropriate shape for the target number.
reversals, for example 4, 1 and 1, 4 at this stage. Ask the learners to record the number pairs by colouring in the squares on a sheet of five frames, or by recording the number sentences. For example, 5 and 0 makes 5; 5 + 0 makes 5; 5 + 0 = 5; or in some other way. Focusing on five again, ask the learners to place one counter in each square of the five frame. Can the learners tell you how many objects they have used without counting them? Ask each learner to take away the counter from the square labelled ‘5’. Explain that we had five and we have taken away one. “How many do we have left? ” (Answer: four). You could ask the learners to record this by colouring in a five frame, or as shown here on the right.
Look out for! Challenge learners who find it easy to work out number pairs, to list or show the number pairs in a logical sequence them.
Example: diagram to record ‘five take away one is four’. 1
Ask learners to return the counter to its original place, then take away two counters. “How many have we left? ” (Answer: three). If you wish, record as before. Continue until learners have taken away five. You could also take away 0. Carry out the same activities using 6, 7, 8 and then 9 as the focus number. You might need to do these in further sessions.
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Example: diagram to record ‘five take away two is three’. 2 5
Summary •
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Learners have begun to know all the number pairs (bonds) for numbers less than ten, and they can record the related addition/subtraction facts. They have developed strategies for finding out the number pairs they cannot recall.
Check up! Use the following question stems for different target numbers up to ten. “If you take two away from five, how many are left? ” “Can you tell me a number pair for five? ” “Can you tell me all the number pairs for five? ” •
Notes on the Learner’s book Number pairs (px): use this page for class discussion. Ask: “Which number pair is each pair of hands showing? ” Encourage learners to explore number pairs for a particular number. Learners write or draw the other number pairs for the number shown by each pair of hands. Some number pairs cannot be easily shown using hands, for example six and two. Invite learners to come up with their own ideas.
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Core activity 4.1: Number pairs less than ten
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More activities Two hands game (class) This activity develops instant recall of number pairs up to ten. Say a number up to ten. Learners show you that number with their fingers. They must use both hands but can make a fist for zero. Pause the game occasionally and ask the learners to sort themselves into groups of matching number pairs. “ Does it matter which hand shows each part of the number pair? ” Discuss which number pairs are th e same. “Which number pairs cannot be made using two hands in this way? ” You could keep a record of how many different number pairs there are for each number; ask learners if they can see a pattern.
Adding number pairs (individuals or pairs competing against one another) You will n eed the 0–10 Number cards photocopy master and a 1–9 dice. Use the cards numbered from 1 to 9, shuffle them and place them face down in a pile. Choose a focus number from one to ten, such as seven. Turn over the top number card, the digit on this card is the first number in the pair to the target number. Learners/teams take turns to roll the dice once until one team rolls the number needed to complete the number pair using addition for the focus number. When this happen that learner/team gets a point and the card is put to the bottom of the pile and a new card is chosen. Work through the cards twice. The learner/team with the most points wins the game. (If the number on the card is larger than the focus number, learners need to realise that it is impossible to make the number pair through addition and so put this card to the bottom of the pile and select another). Extend the game to include subtraction to make the focus number. When a card is turned over that is higher than the focus number, instead of putting it to the bottom of the pile and selecting another card, learners need to roll the number which must be taken away from the card number in order to ma ke the focus number.
Target five to ten (for individuals) You will n eed the Target 5 – Target 10 photocopy masters. Learners circle all the number pairs that make the focus number. Number pairs could be across, down or diagonal. E ach number can only be circled once. There are several different ways to complete each target sheet, so challenge the learners to beat the best score.
Games book (ISBN 9781107646407) Rocket launch (pxx) is a game for two players. It can be used to give learners practise in adding number pairs to 12.
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Core activity 4.2: Ten and a bit more
LB: pXX
Resources: Ten frames photocopy master (Chapter 2, pxx). Counters. Tens and ones arrow cards photocopy master (pxx) (CD-ROM). Number tracks photocopy master 1–10 Number cards photocopy master (CD-ROM). For ordering numbers on a washing line: clothes pegs and string. (Optional: counting objects such as coins or cubes; tray or pot to drop coins/cubes into; Legs cards photocopy master (CD-ROM).)
Ask learners to remind you how many fingers they have and count them together. Remind them that ten is a very important number in our number system, so they already know ten very well. But numbers do not stop at ten, they go on and on. Ask the learners to count up as high as they can in order to determine how many teen numbers they know. If some learners are able to count all the way to 20, chant along as a class. If you want, you could display the 1–10 and 11–20 tracks from the Number track photocopy master. Ask learners if they know how to write the teen numbers in numerals and invite learners to do so at the front of the class. Learners might recognise some or all of the teen numbers (from extending Core activity 3.1or from home or elsewhere) but might not really understand their value; it is important that they realise these numbers are ten and some more. The following activity will help to reinforce this.
Partitioning two-digit numbers
Vocabulary arrow cards: also known as place value cards 1
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teen numbers: all the numbers with one ten and some ones, e.g. 11, 12, 13, 14, 15, 16, 17, 18 and 19.
Example: using ten frames and arrow cards to show the number eleven.
Display a blank frame from the Ten frames photocopy master for the whole class to see. It should be turned so that a row of two spaces is at the top. Draw a circle/cross in each space and check that the learners can tell you t hat there are ten circles/crosses. Draw an arrow card for ten below the ten frame, as per the example (1) on the right, then introduce them to an actual arrow card. Place a second ten frame alongside the first. Fill the second ten frame from the bottom up one circle/cross at a time to show learners how to make 11, 12 and then 13 all the way to 20; each time you place another circle/cross count on from ten. Remind learners that the completed frame on the left is ten, so each time you add a circle/cross to the other ten frame you have ten and some more. Show how to make ea ch number with arrow cards as you make it on the ten frames. See (2) on the right.
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Give each learner two ten frames and some counters. Show them a number between 11 and 20 using the Tens and ones arrow cards photocopy master and ask them to make it on their tens frames. Occasionally reverse the activity by showing them a number on the ten frames and asking them to show the matching number with their arrow cards. Note: It is important that you either follow up the session on 11 to 20 with a session focusing on ordering these numbers, or order the numbers on a washing line as the learners make them. This ensures that the learners begin to get the idea that each number is one more than the one before. Prepare a set of large 1 to 20 number cards. These could be themed according to the learners’ interests such as dinosa urs, flowers, stars, football shirts and so on, or simply write large, clear numbers, with each number on a single sheet of A4 paper. Give the large 1 to 20 number cards out to the learners. Make a washing line that is long enough to hold all the numbers and put it within reach of all the learners. Ask the learner who has the 1 card to come and peg their number on the far left of the washing line, so that all the learners can see it. Ask who has one more than one and invite them to peg their number next to 1. Keep asking who has one more until the number line is complete. Encourage the learners to count to help them name the next number, so that they understand that one more is the next counting number. You could complete one to ten before the 11 to 20 activity and the rest either as the activity progresses or immediately afterwards.
Look out for! •
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Learners who say ‘–ty’ instead of ‘–teen’. Show them that ‘ –teen’ is just ten with an extra ‘e’, so 17 (written ‘seventeen’), is just seven and is just seven and one ten. It is important that this is corrected early on to prevent future issues. Learners who clear both ten frames to prepare for the next number. Remind everyone that the ten part is not changing, so they can keep that ready. Each number is ten and some more. Learners who might be confident enough to make higher numbers. Give them the rest of the set of arrow cards and more ten frames and challenge them by giving them a particular number to make using both arrow cards and ten frames.
Return to the number line later or on another day. This time, ask a learner to remove a number which is one more than a particular number. If you have room, leave the washing line up for the learners to use regularly.
Beyond 20 Extend the activity (or revisit at a later date) by giving learners a third ten frame and a set of arrow cards including the 20 arrow card from the Tens and ones arrow cards photocopy master. Extend the numbers into the twenties. Learners work in pairs and take it in turns to make a twentysomething number using their arrow cards; then their partner has to make this number using counters on three ten frames.
Core activity 4.2: Ten and a bit more
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Summary •
Learners understand how to build numbers from 11 to 20 as ten and some more.
Notes on the Learner’s book Oh no! (px): all the teen numbers have fallen off the number track. Ask the learners to draw a number track starting with ten and finishing with 20, then put the numbers in the correct order. Some learners may need to see a number track in order to draw it.
Check up! •
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Ask learners to show you a teen number using counters. They should arrange the counters as though on ten frames, so that the number is clearly ten and a some more. Ask learners to write a teen, number and how they know what to write.
More activities Number line again (class) You will need large 1 to 20 number cards and the washing line and peg s. Give out the number cards but ask the learner with the 20 card to peg their number on the far right of the washing line. Ask who has one less than 20 and invite them to peg their number next to 20. Repeat until the number line is complete. Encourage the learners to count back from 20 to help them name the next number, so that they understand that 1 less is the previous counting number. Return to the number line later or on another day. This time, ask a learner to remove a number which is one less than a particular number.
Legs (pairs) You will n eed the Legs cards photocopy master. Shuffle the cards. The aim is to collect 20 legs. Players take turns to pick a card and keep it, adding up their total as they go along. Play continues until a player gets 20 legs or goes bust by collecting more than 20 legs.
Teen action (class) You will n eed the Tens and ones cards photocopy master; use the 10–20 arrow cards. For a quick filler activity, show the learners a teen number made from arrow cards and ask them to do a particular activity that number of times, counting their actions as they do them. Actions could include clapping; tapping their head, nose or elbow; slapping their knees; bouncing; stamping and so on. Ask one learner to repeat an action and challenge the rest of the learners to count the actions. Give several learners a turn.
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Counting together (pairs) You will need the 1–10 Number cards photocopy master; the Number track photocopy master and counting items; per pair of learners. Learners receive a ‘10’ card and a single-digit card and show the teen number using their fingers: learners take turns to show all fingers as the ten, with the other showing the ones. They then count their fingers from 1 to check the total and put out that number of items on the number track. Ask each pair of learners “What would be one more? What would be one less? ”
Core activity 4.2: Ten and a bit more
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