The purpose of this unit of sequenced lessons is to develop knowledge and understanding of the place value structure of the numbers from ten to twenty.

- Instantly recognise patterns for teen numbers.
- Make groups of ten and represent teen numbers with materials.
- Recognise and record words and symbols for teen numbers.
- Understand that in a teen number the 1 represents one group of ten.
- Expand teen number notation and understand simple place value.
- Understand and apply a ten for one exchange.
- Understand how to decompose a ten in order to subtract.

When students meet ten they meet a two-digit number for the first time. They begin to become aware that there are no more numerals to learn and we just ‘recycle’ them. This is their entry into the structural world of our tens based number system.

They are introduced to the language of digits, place and value. It is a considerable conceptual shift for children to move from a face value understanding that a numeral represents a number of units that can be counted, to a place value understanding in which a numeral can represent a group or a number of groups that are in themselves made up of units that can be counted. This is is a complex idea.

As children study teen numbers and their meaning and structure (rather than simply ‘saying’ them in a counting sequence), the focus is on developing the understanding that the value of a digit depends on its place. This is not trivial and it is made more challenging by the language of teen numbers.

Children often confuse the number names such as ‘fourteen’ and ‘forty’ because the adult enunciation of the word endings is often unclear. In hearing ‘fourteen’ children may expect to see the 4 appear first in the symbolic form because that is the number that comes first when they say it. Seeing 14 and hearing ‘four – teen’ therefore has the potential for confusion.

Children need many opportunities to make these numbers with materials. When using place value material for the first time, children need the opportunity to group single units to make one ten. By doing this they come to understand that ten **‘ones’ **or units do in fact comprise one '**ten'**. The first equipment to use therefore is that which can be physically grouped, one by one, to make or compose one group of ten, or a ‘ten’, and be able to be unpacked or decomposed again into ten ones. When this is complemented by symbolic recording that accurately matches the representation of the number, understanding of two-digit notation is developed. Equipment in which the tens are already pre-grouped can be used once grouping to make ten is well understood.

It is a considerable shift for children to then use materials in which the ten looks completely different from the ones (for example, money) and to trust the 'ten for one' trade. The greatest abstraction is of course the digits in our number system where the tens and ones look exactly the same but it is only their place that tells their value.

In depth exploration of place value with teen numbers is essential if our students are to work with real understanding of the numbers within our number system.

The activities suggested in this series of lessons can form the basis of independent practice tasks.

#### Links to the Number Framework

Stages 2-4

The learning opportunities in this unit can be differentiated by providing or removing support to students and by varying the task requirements. Ways to differentiate the tasks include:

- Introducing fewer activities in each session to those students who need more support.
- Working with the numbers 11-15 before introducing the numbers 16-19.
- Using some of the suggested activities as independent activities for students who need greater challenge.

Using the place value language structure within Te Reo Māori to develop and reinforce the understanding that teen numbers represent “ten and” is an adaptation that supports Te Reo, the identity and language of Māori students, and the conceptual understanding of teen numbers.

- Tens frames (Material Master 4-6)
- Nursery or ice-block sticks
- Elastic hair ties or rubber bands
- Plastic beans
- Plastic containers
- BSM 9-1-48 (if available)
- Arrow cards (Material Master 4-14)

#### Session 1

SLOs:

- Instantly recognise patterns for teen numbers.
- Make groups of ten and represent teen numbers with materials.
- Recognise and record words and symbols for teen numbers.

__Activity 1__

- Show the students single tens frames. Have them show the same number of fingers as the number of dots, say and write the number with their finger in the air or one the mat.

- Show two tens frames, one of ten and the other of a number less than ten, together making a teen number. Have students ‘write’ with their finger how many dots they see. For example:

13

Repeat with several teen numbers.

- Write the numbers 11 – 19 in symbols and words on chart paper, highlighting the inconsistencies of the language and exploring for fun alternative forms of some of the teen numbers, for example, eleven (oneteen), twelve (twoteen), thirteen (threeteen), fifteen (fiveteen). For each word, as appropriate, underline
__teen__in the word, practice saying it and hearing the final consonant, ‘n’. Make the connection between this ‘teen’ word and ‘ten’. Retain this chart to add to later.

- Ask what the students notice about all of these numbers. (They all have teen at the end and are ten and ‘something’). They are known as teen numbers.

__Activity 2__

Have the students work in pairs to play **Teen Pairs**.

(Purpose: to recognise and match teen number representations and the words ‘ ten and ____’)

Students place between them two piles of cards face down (Attachment 1). Pile 1. Tens frame teen number cards (showing two tens frames) , Pile 2. Word Ten and _____ cards.

Students take turns to turn over one tens frame teen number card and say the number of dots they see. They then turn over a word card and read the words aloud. If the tens frames and word card match they keep the matching pair and the winner is the student with the most pairs.

For example:

__Activity 3__

- Have students now work to ‘make’ their own group of ten. Give each pair forty nursery or ice-block sticks, two elastic hair ties, pens and chart paper.

- Have each student choose and write in symbols a number from eleven to nineteen and take that many sticks. Have them count out and make one bundle of ten using the hair tie, then write and draw what they have. For example:

12 is ten and two - Have them unbundle and return their sticks to the centre then repeat with another teen number making use of spare sticks as required.

- Ask the students to return to the whole group with their drawings, keeping them hidden. Have the students take turns to describe to the class/group what they have drawn, and ask a classmate to say what number it is. The drawing is then shown.

- The teacher concludes by recording the ‘ten and _________’ words beside each of the teen numbers on the class chart begun in the earlier activity. Also consider exploring together the Place Value nursery sticks animation, available from https://e-ako.nzmaths.co.nz/modules/PVanimations/

#### Session 2

SLOs:

- Make groups of ten and represent teen numbers with materials.
- Recognise and record words and symbols for teen numbers.
- Understand that in a teen number the 1 represents one group of ten

__Activity 1__

- Have students sit with a partner. Tell them that each pair is going to be making teen numbers on their fingers and ask them to discuss how they will do this. Look and listen for those students who immediately identify that one of their pair will be the ‘ten person’, holding up ten fingers each time.

- Hold up a mixture of cards with number names in words, symbols and those reading ‘ten and ___’. (Attachment 2). Each time, give the card to the first pair to achieve the cooperative representation on their fingers.

- The teacher makes a teen number from nursery or ice block sticks, having the students count to ten as the ten bundle is made.

Hold up the ten bundle and ask, “Do I still have ten sticks here?” (yes) “How many bundles of ten do I have?” (1). Record on the chart, for example, I have fifteen. 15 is ten and five. 15 is 1 ten and 5 ones. Discuss the language of ‘ones’ and that sometimes ‘ones’ can be called ‘units’.

- Model one more example then have the students individually draw and write about three of their favourite teen numbers. For example "12 is 1 ten and two ones".

__Activity 2__

If available, have the students work in small groups or pairs to explore, find and display the four matching cards in the BSM 9-1-48 card game.

Alternatively have the students make a class puzzle matching game. Provide each student with card, pens and scissors. Have them make their own puzzle pieces which can then be combined with those made by their classmates and mixed up to make a matching pairs game.

__Activity 3__

- Return to the class chart started in Session 1. Record Māori words for teen numbers, highlighting ‘tekau ma’ is ‘ten and’, connecting this mathematics language with the other expressions already recorded.

- In small groups, using BSM 9-1-48 cards, students play
**Teen Teams**(purpose: to match word, pictorial and symbol representations of teen numbers).

Students deal out 7 cards each. The remaining pile of cards is placed in the centre of the group. Students take turns to ask one other player for a card needed to complete a set of 5 teen family cards. If the other player does not have the card sought the requesting player takes one from the pile. As sets are complete, students place these in front of them.

The winner is the player with the most complete sets.

#### Session 3

SLOs:

- Understand that in a teen number the 1 represents one group of ten.
- Expand teen number notation and understand simple place value.
- Understand and apply a ten for one exchange.

__Activity 1__

- Display the chart started in Session 1. Record beside the numbers 11 – 19 the description ‘1 ten and x ones’ for each of the numbers.

- Using enlarged arrow cards demonstrate and discuss the place value notation that we use, highlighting tens and ones language.

- Introduce students to plastic beans and containers. Have them work in pairs to make up containers with ten beans in each and discuss what the containers will be called. (a container is ‘one ten’ or ‘a ten’). Have the students discuss the similarities between the sticks they have been using and the beans.

NB. The container for the beans looks different from the ones, but can still be unpacked. This is a subtle and important shift. Also consider exploring together as a group or class the place value beans animation, available from https://e-ako.nzmaths.co.nz/modules/PVanimations/ - Give students time to become familiar with the beans and the arrow cards. Have them make and model at least three teen numbers with the equipment, explaining this to their partner.

- Have each student complete a think board sheet (Attachment 3) or a mini poster about one of their favourite teen numbers. Display these.

__Activity 2__

Students play **Go Teen** in pairs.

(Purpose: to use ten ones to make one group of ten when adding add two single-digit numbers.)

Students have playing cards (ace - 9), shuffled and face down between them. They have single beans and empty tens containers (or single nursery/ice block sticks and hair ties), single digit and tens arrow cards available.

The players take turns to turn over two playing cards. When the two numbers are added, if they make less than ten they return them face down to a discard pile.

If they make more than ten they keep their playing cards, take the total number of beans, group the materials showing the total as 1 ten and units. They also show the number with the arrow cards.

However, if the number has already been made by their partner, (the arrow cards for that number have been used) the student must simply return their playing cards to the discard pile.

The winner is the player with the most tens (containers with beans) when all the arrow cards have been used up.

#### Session 4

SLOs:

- Understand and apply a ten for one exchange.
- Understand how to decompose a ten in order to subtract.

__Activity 1__

- The teacher models a teen number with containers and beans and asks, ‘What number is shown here?’. For example, 18:

A problem is posed in which the number being subtracted requires the ten to be ‘unpacked’ or decomposed:

“Here are the beans Gardener Gavin is going to plant. He plants 9 in the first row. How many beans are left to plant in the second row? How can we work this out?”

The students discuss strategies for subtracting 9 and suggest what they can do with the materials. The teacher models this and one more example is explored together.

- Students are provided with place value materials and each is given at least two subtraction problems to solve with decomposition (Attachment 4). Students should record with pictures, words and an equation what they did and what their result is.

- Share as a class/group and discuss. The language of making ten (composing) and breaking ten (decomposing) can be introduced.

__Activity 2__

- The teacher asks a student to model twenty using place value material. Discuss what this represents: two tens is the same as twenty.

- Have the students play in pairs or small groups
**First to twenty**.

(Purpose: to understand how to compose and decompose a ten.)

Students have beans and containers, numeral cards 11- 14, a set of playing cards 2 – 5, a dice with a + or – symbol marked on each of the six faces. Numeral cards are spread out face down.

Each student selects a card and makes that number using place value equipment.

Players take turns to roll the dice and turn over a playing card. They follow the instruction, either adding or subtracting from their materials. Each time the student has a turn they are required to write the equation.

The winner is the first student who has two containers of ten beans (twenty).

For example: a student turns over and models 13, rolls + and 3, and makes 16.

At their next turn the student may have to – 4, followed on the next turn by – 3. This will requires the student to decompose the ten.

The student will have recorded for the three turns so far:

13 + 3 = 16

16 – 4 = 12

12 – 3 = 9

- Conclude the lesson with a focus on the words, ‘place value’. The teacher writes ‘place value’ on a chart and asks the students what this could mean. They are encouraged to look at all the recording of teen numbers completed throughout these lessons. Accept all responses, but conclude by highlighting and recording that “the
**place**of a numeral in a number tells us what it is worth or its**value**.’’ Show the enlarged arrow cards drawing attention to the words*tens*and*ones*.

Dear parents and whānau,

In class in maths this week we have been learning about teen numbers and how they are made of ten plus a single digit number. For example thirteen is 10 + 3. We have also been introduced to place value, learning that the 1 in 13 is in fact one group of ten.

You can help your child practice this very important idea by playing the game, **Teenager match**.

Cut up the attached page to make separate cards. Spread them face down on the table. Take turns to choose a pair of cards. If they match, keep the pair. The winner is the person with the most pairs.

[Include a copy of Copymaster 5]