## Late level 1 plan (term 1)

Planning notes
This plan is a starting point for planning a mathematics and statistics teaching programme for a term. The resources listed cover about 50% of your teaching time. Further resources need to be added to meet the specific learning needs of your class, to support your local curriculum and to provide sufficient teaching for a full term.

Level One
Integrated
Units of Work
This unit provides you with a range of opportunities to assess the entry level of achievement of your students.
• Use groupings to efficiently count the number of objects in a set.
• Create picture graphs about category data and discuss patterns in the data.
• Create and follow instructions to make a model made with shapes.
• Order a set of objects by mass (weight).
• Create a sequential pattern and predict...

## Making ten

Level One
Number and Algebra
Units of Work
The purpose of this unit of sequenced lessons is to develop knowledge and understanding of combinations to ten.
• Explore the numerals to ten.
• Instantly recognise patterns within and for ten.
• Make and record groupings within and for ten.
• Recall and apply groupings to ten using te reo Māori.
• Recognise the usefulness of just knowing combinations to ten.
• Use an ‘if I know ___, then I know___’ approach...

## Teddy Bears and Friends

Level One
Geometry and Measurement
Units of Work
In this unit we compare the lengths of the students’ favourite soft toys directly and then indirectly using multi-link cubes.
• Compare a group of 3 or more objects by length.
• Measure length with non-standard units.

## How long now?

Level One
Geometry and Measurement
Units of Work
In these five activities the students compare the duration of events, learn the order of months and read the time to the hour and half-hour.
• Directly compares the duration of two events.
• Uses non-standard units to compare the duration of two or more events.
• Tell time to the hour and half hour using analogue clocks.

## Amazing Mazes

Level One
Geometry and Measurement
Units of Work
This unit introduces some of the key concepts of position and direction in the context of a series of activities around mazes.
• Use the language of direction to describe the route through a maze.
• Use the language of direction to guide a partner through a maze.
• Rotate their body and other objects through 1/4 and 1/2 turns.
• Follow a sequence of directions.
Source URL: https://nzmaths.co.nz/user/75803/planning-space/late-level-1-plan-term-1

Purpose

This unit provides you with a range of opportunities to assess the entry level of achievement of your students.

Specific Learning Outcomes
• Use groupings to efficiently count the number of objects in a set.
• Create picture graphs about category data and discuss patterns in the data.
• Create and follow instructions to make a model made with shapes.
• Order a set of objects by mass (weight).
• Create a sequential pattern and predict further members of the pattern.

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

• having a range of different sized objects in containers for session 1.  Use larger objects for students who are beginning to count one-to-one and smaller objects for those who are more confident
• reducing the number of activities covered in a session so that more time can be spent on the earlier ideas.  For example in session 5, ensure students are confident about identifying the next element in the pattern before connecting the pattern to ordinal positions.
• using a class recording book instead of the individual records that are suggested as part of each session.

The context for this unit can be adapted to suit the interests and experiences of your students. For example:

• In session 1 use counting objects that can be found locally (shells, pebbles, sticks, leaves).
• In session 2 use activities/sports that students in your class engage in.
• In session 5 create patterns using native birds as an alternative to farm animals.
Required Resource Materials
• Digital camera to record students’ work.
• Session One – Countable objects, e.g. counters, cubes, toy animals.
• Session Two – Scissors, glue sticks, plastic containers (2L icecream if possible), large sheets of paper, copies of Copymaster 1 and Copymaster 2.
• Session Three – sets of geometric shapes, e.g. pattern or logic blocks, pieces of card for labels.
• Session Four – balance scales (if available) or make balances from coathangers, string and pegs (to hold items), extra cheap healthy lunch items like apples, carrots, oranges, packets of raisins, muesli bars, etc, kitchen scales, preferably digital, that are sensitive to about 500g (optional).
• Session Five – objects to form patterns, e.g. natural materials like acorns, shells, stones, or toy animals, geometric shapes, blocks, copies of Copymaster 3 to make pattern strips.
Activity

#### Prior Experience

It is expected that students will present a range of prior experience of working with numbers, geometric shape, measurement, and data. Students are expected to be able to count a small set of objects by ones, at least.

#### Session One

1. Talk to your students about the purpose of the unit which is to find out some information about them, so you can help them with their mathematics. In the first session students explore an activity called ‘Handfuls” which was first developed by Ann Gervasoni from Monash University, Melbourne. Handfuls should become a regular part of lessons during the year.

2. Model taking a handful of objects from a container. Use smaller objects for Year 2 students and larger objects for New Entrants or Year one students. Place the collection on the mat in a disorganised arrangement.

3. Estimate how many things I got in my handful (You may need to explain that an estimate is an educated guess).

4. Ask your students to write the number on the palm of their hand and show it to you. This is a way to see who can write numbers, avoids calling out, and buys time for students to think.
How can we check how many things are there?

5. An obvious first approach is to count by ones. Organising the objects in a line then touching each one as it is counted is a supportive approach.

6. Look for students to suggest other ways, such as counting in twos or fives.  Students can find skip counting difficult in several ways, not realising that counting in composites gives the same result as counting in ones, not knowing the skip counting sequence, and dealing with the ‘left overs’ when a composite is not complete, e.g. counting in fives below. What to do with leftovers is an interesting discussion topic.

7. Tell the students that you want them next to take their own handfuls.  Ask the students to record on paper how they counted their collection, particularly what groupings they used. Tell them to count the handfuls in at least two different ways. Try to take digital photographs of the handfuls for use in the group discussion.

8. Watch as you wander around to see if students can:
• Reliably organise their collections and count in ones
• Use composites like twos, fives and tens to skip count collections
• Use tens and ones groupings to count the collections, using place value.

9. After all the students have taken handfuls and recorded their counting methods, use one of these two methods to extend the task:
• Let students travel to the handful collections of other students, estimate or count how many things are in the collection, then compare their methods with that of the original student. The recording of the original student can be turned over then revealed after the visitor has estimated and counted.
• Share the recording strategies students created as a class. Use digital photographs on the Interactive Whiteboard to drive discussion about the best counting strategies for given collections.

10. Apply the counting strategies to two questions:
• Can you get more in a handful with your preferred hand than your other hand?
• Can you get more in a handful when the things are bigger or smaller?

11. Discuss what their ‘preferred hand’ is, that is, are they right or left handed? You might act out taking a handful with your other hand and comparing the number of objects you got with your preferred hand. You might also demonstrate getting a handful or small things, then a handful of larger things. Ask students to predict what will happen, then go off to explore the two questions. Suggest recording on the same pieces of paper so they can compare other handfuls to the original attempt.

12. After a suitable time ask the students to re-gather as a class with their recording sheets. Discuss possible answers to the questions. Interesting questions might be:
• What side are our preferred hands?
• Do we always get the same number in a handful if we use the same hand?
• How big are objects that are too hard to gather in a handful?

13. You might make a display of the recording sheets for other students to look at. Other variations of the handfuls task might be:
• Students trying different ways to increase the number of objects they can gather in one handful.
• Exploring one more or less than a given handful.
• Using tens frames or dice patterns to support counting the objects in a handful.
• Gather multiple handfuls and counting.
• Sharing a handful into equal groups

#### Session Two

In this session called “Our Favourites” students explore category data and how it might be displayed. The data comes from their responses, so the displays provide useful information about the class.

1. Begin by asking the students to choose which of the sports shown on Copymaster 1 they like to play the most. Provide the students with copies of the strips to cut out the square of their choice. It is important that each student makes a single choice, cuts out the square and not the picture, and places it in the container in the centre.

2. Once all the data are in, tip the contents of the container on the mat.
If we want to find out the favourite sport, what could we do?

3. Students usually suggest sorting the squares into category piles. A set display like that is a legitimate way to present the data.
Could we arrange the squares, so it is easier to see which sport has the most and the least squares?

4. Students might suggest putting the squares in line with a common baseline (starting point). They might suggest a ‘ruler’ alongside, so it is not necessary to count the squares in each category. They might suggest arranging the categories in ascending or descending order of frequency and adding a title and axis labels.

5. Create the picture graph on a large piece of paper by gluing the squares in place. Display the graph in a prominent place.

6. Prepare copies of Copymaster 2, cut the copies into strips and put each set of strips with a container and several pairs of scissors. Spread the containers out throughout the room. The students visit each ‘station’ and make a choice by cutting out a square and putting the square into the container. You may need to discuss what each strip is about before students do this. The strips are about favourite fruit, fast food, pet, vegetable, way to travel to school, and after school pastime.

7. Once the data gathering is complete put the students into small groups with a set of data to work on. Remind them to create a display that tells someone else about which category is the most and least favourite. Watch to see if your students can:
• sort the data into categories
• display the data using a common baseline and possibly a scale
• label each category and provide a title for the graph

8. After a suitable period bring the class together to discuss what the data displays show. Can your students make statements about…?
• highest and lowest frequencies
• equal frequencies
• patterns in the distribution, such as the way it is shaped
• inferences about why the patterns might be, e.g. It is summer so people might like vegetables like tomatoes.

#### Session Three

In this session your students use the language of two-dimensional shapes to provide instructions to other students. “Make Me” is an activity that can be used throughout the year with different materials to develop your students’ fluency in using geometric language for shape and movement.

You need multiple sets of shapes. Ideally there is a set of shapes for each pair or trio of students. Attribute blocks are used below to illustrate the activity but other shape-based materials such as those below are equally effective.

 Pattern Blocks Logic (Attribute) Blocks Geometric Solids

1. Begin by discussing the shapes in a set. Ask questions like:
• What shape is this? How do you know?
• What features does the shape have to be called a …?

2. Draw students’ attention to features like sides and corners. You might also venture into symmetry if you have a mirror available.
Where could I put the mirror, but it still looks like the whole shape?

3. Use two shapes positioned together to draw out the language of position. For example:
 The circle is below the square. The circle is in front of the square. The circle is on the right side of the square.

4. Show students how to play the “Make Me” game. Create an arrangement of four shapes. Here is an example:

5. Ask students to give you instructions so you can make this arrangement using your set of shapes. Respond to what students tell you very literally. For example, if they say “The circle is on top of the square” you might put the circle in front of the square. An important point is that the person giving instructions cannot point or touch the blocks.

6. Next, ask a student to arrange three or four blocks in a place that nobody else can see. Send a different student to look at the arrangement and come back to tell you how to make it. The instruction giver may need to make return trips to the arrangement to remember exactly how it looks. At the end, check to see that what you make matches the original arrangement.

7. Students then work in pairs or threes, each with a set of shapes. You go to a place they cannot see and arrange a set of shapes. Be mindful of drawing out the need for students to use language about features of shapes (side, corner) and position (right, left, above, below, etc.). One student from each team is the instruction giver, the other students are the makers. The instruction giver views the arrangement and returns to the group as many times as they need. The makers act on the instructions. When they feel the arrangement is correct the whole team can check with the original. Make sure each student has opportunity to be the instruction giver.
Look to see whether your students:
• give precise instructions using correct names for shapes, features and position
• act appropriately to instructions for action with shapes.

8. Students can independently make their own arrangements of shapes. Take digital photographs of the arrangements. Use one or two images to help students to reflect on the intentions of the session. Create a list of important words for display (not all may be relevant to your set of shapes):

9. Students could write a set of instructions to build an arrangement from a photograph. This might also be done as a class if the literacy demands are too high.

#### Session Four

In this session students compare items by mass (weight).

1. Begin by asking students what the words light and heavy mean. Ask a couple of students to find a light object in the classroom and identify a heavy object. Young students frequently identify heavy as immovable so expect them to point out bookshelves and other objects they cannot personally move. Create two cards with the words light and heavy.

2. Get two objects from around the room that are similar but not equal in mass.
How could we find out which thing is heavier?
Students usually suggest that the objects can be compared by hefting, that is holding one object in each hand.

3. You might have several students heft the objects to see if there is a consistent judgement.
What can we say about the weight of these two objects?
Look for statements like, “The book is heavier than the stapler,” or “The stapler is lighter than the book.”

4. Make two cards with the words “lighter” and “heavier” and set them a distance apart on the mat.

5. Next, get a collection of five objects of different weights and appearances.
Let’s put these objects in order of weight. Who thinks they could do that?

6. Let students come up and heft the objects and place them somewhere on the lighter to heaver continuum. Be aware of these issues:
• Students may have trouble controlling the order relations. Ordering five objects by twos involves complex logic.
• Objects of equal weight (or indiscernible difference in weight) occupy the same spot on the continuum.
• Size, as in volume, is not a good indicator of weight. Small objects, such as rocks, can be heavier than big objects, such as empty plastic containers.

7. After the five objects are place on a continuum give the students a personal task.
I want you to put the items in your lunchbox in order of weight. You can use hefting if you want but we have other balances you can use. You will need to record for us, so we know the order of the objects.
Many students have an extraordinary number of items in their lunchbox but be aware that some students may have no lunch. Ensure you have a collection of healthy foods they can use and consume afterwards.

8. Let the students order their lunch items and record their findings.
Look to see if your students can:
• Recognise which of two items is heavier by hefting or using a balance.
• Co-ordinate the pairs of objects to get all five objects in order.

9. After a suitable time gather the class to compare their findings and discuss issues that arose. Frequently, students are surprised that similar looking items do not have the same weight. Apples and metal spoons are good items to illustrate the point that same kind of objects does not mean equal weight.

#### Session Five

In this session students look for repeating patterns and connect elements in the pattern with ordinal numbers.

1. Play the patterns video, which contains four repeating patterns. Pause the video at the end of each pattern progression and ask questions like:
• What do you notice about the pattern? (You are looking for students to see the element of repeat)
• What comes next?
• What object will be at … number 10? … number 15?... etc. (You are looking for students to apply generalisation about the element of repeat, e.g. All even numbers have a red square.)

2. Note that patterns 3 and 4 have two variables and the sequence is different for those variables.

3. In pattern 3 the colour variable has a yellow, red, yellow, red, … sequence while shape has a circle, hexagon, rectangle, circle, hexagon, rectangle, … sequence.

4. In pattern 4 the animal variable has a goat, cat, cow, dog, … sequence while orientation has a right, left, right, left,… sequence.

5. Provide students with a range of materials to form sequential patterns with. The items might include bottletops, corks, blocks, toy plastic animals, pens and pencils, geometric shapes, etc. Give them a copy of the strip that can be made from Copymaster 3 after it is enlarged onto A3 size (x 1.41).

6. Let students create their own patterns. Look for students to:
• create and extend an element of repeat
• use one or more variables in their pattern
• predict ahead what objects will be for given ordinal numbers, e.g. The 16th object.

7. Take digital photographs of the patterns to create a book, and ask students to pose problems about their patterns.  Students can record the answers to their problem on the back of the page.

8. Discuss as a class how to predict further members of a pattern. Strategies might include:
• Create a word sequence for each variable, e.g. blue, yellow, red, blue, yellow, red...
• Use skip counting sequences to predict further members, e.g. If the colour sequence is blue, yellow, blue, yellow,… then every block in the ordinal sequence 2, 4, 6, … etc. is yellow.

## Making ten

Purpose

The purpose of this unit of sequenced lessons is to develop knowledge and understanding of combinations to ten.

Achievement Objectives
NA1-1: Use a range of counting, grouping, and equal-sharing strategies with whole numbers and fractions.
NA1-3: Know groupings with five, within ten, and with ten.
NA1-4: Communicate and explain counting, grouping, and equal-sharing strategies, using words, numbers, and pictures.
Specific Learning Outcomes
• Explore the numerals to ten.
• Instantly recognise patterns within and for ten.
• Make and record groupings within and for ten.
• Recall and apply groupings to ten using te reo Māori.
• Recognise the usefulness of just knowing combinations to ten.
• Use an ‘if I know ___, then I know___’ approach to solving number problems.
Description of Mathematics

These lessons build upon the student’s recognition and knowledge of groupings within ten, to scaffold ready combinations and separations in numbers that make ten.

A goal within primary mathematics is for students to use partitioning strategies when operating on numbers. By building images and knowledge of these combinations at an early age, the ability to naturally partition larger numbers will be strengthened. Students should have many opportunities to combine and separate numbers to ten and come to clearly see and understand how these ‘basic facts’ are fundamental building blocks of our number system.

As they work with numbers greater than ten, students will come to know about ‘tidy numbers’ and about ‘rounding to ten’. Students should be encouraged to know and have an intuitive feeling for ten to enable them to readily apply this in solving problems that involve partitioning and combining larger numbers and sets.

Our place value system has ten digits only. It is the place of a digit in a number that determines its value. Ten is the basis of this system. By having the opportunity to briefly explore other number systems (Roman and Mayan), and by considering notation to create their own system, students will better understand the numerals and number representations that we may take for granted within the base ten system we use.

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 support students include:

• Providing more practice with the tens frames to develop the students knowledge of the number facts to 10. Encourage them to subitise (to recognise, without counting) the number of counters and the number of gaps.
• If the students are unfamiliar with the Māori numbers to ten, spread session 4 over two or more sessions.

Numbers to ten in other languages can be used in this unit in response to the languages and cultures of your students.  For example: numbers from Pasifika cultures could be included in a similar way to how te reo is used in session 4.

Required Resource Materials
• Slavonic abacus
• Tens frames
Activity

#### Session 1

SLO: Explore the numerals to ten.

Activity 1

1. Make paper, crayons/felts, pencils, counters (or similar mathematics equipment) available to the students. Set a time limit as appropriate. Have the students write, draw and show you everything they know about ten.

2. Have the students pair share their work.

3. Write the word ‘ten’ and the numeral 10 on chart paper or in a modeling book. Collect and record the important ideas that the students have generated. Be sure to use words, symbols and drawings of equations, stories or materials. Highlight the fact that 10 is made up of two digits that we have seen before, 1 and 0 making it clear that ten doesn’t have its own special digit. Develop this idea by writing some other shapes, for example suggesting that these could be digits for the number ten, but instead we combine two that we already know and use, 1 and 0.

4. Ask if the students know why ten is an important number. Accept the student ideas and say they will be learning more about why ten is so important.

Activity 2

1. Explain that the class will look briefly at other number systems. Locate Italy on a map, show where Rome is and explain that many hundreds of years ago these people, the Romans, wrote numerals to ten this way.

2. Have the students talk in pairs about what they see. Record all their ideas.

3. Talk about the similarities and differences in the way we record ten now, 10 compared with X (ten has its own unique symbol).

4. Locate Mexico and Central America on a map. Explain that the Mayan people who lived there hundreds of years ago used these symbols. Have the students talk in pairs about what they see. Record all their ideas.

5. Talk about the similarities and differences in the way we record ten now, compared with the Mayan symbol. Discuss why ten is recorded in this way.

6. Have students in pairs invent and record their own numerals to ten. Have them write some simple equations using their symbols, then pair share their numeral system with another group.

7. Conclude by reviewing different ways of writing ten and our system, 10. Highlight the fact that in our system we have just ten numerals which we ‘reuse’.

#### Sessions 2-3

SLOs:

• Instantly recognise and describe patterns within and for ten.
• Make and record groupings within and for ten.
• Review families of facts within ten (introduced in the Using five unit).

Introduce the following activities over the next two sessions.

Activity 1

1. Show a frame with ten dots.

Have the students show ten on their fingers, then have them describe to a partner how many dots they see and how many fingers they see, using ‘ten and no more.’ Record 10 + 0 = 10

2. Show other tens frames out of order. Each time the students take turns with a partner to say how many dots they see and describing to a partner what they see on the tens frame. For example, “Eight. That’s five dots, and three dots and two empty spaces. That's eight dots and two spaces.”

3. Record several examples as a class using words and symbols. Seven dots and three spaces, four dots and six spaces, one dot and nine spaces.
Record equations with unknowns representing some of the tens frames; For example, for dots: 7 + ☐ = 10, 10 = 4 + ☐, 10 = 1 + ☐
Make it clear that the spaces ask us ‘how many more to make ten?’

4. Model using different coloured counters to fill the spaces, showing and saying ‘seven dots plus three dots is the same as ten dots’.

Record equations, 7 + 3 = 10 and 3 + 7 = 10.
Ask what subtraction equations can be recorded using these numbers. Accept student responses, write and model by removing counters, 10 – 3 = 7 and 10 – 7 = 3
Highlight that that four equations are related because they use the same 3 numbers. They are known as a family of facts.
Model with other tens frames: for example 10 = 4 + 6, 6 + 4 = 10, 10 – 4 = 6 and 10 – 6 = 4.

5. Hold up tens frames in random order. Students call out how many dots they see then record with a “magic finger” on the mat or with writing materials how many more to make ten. For example, show:

Students say, “Eight,” and write 2.

Activity 2

1. Students play Clever Fingers in pairs. (Purpose: to practice seeing, saying and writing combinations to ten) They need ten counters, pencil and paper to record winning equations. For each “hand” played they move a counter into a ‘used’ pile.
2. Students, with their hands behind their backs, make a number on their fingers.

They take turns to call ‘Go.’ On ‘Go’ they show their fingers. If the combination of raised fingers makes ten, they say, “Clever fingers” and one student records the equation. 3 + 7 = 10 When all the counters are used (they have had ten turns). They count their equations. Student pairs compare results.

Activity 3

Students play Snap for Ten.
(Purpose: to practice seeing, saying combinations to ten)
In pairs, using playing cards with Kings and Jacks removed, and using the Queen as a zero:
Turn over a card to begin the game.
Students take turns to turn over a card from the pack, placing the turned card on top of the card before. If the turned card can combine in some way with the previous card to make ten the student says, ‘Snap’, states the equation and collects the pile of cards.
For example: if 9 is turned, followed by a 1, 9 + 1 = 10 is stated and the pile of cards is collected.

Activity 4

Students play Memory Tens.
(Purpose: to practice seeing and saying combinations to ten)
In pairs, using playing cards with Kings and Jacks removed, and using the Queen as a zero:
Cards are turned down and spread out in front of the students.
Students take turns to draw pairs. If the numbers on the two cards combined make ten, the pair is kept by the player.
For example: A player draws 6 and 4 and states 6 + 4 = 10 and keeps the pair.
The game continues till all cards are used up.
The winner is the person with the most pairs.

Activity 5

Students play Fast Families
(Purpose: to practice writing and demonstrating family of fact combinations to ten)
Players have pencil and paper.
Students place ten counters of one colour on a blank tens frame.
They take turns to roll a ten-sided dice. The dice roller removes the number of counters indicated by the dice roll and says, “Go.”
The players quickly write the four family of fact members associated with 10, 6 and 4: beginning with the equation just modeled.
10 – 6 = 4, 6 + 4 = 10, 10 – 4 = 6, 4 + 6 = 10.
The first to write these calls stop.
That player choses another player to demonstrate and say the other three family members in logical order by adding 6 onto the 4, saying 4 + 6 = 10, then removing 4 counters saying 10 – 4 = 6 and finally adding 4 back onto the 6 and saying 6 + 4 = 10.
If this player is correct, he rolls the dice and the game begins again.
The winner is the student who accurately records the most families of facts.

#### Session 4

SLO: Recall and apply groupings to ten using te reo.

1. Students count in Māori up to and back from ten: “Tahi, rua, toru, whā, rima, ono, whitu, waru, iwa, tekau. Tekau, iwa, waru, whitu, ono, rima, whā, toru, rua, tahi.”
If students are unfamiliar with nga tau, have a number chart displayed.

Each student has a set of number words to ten in Māori (Attachment 1).
A ten-sided dice is passed around the class circle. Each student takes a turn to roll the dice and call the number in English and in Māori and classmates must hold up the Māori word.

2. Students play in pairs Nga Tau Pairs
(Purpose: to recognise and come to know Māori number words)
A mixed piles of tens frames are provided with a mixed pile of Māori number word cards to ten.
Both are turned down. The students take turns turning over a tens frame and a word card. If they match they keep the pair.
The winner is the player who has the most pairs when all the cards are used.

3. Students play in pairs Total Tekau (like Snap for Ten)
(Purpose: to recognise and come to know number combinations to ten using Māori number words)
Each student shuffles a double set of Māori number word cards to ten and places the pile face down in front of them.
They take turns to turn over one word card at a time and place these in one pile, one on top of another. If two consecutive numbers together make ten, the player who played the second card calls, ‘Tekau’ and collects the whole pile and begins the game again.
The winner is the player with all the cards or with the biggest pile when the game is stopped.

#### Session 5

SLO: Recognise the usefulness of knowing combinations to ten.

1. Review and practice known facts.
Have a set of tens frames displayed to support some students.
Provide each student with a number fan.
As the teacher shows a digit, each student finds and shows the complementary digit to ten.
For example: the teacher shows 3 and each student shows 7.

2. The teacher records subtraction problems and has the students find and show the result.
For example, the teacher writes 10 – 2 = ☐ and the students show 8, the teacher writes ☐ - 5 = 5 and the students show 10.

3. Register students on e-ako Maths. Support them to become familiar with the addition and subtraction facts learning tool. This tool supports the student to learn unknown facts to ten by building on already known facts. Tens frames images are used.

4. Introduce the term “basic facts”.
Ask the students, “What is a fact?” and record their responses. (A fact is something that has really occurred or is actually the case. It is something that can be tested and can be found to be true).
Ask the students, “What does ‘basic’ mean?” and record their responses. (Something that is basic is essential, fundamental. A ‘base’ is the bottom support of anything or the thing upon which other things rest. It is a foundation.)

5. Identify which are our basic addition and subtraction facts by showing this grid to the students and by exploring how it works.

6. Highlight the importance of knowing combinations to ten and conclude with a game of Memory Tens, as played in session 2.

#### Session 6

SLOs:

• Recognise the usefulness of knowing combinations to ten.
• Use an ‘if I know, so I know’ approach to solving simple number problems.
1. Review content of sessions 1 – 4. Focus on inverse operations of addition and subtraction as shown in the family of facts.
Demonstrate this by developing with the students and “If I know this, then I know that ” flow diagram. For example:

The students are being introduced to this idea. They are not expected to immediately apply the principle to the bigger numbers.
Highlight the important idea that maths is about relationships between numbers, like fact families, and if we look for these and for number patterns, they help us.

2. Begin to complete the addition grid together. Write a sentence together describing something the students notice.
Have students complete their own copies of the grid (Attachment 2) and write (up to) five things they notice.
Have them share with a partner what they have discovered.

3. As a class, discuss and record the students’ ‘discoveries’. Make a list together of how knowing about these patterns helps us.

4. On their own paper, have the students each write their own favourite equation within or to ten. Have them create their own “if I know this, then I know that" brainstorm chart as modeled in 5a.
Attachments

## Teddy Bears and Friends

Purpose

In this unit we compare the lengths of the students’ favourite soft toys directly and then indirectly using multi-link cubes.

Achievement Objectives
GM1-1: Order and compare objects or events by length, area, volume and capacity, weight (mass), turn (angle), temperature, and time by direct comparison and/or counting whole numbers of units.
Specific Learning Outcomes
• Compare a group of 3 or more objects by length.
• Measure length with non-standard units.
Description of Mathematics

In this unit the students begin by making direct comparisons between objects and putting a number of objects into order according to length. They are also introduced to measuring with multi-link cubes which allows them to compare objects which cannot be placed together.

Multi-link cubes are an example of a non-standard measuring unit. They reinforce most of the principles that underpin measurement and allow students to find out that:

• You must not change the unit being used when you are measuring an object.
• Units are chosen for their convenience and appropriateness to the object being measured.
• Units are placed end to end in a straight line and then counted to find the distance (length) between two points.
• You express measurements to the nearest whole unit or to a specified degree of accuracy, for example, almost 5 handspans, or about 6 ½ straws long.

The students will also be encouraged to estimate. Initially these estimations may be little more than guesses, but estimating involves the students in developing a sense of the size of the unit. As everyday life involves estimates at least as frequently as exact measures the skill of estimating is important.

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

• Helping students, as needed, draw their outlines.
• Working with individual students or pairs of students to make measurements using cubes. This provides an opportunity to support those who need help with the correct placement of cubes or help in counting the number of cubes needed.

As the focus of this unit is making measurements of themselves it is already in a context that is meaningful.  In some situations, it may be more appropriate to use a collection of classroom objects rather than ask students to bring toys to school.

Required Resource Materials
• Rods (the 10 rod is best)
• Scissors
• A teddy bear or soft toy from home
• Large sheets of paper for drawing around the toys
• A roll of paper for drawing outlines of the students
Activity

In preparation for this unit have all students bring a favourite soft toy to school.

#### Getting Started

1. We begin the week by looking at all the soft toys the students have brought to school. Ask the students, seated in a circle, to introduce their soft toy to the class.
2. Ask a student to put her toy in the centre of the circle.
Do any of you have toys that are taller than this?
3. Let the students take turns bringing their toys into the centre to compare.
4. Put taller toys in one group, shorter toys in another and toys of the same height in the third group.
5. After heights have been compared ask the students to suggest other ways that the toys could be compared. For example: bigger or smaller feet, longer or shorter legs, and bigger or smaller puku.
6. Ask groups of 3 students to put their toys into an order. As they do this ask questions that require them to describe the size of the attribute they are using a referent.
7. See if the other students can guess the attribute that the groups have used to order their toys.
8. Show the students how to trace outlines of their toys on paper which they can colour to make life-sized portraits for use later in the week.

#### Exploring

For the next 3 days we make comparisons using the students. In pairs the students take turns drawing outlines of their bodies. They use these outlines to make measurements using multi-link cubes or rods.

1. Demonstrate how to draw around a student to get an outline. Show that they need to draw around both arms and legs.
2. Give each of the students a cube and ask them to estimate (guess) how many cubes you would need to measure the length of the arm.
3. Check the estimates by measuring with the cubes.
4. Now give them a rod and ask them to estimate again. By asking them to explain or justify their guess you can focus their attention on the size of the rod in comparison to the cube.
5. Check the estimates by measuring with the rods.
6. Ask the students what other parts of the body they would like to measure. List these on a chart (with drawing) for later reference.
7. Have the students draw outlines of each other and then measure the length of their legs, feet, fingers using either cubes or rods.
8. If the students choose to measure their waist you will need to discuss how they can measure around something. Discuss how they could use string to mark off the distance around their waist and then measure the string with cubes.
9. Ask the students to record their measurements on their outline.
10. If the students complete measuring their outline ask them to measure the outline of their toy.
11. At the end of each day, share work and make comparisons.

Whose arm measured more than 25 cubes?
Tell me how many more.
What have you measured with rods? Why did you choose rods?
Have you ever been to a place where you were measured? Tell us about it.

#### Reflecting

Today we line up the outlines of our soft toys ready to go to school assembly (the shortest in the front.)

1. Ask the students to measure the height of their soft toy using linker cubes and record this on the outline. Have them cut off any extra paper from the top and bottom of the outline.
2. Tell the students that the toys want to go to the school assembly and so that everyone can see them arriving they will need to stand in order from the short ones to the tall ones.
3. Ask four students to come to the front of the room with their outlines. Ask them to put their outlines in order (using the edge of the board). Let the other students check the order.
4. Now let the other students, in turn, put their toy outlines in the line. As they place their outline ask them why they have chosen that place.
5. Continue discussing, comparing and moving outlines until all the toys have been ordered.
6. Display the line in the hallway so that other students and parents can see it.

## How long now?

Purpose

In these five activities the students compare the duration of events, learn the order of months and read the time to the hour and half-hour.

Achievement Objectives
GM1-1: Order and compare objects or events by length, area, volume and capacity, weight (mass), turn (angle), temperature, and time by direct comparison and/or counting whole numbers of units.
Specific Learning Outcomes
• Directly compares the duration of two events.
• Uses non-standard units to compare the duration of two or more events.
• Tell time to the hour and half hour using analogue clocks.
Description of Mathematics

Students’ experiences with time throughout the learning sequence has two aspects:
duration and telling time.

Duration
Comparing the duration of two events is the second stage in developing an understanding of time passing. This can be done by directly comparing two activities that have common starting points, for example, a song on a tape or running around the building.

After the students have directly compared the duration of two events we use sand-timers and other non-standard measures to compare two or more events.

Telling time
In this unit we learn the skills to tell time to the hour and and half-hour. Telling time must enable them to:

• develop an understanding of the size of the units of time. This includes being able to estimate and measure using units of time
• read and tell the time using both analogue and digital displays.

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 include:

• Including images on the chart used in session 2 to support beginning readers.
• Introducing 1/4 hour times to those students who are confident with telling time to the 1/2 hour in session 3.

The contexts for the duration activities are based on activities that are undertaken by students in your classroom so should be engaging to them.  Asking the students to identify which activities they could compare provides further opportunities for their engagement.

Required Resource Materials
• Chart paper
• 2 skipping ropes of different length
• Large number cards (1-12)
• A large space
• Paper plates
• Card board hands
• Split pins
• Analogue clocks
• Pictures of clocks from home
Activity

#### Session 1: Who finishes first?

In this activity we directly compare two activities to see which takes the longest.

Resources
• Chart paper
1. Begin by asking the students which they think takes longer.
Making a tower with 10 cubes or hopping 10 times on each foot?
2. Write the 2 events on a chart
3. Get 2 volunteers to complete the activity.
4. Tell the students that today they are going to work with a partner comparing things they do to find out which takes longer. Ask the students for their ideas and add these to the chart.
5. Get the students to work on the activities in pairs.
6. Share findings.

#### Session 2: Clapping time

In this activity we indirectly compare "quick" events by clapping, stamping and linking cubes.

Resources
• Chart paper
1. Begin by asking the students which they think would take them longer, writing their name or walking to the board and back to their desk.
2. Select a volunteer to complete the two events while the rest of the class time the events by clapping. Help the class keep a steady beat.
3. Record the results:
Writing my name 9 claps
Walking to the board 11 claps
4. Ask for other ideas for timing events, for example. clicking fingers, stamping, linking cubes.
5. List events that could be timed. Ask the students to add their ideas.
6. Ask each pair of students to select one of the timing methods and use it to time the events. Give each pair a sheet of paper to record the times on.
7. Display and share the results.

#### Session 3 : A big clock

In this activity the students form a large clock which is then used to show hour times. As you need a large space for the "people clock" this may be best done outside.

Resources:
• 2 skipping ropes of different length
• large number cards (1-12)
• A large space
1. Ask the students to tell you all they know about clocks. This will include both digital and analogue.
2. Ask questions that focus their thinking on what an analogue clock looks like.
3. Draw a large circle with chalk.
4. Choose 12 students to hold the number cards.
5. Get the rest of the students in the class to direct the number holders so that they form a large clock face.
6. Give another student the two ropes to hold in the centre of the "clock".
7. Move the ropes so that the clock shows 3 o’clock. Ask the students to tell you the time.
8. Ask volunteers to move the hour hands of the clock to a time they know. Everyone else then reads the time. Draw their attention to the minute hand, and that it always points to the 12. Make sure they understand that at this time there are 0 minutes.
9. Depending on the success with hour times this activity can be easily extended to 1/2 hours.  If you move onto 1/2 hours, support students to see the connection between 1/2 of a circle and the 1/2 past position on the clock.

#### Session 4: Making Clocks

In this activity the students create their own clocks using paper plates and then use the clock to show times during the school day.

Resources:
• Paper plates
• Card board hands
• Split pins
• Analogue clocks
1. Look at the clocks and discuss their features:
- A large and a small hand fixed at the centre.
- Digits 1 to 12.
2. Discuss ideas for positioning the numbers evenly around the clock.
3. Construct clocks fixing the hands in place with a split pin.
4. Now use the clocks to show hour and then half-hour times. Display both the analogue and digital written forms.
5. Throughout the day ask the students to change their clocks to show the "real" time. Do this several times on the hour and half-hour. Each time look at tell the time using both digital and analogue forms.

#### Session 5: The best times of the day.

In this activity we look at different kinds of clocks and talk about telling the time. We draw a picture of our favourite time of the day.

Resources:
• Pictures of clocks from home
• Paper plate clocks (previously constructed from Station 4)
1. Let the students share the pictures that they have drawn of clocks found at home.
2. Discuss the different types of clocks, for example, watches, clock radios, clocks on appliances, Grandfather clocks, novelty clocks.
3. Discuss why most of us have so many clocks and when it is important to know the time.
– so we won’t be late to school
– so we won’t miss our favourite TV programme
– so that we get to our sports practice on time
– so we know when our food is cooked
4. Ask the students to show their favourite time of the day on their paper clocks.
5. Get the students to draw a picture of their favourite time. The pictures should include a clocks showing the time.
6. Share and display pictures.

## Amazing Mazes

Purpose

This unit introduces some of the key concepts of position and direction in the context of a series of activities around mazes.

Achievement Objectives
GM1-3: Give and follow instructions for movement that involve distances, directions, and half or quarter turns.
Specific Learning Outcomes
• Use the language of direction to describe the route through a maze.
• Use the language of direction to guide a partner through a maze.
• Rotate their body and other objects through 1/4 and 1/2 turns.
• Follow a sequence of directions.
Description of Mathematics

At Level 1 the Position element of Geometry consists of gaining experience in using everyday language to describe position and direction of movement, and interpreting others’ descriptions of position and movement. In this unit students will gain experience using the language of direction, including up, down, left, right, forwards, backwards in the context of mazes. For more activities that involve students giving and following instructions using the language of position and direction you might like to try Directing Me.

Spatial understandings are developed around four types of mathematical questions: direction (which way?), distance (how far?), location (where?), and representation (what objects?). In answering these questions, students need to develop a variety of skills that relate to direction, distance, and position in space.

Teachers should extend young students' knowledge of relative position in space through conversations, demonstrations, and stories. For example, when students act out the story of the three billy goats and illustrate over and under, near and far, and between, they are learning about location, space, and shape. Gradually students should distinguish navigation ideas such as left and right along with the concepts of distance and measurement.

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 include:

• Increasing the complexity of the mazes for those students who need more challenge.
• Working alongside individual students who need support navigating through the maze.
• Providing students with arrow cards that match the directional words (left, right, up, down).

The context for this unit can be adapted to suit the interests and experiences of your students by engaging them in identifying the character and destination for each maze.

Required Resource Materials
• Maze copymasters:
• Grid copymasters:
• Counters with an arrow drawn on them.
• Chalk for drawing outside maze.
Activity

There are many books of mazes and online interactive mazes available. Try to have different resources available in the classroom while you are working on this unit. Early finishers or students who need more challenge could be given the opportunity to work with the other mazes or draw their own.

#### Session 1

Many students may have some experience of using mazes, whether it is walking through mazes, or solving pen and paper mazes in puzzle books.

1. Draw a simple maze on the board (or photocopy one up to A3). Personalise by creating a scenario that gives purpose to the maze.  For example, a rabbit finding it way back to its burrow, a bee flying to its hive, a pirate finding the treasure.
2. Ask students if they can use their eyes to see the path through the maze. Alternatively give the students copies of the maze and ask them to trace the path using their fingers and once they have found to trace the path using a pencil.
3. Choose a volunteer to come up and draw the path through the maze.
4. Ask students how they could explain to someone who can’t see the maze where the line has been drawn. Encourage the use of accurate terms like up, down, left, and right. Follow the line through the maze as students describe it.
5. Draw another example on the board.
6. Ask students to describe the route they would take to get through the maze. Draw the route as they describe it. Individual students should only give one direction at a time (ie. Go down first). If students give unspecific instructions such as go round the corner draw the line incorrectly to force them to describe the route accurately.

#### Sessions 2-3

Maze Pairs

In this activity one student has a picture of a maze and the other has a blank grid. There are 4 mazes (two basic and two harder), and two blank grids (one for the basic mazes and one for the harder ones) available as copymasters. You can also easily make more mazes by using a vivid to draw walls on the blank grids.

1. The student with the maze has to solve the maze and then give their partner instructions for the route to follow through the maze (the instructions should include a direction and a number of squares eg. go down 2 squares). The partner with the grid should draw a line on a grid to show the route described to them. Make sure they start in the correct place.
2. Once the person following the instructions has completed a line across their grid they can check the answer by comparing the mazes and looking to see if the path drawn goes through any walls.
3. This could also be done as a whole class activity, with all students having a blank grid and the teacher giving instructions. Then a student could be given the opportunity to give instructions to the class, or students could break off into pairs.

Put Yourself in the Maze

For this extension to Maze Pairs tell students that they have to imagine that they are actually in the maze themselves, and that the only things they can do are to move forward or to turn left or right. This makes the activity much more challenging, as they now need to keep track of the direction they are facing as well as where in the maze they are. Counters with an arrow drawn on to indicate direction faced would be a useful aid.
The activity proceeds as in Maze Pairs above but both partners should use a counter with an arrow as they plot their route through the maze.

Outdoor maze

In this activity students take the direction giving skills they have used in the classroom outside and onto a larger scale.

1. Draw a large but fairly simple maze on the tennis court with chalk.
2. Get students to take it in turns to be blindfolded and directed through the maze by a partner who is not allowed to touch them, but has to give instructions about direction and distance.
3. The challenge is to get through the maze with as few instructions as possible and without touching or crossing the lines.
4. This could be a good opportunity to talk to students about the difficulties faced by people with impaired vision. Was it easy to get through the maze? Was it easy to give someone else directions through the maze?

#### Session 4

Let students draw their own mazes on grid paper, and challenge a friend to first solve it, and then give instructions for how to get through it.
You may need to give some guidance in drawing mazes – ensure that they are solvable, but try to have plenty of false paths and dead ends.
Possibly students could take their mazes to another class and show them how they have learned to give accurate directions through the maze.