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.
Resource logo
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 further members...
Resource logo
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 to solving number...
Resource logo
Level One
Geometry and Measurement
Units of Work
In this unit we compare the lengths of ākonga soft toys directly, and then indirectly using non-standard measurement units.
  • Compare a group of 3 or more objects by length.
  • Measure length with non-standard units.
Resource logo
Level One
Geometry and Measurement
Units of Work
In this unit students compare the duration of events and learn to read time to the hour and half-hour.
  • Directly compare the duration of two events.
  • Use non-standard units to compare the duration of two or more events.
  • Tell time to the hour and half hour using analogue clocks.
Resource logo
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

All about us

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.
Opportunities for Adaptation and Differentiation

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, acorns, leaves).
  • In session 2 use activities/sports that students in your class engage in. 
  • In session 3, te reo Māori vocabulary terms such as porowhita (circle), tapawhā rite (square), and tapatoru (triangle) could be introduced and used in this unit and used throughout other mathematical learning.
  • In session 5 create patterns using pictures of native birds such as Tuī and Kererū or natural materials found locally (shells, pebbles, acorns, leaves). 
Required Resource Materials
  • camera to record students’ work.
  • Session One – Countable objects, e.g. counters, cubes, toy animals, natural resources (shells, pebbles, leaves, acrons), post it notes or small pieces of paper. 
  • 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 (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), kitchen scales, preferably that are sensitive to about 500g (optional).
  • Session Five – images and objects to form patterns, (images of native birds, natural resources (shells, pebbles, leaves, acorns), 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 shapes, measurement, and data. Students are expected to be able to count a small set of objects by ones, at least.

Session One

In this first session students explore an activity called ‘Handfuls' which was first developed by Ann Gervasoni from Monash University, Melbourne. Handfuls could become a regular part of lessons during the year.

  1. Ignite the students' prior knowledge by asking them what they already know about mathematics. Discuss the purpose of the unit, which is to find out some information about the class and use it to help them with their maths learning.
     
  2. Begin the 'Handfuls' activity by modeling taking a handful of objects from a container. Place the collection on the mat in a disorganised arrangement.
     
  3. Estimate how many things you got in your handful (You may need to explain that an estimate is an educated guess).
     
  4. Ask your students to write the number on a small piece of paper 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 there are?
     
  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.
    A handful of acorns, with an arrow pointing to the same acorns organised into a line.
     
  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 ‘leftovers’. What to do with leftovers is an interesting discussion topic.
    Diagram showing acorns organised into pairs or groups of 5, with some left overs.
     
  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 their handfuls in at least two different ways. Try to take photographs of the handfuls for use in the group discussion.
     
  8. Observe 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 photographs 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 try 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. You may wish to replace the images provided in Copymaster 1 with images of sports that you know are popular with your students.

  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 of the data is 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.
    Graph showing the favourite sports of the students in Room 1.
     
  5. Create the picture graph on a large piece of paper by gluing the squares in place. Display the graph in a prominent place.

    The students will now choose other ‘favourites’ to use as data. Copymaster 2 provides some strips of favourites including favourite fruit, fast food, pet, vegetable, way to travel to school, and after school pastime. You may wish to create your own strips using ‘favourites’ that are relevant to your group of students.
     
  6. If using 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.
     
  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. The use of te reo Māori vocabulary for shapes could also be introduced and used within this session.

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.

“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.

Pattern blocks.Logic (attribute) blocks.Geometric solids.
Pattern BlocksLogic (Attribute) BlocksGeometric Solids

 

  1. Begin by discussing the shapes in a set. Ask questions like:
    • What shape is this? How do you know?
    • What is the te reo Māori name for this shape?
    • What features does the shape have to 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:

    Diagram of a circle below a square.Diagram of a circle in front of a square.Diagram of a circle on the right side of a square.
    The porowhita/circle is below the tapawhā rite/square.The porowhita is in front of the tapawhā rite.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:
    Picture of an arrangement of four shapes.
     
  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. Encourage the students to use the te reo Māori words for the shapes.
     
  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 an 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 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 including the te reo Māori words (not all may be relevant to your set of shapes):
    List of important words to do with shapes and positions.
  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. 
     
  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 judgment.
    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. Create 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 heavier 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 placed on a continuum, give the students a personal task.
    I want you to find five things from around the classroom and put them 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.
     
  8. Let the students order their five chosen 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. Crayons, glue sticks and books are good items to illustrate the point that the 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. Demonstrate creating four different repeating patterns using geometric shapes, images of native birds, natural materials, etc. At the end of each pattern progression 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. Ensure that patterns 3 and 4 have two variables and the sequence is different for those variables. For example, in pattern 3 geometric shapes could be used to show shape and colour variable (e.g. a yellow, red, yellow, red… colour sequence while shape could have a circle, hexagon, rectangle, circle, hexagon, rectangle, … sequence) and in pattern 4 images of native birds could be used to show animal and orientation variables (e.g. Kiwi, Tuī, Kererū, Takahe, … sequence while orientation could be a right, left, right, left, … sequence). 
     
  3. Provide students with a range of materials to form sequential patterns with. The items might include milk lids, blocks, toy plastic animals, locally sourced natural resources, images of native birds, 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).
     
  4. 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.
       
  5. Take 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.
     
  6. 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.
Attachments

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 develop knowledge of ‘tidy numbers’ and about ‘rounding to ten’. Students should be encouraged to know and have an intuitive feeling for "ten". Ultimately, they should be able to readily apply this knowledge 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.

Opportunities for Adaptation and Differentiation

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.
  • spreading  session 4 over two or more sessions if the students are unfamiliar with the Māori numbers to ten

The contexts for this unit can be adapted to suit the experiences of your students.  For example, 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 Māori is used in session 4. 

Te reo Māori vocabulary terms such as mati (digit) and meka matua (basic facts) could be introduced in this unit and used throughout other mathematical learning.

Required Resource Materials
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.
     
  4. Highlight the fact that in our systems we have ten digits which we ‘reuse’ (for example, the number 10 is made up of the numbers one and zero). On the board show the students 1, 10 and 100 as an example. 
     
  5. 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.
    Image showing the Roman numerals for the numbers 1 to 10.
     
  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.
    Image showing the Mayan numerals for the numbers 1 to 10.
     
  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 share their numeral system with another group.
     
  7. Conclude by reviewing different ways of writing ten. 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.
    A tens frame with ten dots in it.
    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. Direct students to take turns with a partner. Each turn, they should say how many dots they see and describe 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.” Model this for the class before allowing them to work in pairs. Consider organising the pairs to group together students with mixed mathematical abilities. There may be some students who would prefer to work with the teacher in a small group whilst the rest of the class works in pairs.
    A tens frame with eight dots in it.
     
  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 two different coloured counters to fill the spaces, showing and saying ‘seven dots plus three dots is the same as ten dots’.
    A tens frame with seven black dots and three red dots in it.
    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 the 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 the tens frames in random order. Direct students to 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:
    A tens frame with eight dots in it.
    Students say, “Eight,” and write 2. Students with emergent writing skills could be paired with a student with more developed writing skills, or could use counters to demonstrate their understanding of how many more are needed to make ten.

Activity 2

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.
Students, with their hands behind their backs, make a number on their fingers.

A hand showing 3 raised fingers.  A hand showing 0 raised fingers.               A hand showing 5 raised fingers.  A hand showing 2 raised 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 in pairs.
(Purpose: to practice seeing, saying combinations to ten)
They need playing cards with Kings and Jacks removed, and use 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 in pairs..
(Purpose: to practice seeing and saying combinations to ten)
They need playing cards with Kings and Jacks removed, and use 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)
They need 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 chooses 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 Māori.

  1. Students count in te reo 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.
    A chart of Māori words for the numbers 1 to 10.
    Each student has a set of number words to ten in te reo Māori (Copymaster 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 number words in te reo Māori)
    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. Students will need to be confident using a Chromebook/iPad/laptop to participate in this task. 
     
  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. Draw focus to the basic facts that your students are familiar with. Students with more advanced knowledge may be able to share some of the basic facts they know, that make use of higher numbers, with the rest of the class.
    Grid showing basic addition and subtraction facts.
  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:
    A flow diagram showing "If I know this, then I know that" for 7 plus 3 equals 10.
    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 (Copymaster 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 modelled in 5a.
Attachments

Teddy Bears and Friends

Purpose

In this unit we compare the lengths of ākonga soft toys directly, and then indirectly using non-standard measurement units.

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 ākonga 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 ākonga 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.

Ākonga will also be encouraged to estimate. Initially these estimations may be little more than guesses, but estimating involves ākonga in developing a sense of the size of the unit. The skill of estimating is just as important as finding exact measurements, as both skills are used frequently in everyday life, for example, estimating shoe size before trying on a shoe, knowing exact height to go on a waterslide.

Opportunities for Adaptation and Differentiation

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

  • providing or removing help to ākonga to draw outlines
  • supporting ākonga 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
  • providing some ākonga with other units of non-standard measurement they could use to measure (for example, finger length, lego, strips of paper). Some ākonga may wish to explore with a ruler (standard form of measurement) as well.

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. 

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

  • providing other objects to measure that your ākonga may enjoy, for example, shoe length, rocks from playground or lunchbox lengths
  • ākonga could go beyond the classroom and measure other objects from around their kura and community, for example, playground equipment, parts of marae, gates and pathways.

Te reo Māori vocabulary terms such as ine (measure), roa (long), poto (short), nui (big) and iti (small) could be introduced in this unit and used throughout other mathematical learning.

Required Resource Materials
  • Multi-link cubes (or blocks)
  • Cuisenaire rods (the 10 rod is best)
  • Scissors
  • A teddy bear or soft toy from home
  • Large sheets of paper for drawing around the toys (A3 or A2)
  • A large roll of paper for drawing outlines of ākonga
Activity

In preparation for this unit, ask ākonga to bring a soft toy to kura. Have a supply of soft toys available to use in the classroom (e.g. for ākonga that forget).

Getting Started

  1. We begin the week by looking at all the soft toys ākonga have brought to kura. Ask the ākonga to introduce their soft toy to the class. The picture book There's a Bear in the Window by June Pitman-Hayes, and translated by Pānia Papa, could be used to ignite interest in this context.
  2. Ask a ākonga to put their toy in the centre of the circle.
    Who has a toy that is taller than this?
    Who has a toy that is shorter than this?
    Who has a toy that is the same height as this?
  3. Let ākonga take turns bringing their toys into the centre to compare. Ask ākonga to show you how they know the toys are taller, shorter, and the same height. Encourage students to identify that the starting point of the measurement must be the same when comparing the height of the toys.
  4. Put taller toys in one group, shorter toys in another and toys of the same height in the third group.
  5. After the heights have been compared, ask the ākonga to suggest other ways that the toys could be compared. For example: bigger or smaller feet, longer or shorter legs, bigger or smaller puku.
  6. Ask groups of 3 ākonga to put their toys into an order. As they do this, ask questions that require them to describe the size of the attribute (type) they are using as a referent. For example, What order have you put these toys in? Why is this toy placed here? Can you order them in a different way?
  7. See if other ākonga can guess the attribute that the groups have used to order their toys.
  8. Show ākonga 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 ākonga. In pairs, ākonga take turns drawing outlines of their bodies. A tuakana/teina model could work well here. They use these outlines to make measurements using multi-link cubes or cuisenaire rods (the 10 ones work best). Kaiako or ākonga can record their estimates and actual measurements as appropriate.

  1. Demonstrate how to draw around an ākonga to get an outline. Show that they need to draw around both arms and legs. This could be done with chalk outside if it is a fine day.
  2. Give each of ākonga 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 cuisenaire 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 ākonga what other parts of the body they would like to measure. List these on a chart (with drawing) for later reference. Be wary of students' feelings about their bodies.
  7. Ākonga can then go back to their pairs and outlines and measure the length of their legs, feet, fingers (for example) using either cubes or rods.
  8. If ākonga 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 ākonga to record their measurements on their outline.
  10. Once ākonga complete measuring their outline, ask them to measure the outline of their toy.
  11. At the end of each day, share mahi and make comparisons. Remember to make comparisons amongst the same type (toys or ākonga, in this case).

    Whose arm measured more than 25 cubes?
    How many more?
    Which parts of your body were measured shorter than your arm?
    Which is your smallest measurement?
    Which is your largest measurement?
    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 kura assembly with (the shortest in the front.)

  1. Ask ākonga to measure the height of their soft toy using multi-link cubes and record this on the outline. Have them cut off any extra paper from the top and bottom of the outline.
  2. Tell ākonga that the toys want to go to the kura assembly, and so that everyone can see them, they will need to stand in order from the short ones to the tall ones.
  3. Ask four ākonga to put their toy outlines in order. This could be done using a line on the floor/corridor or the edge of the whiteboard. Let other ākonga check the order.
  4. Other ākonga can now put their toy outlines in the line. As they place their toy outline in the line, 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 ākonga and whānau can see it.

A teddy bear with an arm length of 8 cubes and a height of 20 cubes.

How long now?

Purpose

In this unit students compare the duration of events and learn to read 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 compare the duration of two events.
  • Use 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

Duration
Comparing the duration of two events is an important part of developing an understanding of time passing. This can be done by directly comparing two activities that have common starting points, for example, singing a waiata or running around the building.

After ākonga have directly compared the duration of two events we use sand-timers, counting, 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.
Opportunities for Adaptation and Differentiation

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

  • including images, words and numbers on the chart used in session 2 to support beginning readers
  • introducing quarter hour times to those ākonga who are confident with telling time to the half hour
  • providing clocks (if available) that have a minute hand that moves with the hour hand (for example, to show that half-past an hour is halfway between two different hours)
  • providing a selection of different clocks to see and use in the classroom, for example, a digital clock with hours, minutes and seconds displayed, alarm clocks, watches and wall clocks..

The contexts for the duration activities are based on activities that are undertaken by ākonga in your classroom so should be engaging to them. Asking ākonga to choose which activities they would like to compare provides further opportunities for their engagement. For example, they could sing a waiata, complete a hand game or do a short obstacle course.

Te reo Māori vocabulary terms such as karaka (clock), karaka mati (digital clock), karaka ringa (analogue clock), haora (hour), and meneti (minute) could be introduced in this unit and used throughout other mathematical learning.

Required Resource Materials
  • Chart paper/whiteboards
  • Multi-link cubes
  • 2 skipping ropes of different length
  • Large number cards (1-12)
  • A large space
  • Paper plates
  • Cardboard 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/whiteboards
  1. Begin by asking ākonga which they think takes longer, making a tower with 10 cubes or hopping 10 times on each foot.
  2. Write the two events on a chart/whiteboard.
  3. Get two volunteers to complete the activity and discuss the findings as a class (mahi tahi model).
  4. Tell ākonga that today they are going to work with a partner comparing things they do to find out which takes longer. Ask ākonga for their ideas and add these to the chart.  Ideas could include: sing a waiata or draw a picture or a rainbow, collect 3 kākāriki items or collect 3 kōwhai items, say the names of five teachers or say the names of ten friends. Encourage links to relevant learning from other curriculum areas, and to the current interests and events that are a part of the lives of your ākonga.
  5. Get ākonga to work on the activities in pairs. A tuakana/teina model could work well here.
  6. Share and discuss findings.

Session 2: Clapping time

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

Resources
  • Multi-link cubes
  • Chart paper/whiteboards
  1. Begin by asking ākonga 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 ākonga to add their ideas.
  6. Ask each pair of ākonga to select one of the timing methods and use it to time the events. Give each pair a sheet of paper or whiteboard to record the times on.
  7. Display and share the results.

Session 3 : A big clock

In this activity ākonga 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 (potentially outside)
  1. Ask ākonga to tell you all they know about clocks. This will include both digital and analogue. They could draw pictures of different clocks they know about  (for example, grandfather clocks, large clocks in your community, sundials,  watches). 
  2. Ask questions that focus their thinking on what an analogue clock looks like.
  3. Draw a large circle with chalk  or use a pre-painted one from your kura playground.
  4. Choose 12 ākonga to hold the number cards.
  5. Get the rest of ākonga in the class to direct the number holders so that they form a large clock face.
  6. Give another ākonga the two ropes to hold in the centre of the "clock".
  7. Move the ropes so that the clock shows 3 o’clock. Ask ākonga 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 half hours.  If you move onto half hours, support ākonga to see the connection between half of a circle and the half past position on the clock.  

Session 4: Making Clocks

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

Resources:
  • Paper plates
  • Cardboard hands
  • Split pins
  • Analogue clocks
  1. Look at the analogue clocks and discuss their features:
    • a large hand 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 ākonga 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 Session 4)
  1. Let ākonga share the pictures that they have drawn or photographs of clocks found at home or in the community.
  2. Discuss the different types of clocks, for example, watches, clock radios, clocks on appliances, grandfather clocks, novelty clocks, large clocks in the community.
  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 kapa haka practice on time
    • so we know when our food is cooked
  4. Ask ākonga to show their favourite time of the day on their paper clocks.
  5. Ask ākonga 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. 

Opportunities for Adaptation and Differentiation

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)
  • giving students materials such as teddies to move through mazes. 

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. Simple Māori designs can be used for mazes. Images of Native Garden Mazes can be shared with the children to engage them in the unit.

Required Resource Materials
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 ruru finding its nest in a tree, a kiwi going back to its burrow, a rabbit finding its 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 the end, 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. Provide a context for the maze such as a wētā finding its way to its home in a hole in a log.
  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. You may like to provide a context for the maze, such as a tuatara is finding its way back to its burrow.
  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. Display some examples of a variety of simple mazes as inspiration.
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, or take them home to share with whānau.

Printed from https://nzmaths.co.nz/user/75803/planning-space/late-level-1-plan-term-1 at 12:20am on the 29th March 2024