Early level 1 plan (term 2)

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.
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Level One
Statistics
Units of Work
In this unit we explore ways to pose and answer investigative questions about cats by gathering and analysing data and discussing the results.
  • Pose investigative questions with support from the teacher.
  • With the teacher, decide on how to collect the data to answer the investigative question.
  • Sort objects into categories for display.
  • Make a display of the data collected (pictograph).
  • Make statements about data displays.
Resource logo
Level One
Number and Algebra
Units of Work
This unit develops students’ understanding of, and proficiency in, using five-based grouping.
  • Identify five-based groupings.
  • Represent five-based groupings in a variety of ways.
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Level One
Geometry and Measurement
Units of Work
In this unit ākonga describe and classify 2D and 3D shapes. They will use their own language in their descriptions, will explore similarities and differences, and will informally consider sides, corners, curved and straight lines.
  • Sort, compare and classify 2D and 3D objects such as triangle, square, oblong, circle, box, cylinder and sphere.
  • Describe shape attributes in their own language.
Resource logo
Level One
Number and Algebra
Units of Work
In this unit students explore and create patterns of two and three elements using the rhyme "Mary, Mary Quite Contrary" as a focusing theme.
  • "Read" a repeating pattern and predict what may come next.
  • Create a repeating pattern with two elements.
  • Create a repeating pattern with three elements.
Resource logo
Level One
Integrated
Units of Work
This unit consists of mathematical learning, at Level 1 of the New Zealand Curriculum, focused around celebrations of Matariki, the Māori New Year. The sessions provide meaningful contexts that highlight Māori culture and provide powerful learning opportunities that connect different strands of...
  • Assemble parts of a shape to form the whole.
  • Create symmetrical figures (reflection and rotation).
  • Calculate the number of direct ancestors they have.
  • Use fractions to create rhythmic percussion patterns.
  • Order events.
  • Describe the likelihood of outcomes using the language of chance.
  • Measures quantities...
Source URL: https://nzmaths.co.nz/user/75803/planning-space/early-level-1-plan-term-2

Greedy Cat

Purpose

In this unit we explore ways to pose and answer investigative questions about cats by gathering and analysing data and discussing the results.

Achievement Objectives
S1-1: Conduct investigations using the statistical enquiry cycle: posing and answering questions; gathering, sorting and counting, and displaying category data; discussing the results.
Specific Learning Outcomes
  • Pose investigative questions with support from the teacher.
  • With the teacher, decide on how to collect the data to answer the investigative question.
  • Sort objects into categories for display.
  • Make a display of the data collected (pictograph).
  • Make statements about data displays.
Description of Mathematics

In this unit, students pose investigative questions with the teacher, then gather, sort, display and discuss data. This data is then used to answer the investigative questions. These skills are foundational to statistical investigations. In particular, posing investigative questions is fundamental to a good statistical investigation. At Level 1 the investigative question is driven by the teacher who models good structure without being explicit about the structure. 

In this unit the students are extensively involved in the sorting and display of the data (cat pictures). Sorting is an excellent way to encourage students to think about important features of data and this leads to classifications that make sense to them. In this unit the students compare the groups formed when the data is sorted by one-to-one matching. This one-to-one matching leads to the development of a pictograph. In turn, this provides an opportunity to strengthen the counting strategies of the students as the objects in the data sets are counted and compared.

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:

  • reducing the number of cat pictures in the data set for students who are beginning to count one-to-one when they are doing individual or small group work
  • extending the data to include counts of the number of cats (dogs, pets) students have. 

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

  • looking at another type of pet e.g. dogs, fish, native animals
  • adapting the context to focus on other items that could form a categorical data set (i.e. the items are able to be counted as individual items). The key learning in this unit is posing investigative questions, and gathering, sorting, displaying and discussing data that is generated as a result of using the investigative questions. Therefore, when adapting the context of this learning, you should consider what items (i.e. data set) might reflect the cultural diversity and current interests of your class. 

Consider how the text Greedy Cat, and the relevant learning done in this unit, can be integrated in your literacy instruction. If choosing to focus the unit of learning around a different set of categorical data, consider finding a relevant picture book to engage your students in the context.

Te reo Māori vocabulary terms such as ngeru (cat), kuri (dog), and ika (fish) as well as counting in te reo Māori could be introduced in this unit and used throughout other mathematical and classroom learning.

Required Resource Materials
  • Greedy Cat by Joy Cowley (Ready to Read)
  • A4 paper for drawing (cut into 8 pieces)
  • Chart paper
  • Scissors
  • Glue
  • Crayons
  • "Big Cat" pictures
Activity

Getting Started

Begin the week by sharing the book Greedy Cat. If you do not have the book, a copy or a video is available online.

(For very young students the teacher may need to record a statement about the cat under the picture, for example, "a fluffy cat").

  1. Discuss the pictures in the book. Talk about the things the students notice about Greedy Cat. Emphasise the attributes of Greedy Cat. 
  2. Students talk about their own cat (ngeru) or the pet or cat that they would like to have.
  3. Students draw a cat on their rectangle of paper (1/8 of the A4).

Exploring

Collect the cat pictures and photocopies these onto A4 sheets. One copy of all the cats will be needed for each pair of students. (Note: If colour is the attribute used you will need to colour copy the cats).

  1. Explain that we are going to investigate "What are the types of cats the students in our class have or would like to have? (this is the investigative question).
    In our last session we drew pictures of cats. We will use these pictures to collect information (data). What information do you think we could collect from looking at these cards? Record students' ideas somewhere visible. 
  2. The teacher spreads the original drawings out for the class to see.
    Can you see any cats that are the same or similar? How?  
    What cats are different? How?
  3. These cats are placed in a pile and given to the child who named the category.
    How many cats are there in the pile? One, two, three... tahi, rua, toru .....
    As a class, count the number of cats in the pile.
    The question is repeated until all the cats are sorted.
    Use this counting activity as an opportunity to strengthen the number sequences and one-to-one correspondence of the word name with the item with, students who are emergent (stage 0) on the Number Framework. Ask for volunteers to count the objects, asking them to justify their count. Students at stages 1 and 2 might count by pointing to or touching the objects while students at higher stages may use images of the numbers and be able to 'see' that a group is, for example, four, without needing to count the objects. Discuss the different counting strategies demonstrated by students.
  4. Repeat the process encouraging the students to be more "creative" in their nomination of categories. Get the students who already have a pile of cats to restate the category that they used so that they don’t forget this category. This reinforces the sorting of data.
    Who do you think has the most cats?
    How do you know? Show me.
    If the students do not use one-to-one matching you may need to model this.
    Students at stage 4 or above may be able to find the difference between the sets by counting-on or back.
  5. How can we tell who has the most cats?
    Once the categories have been matched 1-1 (in a line) attach the pictures onto a chart.
    Record statements beside the chart of cats about the number in each category, and some comparisons between categories.

Over the next two days work with the students to develop investigative questions about cats and to use the photocopied pictures (data) to find the answers.

  1. Brainstorm possible areas we could explore and develop investigative questions.
    What size cats do we have?
    What types of coats do our cats have?
    What sorts of tails do our cats have?
  2. The pairs select and record the investigative question they want to work on. They then sort and display the cat pictures (1-1 to form a pictograph) to answer their investigative question.
    Repeat this with another investigative question (if time allows).
  3. Conclude the exploration by pinning up the cat displays on the wall to share with everyone (this may include parents and whānau). Each pair selects one of their displays to tell the class about. Question, prompt and support as needed to elicit appropriate oral language including statistical language.

Reflecting

Today we look at a set of "big cats" (for instance, lions and tigers) and pose possible investigative questions. Other animals could be used here depending on the interests and experiences of the children.

  1. Display photos of cats. Discuss the photos.
    Does anyone know the names of these animals?
    Where might they live?
    Have you ever seen any of these? Where?
  2. After a general discussion focus on the possible questions areas of interest that could be answered explored using the photos.
    What kind of things could we find out about "big cats" from these pictures?
    (For example: patterns on their coat, types of tails Are there more spotty cats than stripey cats? Do all cats have bushy tails?)
  3. Develop investigative questions together and list the questions on a chart. E.g. What are the patterns on the coats of the big cats?
  4. Leave the investigative questions and the pictures for the students to explore.
Attachments

Learning to count: Five-based grouping

Purpose

This unit develops students’ understanding of, and proficiency in, using five-based grouping.

Achievement Objectives
NA1-1: Use a range of counting, grouping, and equal-sharing strategies with whole numbers and fractions.
Specific Learning Outcomes
  • Identify five-based groupings.
  • Represent five-based groupings in a variety of ways.
Description of Mathematics

Gelman and Gallistel (1978) provided five principles that young students need to generalise when learning to count. These principles are:

  1. The one-to-one principle
    Just like in reading when one spoken word is matched to one written word, counting involves one-to-one correspondence. One item in a collection is matched to one spoken or written word in the whole number counting sequence.
  2. The stable order principle
    The spoken and written names that are said and read have a fixed order. If that order is altered, e.g. “One, two, four, five,…”, the count will not work.
  3. The cardinal principle
    Assuming the one-to-one and stable order principles are applied then the last number in a count tells how many items are in the whole collection.

The first three principles are about how to count. The final two principles are about what can be counted:

  1. The abstraction principle
    Items to count can be tangible, like physical objects or pictures, or they can be imaginary, like words, sounds, or ideas, e.g. Five types of animal.
  2. The order irrelevance principle
    The order in which the items are counted does not alter the cardinality of the collection. This is particularly challenging for students who think that counting is about assigning number names to the items, e.g. “This counter is number three.”
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:

  • providing extended opportunities to use equipment to explore five based groupings
  • ensuring students are confident with groupings of 5, before moving onto groupings with 5
  • supporting students to use counting strategies to identify grouping patterns, if needed.

The contexts for activities can be adapted to suit the interests and experiences of your students. For example:

  • introducing counting in te reo Māori from tahi ki tekau ma rua (zero to 20)
  • using materials (e.g. finger puppets, shells, plastic jelly beans) that can be linked to learning from other curriculum areas, or events and interests from the lives of your students. 
Required Resource Materials
  • Five based Tens Frames
  • Slavonic abacus
  • Unifix cubes
  • Numeral cards, 1–20
Activity

Use a variety of equipment to explore five based grouping: a slavonic abacus, five-based tens frames, unifix (or similar) linking cubes, and students’ hands. Using a variety of representations is a powerful way to develop grouping knowledge. These tasks illustrate grouping with numbers from 5 – 10 but can be used with smaller and larger quantities.

Session 1: Finger pattern pairs

An important connection is between the parts that make ten. If a student knows that in 7 + ? = 10 the missing number is three, then they may transfer that fact to the answer to the problem 3 + ? = 10. For example:
Show me seven fingers.
How many more fingers make ten? How many fingers are you holding down?
Write 7 + 3 =10 and say, “Seven plus three equals ten.”
Show me three fingers.
How many more fingers make ten? How many fingers are you holding down?

Variations
Students work in pairs. One student makes a number up to ten with their fingers. The other says the number and writes the numeral for it big in the air.
Find different ways to make a number to ten, for example, seven can be 5 + 2, 3 + 4, 1 + 6 and 0 + 7. Finding ways to make numbers between 10 and 20 is possible in pairs or threes.

Session 2: Slavonic abacus and finger patterns

The Slavonic abacus is five based. The purpose of the colouring is to enable instant recognition of a quantity without counting. Try not to use counting to confirm a quantity as that is counter-productive to the intention of either knowing the quantity or working it out from known facts.
For example:
Make a number between 5 and 10 on the top row. Shift the quantity in one move, not one counter at a time.
Show me that many fingers. Note that this gives all students time to work out an answer and it also provides a way for you to see what each student is thinking.
How many beads are there?
How did you know there were eight?
Encourage grouping-based strategies, such as “I can see five and three” and “There are two missing from ten, so I held two fingers down.”

Variations
Ask the students to convince a partner how many beads have moved.
Ask the students to write the number for the beads on the palm of their hand in invisible ink then show you.
Move to “ten and” groupings such as ten and four to develop teen number knowledge. Students work in pairs to show that many fingers or write the number on the palm of their hand.

Session 3: Five based tens frames

Hold up a single tens frame, such as nine, for no longer than one or two seconds. The aim is for students to image the five-based patterns rather than count the dots one by one.
How many dots did you see?
Show me that number on your fingers.
Write that number big in the air for me.
Discuss the structure that students saw. “I saw five and four.” “I saw one missing from ten.” I saw three threes.”

Variations
Play 'tens frame flash' in pairs or threes. Players take turns to be the ‘flasher’ and show the tens frames, with the other students stating the number of dots on each tens frame as quickly as possible.
Instead of writing the number, talk to a partner about what you saw.
Write what is found with symbols like, 8 + 2 = 10, 10 – 2 = 8.
Progress to two tens frames being shown. Start with numbers less than five, e.g. four and three. Move to ten and another tens frame for teen numbers, e.g. ten and six. Try ‘close to ten’ frames, like nine and eight, with another tens frame, e.g. nine and five.

Session 4: Cube stack

  1. Begin with a stack of ten cubes made from five cubes of two colours. Like the slavonic abacus the colours are used to support non-counting methods to establish quantity.
  2. Like the tens frame and abacus activities students can match a quantity you hold up, using their fingers or writing the number. However, finding a missing part encourages part-part-whole knowledge. Show the students a stack of cubes with some missing (put into your pocket). Show the stack for a second or two then hide it.
  3. Ask: How many cubes did you see? How do you know? How many did I put in my pocket?
  4. Praise risk-taking even if the answers are incorrect and try to offer knowledge that might be helpful. For example:
    I think there are eight because I saw five and two.
    Good work. This would be eight (showing five and three). Can you fix it?
  5. After the students have found the missing part, reveal it from your pocket to check.


Variations
Students play in pairs with one being the hider and the other the estimator.
Start with a number other than ten, e.g. eight stacks made of five and three.
Students match stacks to finger patterns to help them find the number of missing cubes.
Students write equations for the stacks problems, e.g. 7 + ? = 10.
Progress to taking some cubes from each end. Progress to using two stacks of ten to start, depending on the number knowledge of the students.

Session 5: Ordering fitness fun

  1. Organise students into 5 or 6 relay lines.  Each relay line has an ice cream container with the numeral cards 1-10 or 10-20 in them.  At the other end of the court place the empty number line.
  2. When the teacher says go. The first student in the line closes their eyes and picks a numeral card out of the container.  They run to the other end of the court and place the number in the correct place on the number line.  Then they run back and tag the next person in line.  This continues until all the numbers are placed on the number line. 
  3. When all the numbers have been removed from the container, the whole team runs in a line to the end of the court to check that the sequence is in the right order.  When they are satisfied it’s correct they sit around the number line in a circle.
  4. Conclude the session with students by talking about how they knew that they had put the number in the correct place.
    How can the shading help to work out where number 6 would go, without having to count?
    For example, I knew that 5 went there because it’s at the end of the shaded box.

Shape Makers

Purpose

In this unit ākonga describe and classify 2D and 3D shapes. They will use their own language in their descriptions, will explore similarities and differences, and will informally consider sides, corners, curved and straight lines.

Achievement Objectives
GM1-2: Sort objects by their appearance.
Specific Learning Outcomes
  • Sort, compare and classify 2D and 3D objects such as triangle, square, oblong, circle, box, cylinder and sphere.
  • Describe shape attributes in their own language.
Description of Mathematics

Spatial understandings are necessary for interpreting and understanding our geometric environment. The emphasis in the early years of school should include: recognition and sorting of shapes, exploration of shapes, and investigation of the properties of shapes.

In the van Hiele model of geometric thinking there are five levels. The first (Visualisation) is emergent. At this stage, ākonga recognise shapes by their appearance rather than their characteristics or properties. The second level (Analysis) is where ākonga differentiate specific properties of shapes, for example, the number of sides a triangle has or the number of corners in a square. Ākonga recognise certain properties that make one shape different from others.  This unit is focused on this second level of the van Hiele model.

Ākonga discover 2D and 3D shapes within their environment (for example, square, cube, poi, desk, bed, starfish) and there is much discussion about which is easier to consider first.  Both need to be explored extensively. Sufficient opportunities need to be given for ākonga to communicate their findings about 2D and 3D shapes. 

This unit could be followed by the unit Shape explorers.

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:

  • reducing the number of shapes that are sorted and the number of categories that they are sorted into
  • limiting or increasing the feely bag to either 2D or 3D shapes, or reduce or increase the number of shapes
  • providing or co-creating a reference poster to display in the classroom of the different shapes you discover. This could include images, words (including in te reo Māori) and symbols (this may help beginner readers)
  • introduce more or less types of 2D and 3D shapes according to the needs of ākonga.

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

  • use objects from the local environment to place in the feely bag (for example, stones, cones, leaves, seed pods, shells, buds)
  • make reference to 2D and 3D shapes in your local community (for example, circle, sphere, marae, community garden, playground or public transport).

Te reo Māori vocabulary terms such as āhua (shape), tapawha rite (square), porowhita (circle), and torotika (straight) could be introduced in this unit and used throughout other mathematical learning.

Required Resource Materials
  • Mosaic tiles
  • Shape attribute blocks
  • Small blocks
  • String
  • Geoboards and rubber bands
Activity

Session 1: Loopy Shapes

In this activity we sort shapes according to attributes. Working with blocks in this exploration gives ākonga a chance to construct their own understandings about shapes and how they are related.

  1. Gather ākonga around a supply of shape blocks, mosaic tiles and attribute blocks.
    Do you see any ways that these blocks are alike? How are they alike?
    Can you see any blocks that are different? How are they different?
  2. Use one of the categories suggested by the ākonga to sort the blocks.
    Let’s sort the shapes by size and see how many we have.
  3. Put three loops of string or make chalk circles or set rings/hula-hoops out for ākonga to sort the blocks in.
  4. Begin by putting a small shape in one of the loops.
  5. Distribute the shapes and have ākonga sort them into the three loops.
  6. Look at and discuss the shapes in the loops.
    Which loop has the most? Check by counting.
    Do the shapes in this loop have other things in common?
  7. Sort the blocks using another attribute. Some possibilities are:
    • colour
    • shapes with 3, 4, 5 or 6 sides
    • shapes that are round and shapes that aren’t

Let ākonga work in small groups to sort sets of shapes in a number of different ways. Circulate among the groups encouraging ākonga to describe the classification used. Tuakana/teina groupings could work well here. 

Session 2: I spy a shape

In this session we play a version of ‘I spy’ ( or 'Kei te kite ahau') that helps ākonga focus on the shapes around them and the number of sides the shapes have.

  1. I spy a shape with four sides. You walk through it when you come into the classroom. What is the object?
  2. Have the ākonga who guesses correctly go to the door and count the number of sides. Record this on a chart.
  3. I spy another object with four sides. This one we look out of. What is the object?
  4. Once more get the guesser to count and check the number of sides.
  5. Let ākonga take turns giving clues about a shape in the class for others to guess. Each time get the guesser to check the number of sides.
  6. Encourage ākonga to give information about the relative length of the sides of the shape. For example, all sides are the same length; this side is longer.

After the game has been played several times get ākonga to draw pictures of 3- or 4-sided shapes in the room. Alternatively you could go for a walk outside to look for shapes and then get ākonga to draw these. Some ākonga may draw irregular 3- or 4- sided shapes such as a trapezium or isosceles triangle, this could be used as a teachable moment to extend some ākonga. Glue the drawings onto charts according to the way that ākonga classify them.

Discuss the charts.
What are some of the things you notice about the shapes you found?
Which did you find more of? Why do you think this is?
Do you know what we call these shapes?

Session 3: In the bag

Which shape is in the bag? Today we reach into feely bags to see if we can work out the shape by touch alone.

  1. Gather ākonga together in a circle on the mat (mahi tahi model). Show them 5 shapes on the floor including 2D and 3D shapes. These could be small blocks, mosaic tiles or attribute blocks.
  2. Show ākonga the feely bag.
    One of these shapes is in the bag. I wonder if you can tell me which one just by feeling it?
  3. Pass the bag around the circle so that each ākonga can feel the shape. Encourage them to think about the shape. Remind them that they shouldn’t point or call out which shape they think it is so that everyone gets a chance.
  4. As each ākonga feels the shape in the bag, get them to say one thing they notice about it.
    Tell me something you notice about the shape in the bag.
  5. Once each ākonga has had a turn to feel in the bag, ask them to say which shape they thought it was. Then reveal the hidden shape.
    Is this the shape you were expecting?
  6. Secretly change the shape in the bag and play again as a whole class.
  7. In small groups or pairs, ākonga play the game again as the teacher circulates and questions. Change the types of shapes according to the needs of your ākonga. 
    Can you describe what you can feel?
    Which shape do you think it is? Why?

Session 4: Dominoes

In this session we use the mosaic shapes as dominoes for ākonga to explore shapes and match side lengths as they form a trail of shapes.

  1. Gather ākonga in a circle on the mat. Tip the mosaic tiles onto the mat in the middle of the circle.
  2. Tell them they are going to play a game of shape dominoes. They are going to match shape sides that are the same length to make a trail around the mat.
  3. Let ākonga informally explore sides of the same length by fitting two or more shapes together.
  4. Place a tile on the floor and get ākonga next to you to choose a shape that could go next.
    Are there other ways that you could place that shape tile?
    Are there any ways that shape tiles wouldn’t work?
  5. Continue around the circle until each ākonga has had a turn.
  6. Ākonga can continue playing the game in small groups (a tuakana/teina model could work well), with the teacher circulating and questioning.
    What can you tell me about the shape tile you have chosen to go next?
    Why did you choose that shape tile?

Session 5: Shape makers

In this session we use loops of string or wool to form shapes using ourselves as the corners. We extend the idea using geoboards and rubber bands.

  1. Gather ākonga on the mat.
  2. Have a long piece of thick string or wool and talk about the shape of the string.
    Who can tell me about this piece of string? (Long, curly, wiggly, etc.)
  3. Hold the string in a long straight line and then let it fall onto the floor in a muddle and get ākonga to describe how the shape has changed.
    What was the string like when we held it tight?
    What was it like on the floor?
    How else could we hold the string or put it on the floor to change its shape?
  4. Encourage ākonga to make suggestions about the form of the string and to use their own language to describe it.
  5. Get each ākonga to hold part of the string and get them to move backwards to form a circle using the whole class and again encourage them to describe the shape in their own language.
  6. Using a shorter length of string.  Get small groups of ākonga to hold the string and to explore the shapes that can be made.
    What sort of shapes can you make with three people? (or 4 or 5 people etc.)
    How many sides will the shape have?
    Do all the sides have to be the same length?
  7. Get ākonga to continue exploring string shapes in small groups as the teacher circulates and questions.
  8. Using rubber bands and geoboards, ākonga can to explore the same ideas.
  9. The geoboard shapes can be sorted into several sets (as with Loopy Shapes, Session 1) and ākonga can talk about the similarities and differences between the shapes they have made including, number of sides and lengths of sides.
  10. This can be used to make a chart for display. Photos could be taken of the geoboard shape creations.

Mary, Mary, Quite Contrary

Purpose

In this unit students explore and create patterns of two and three elements using the rhyme "Mary, Mary Quite Contrary" as a focusing theme.

Achievement Objectives
NA1-6: Create and continue sequential patterns.
Specific Learning Outcomes
  • "Read" a repeating pattern and predict what may come next.
  • Create a repeating pattern with two elements.
  • Create a repeating pattern with three elements.
Description of Mathematics

This unit is about the simplest kinds of patterns that you can make – those with just two things. So this unit lays the foundation for much more complicated patterns to come. The skills that the student will develop here, such as creating a pattern, continuing a pattern, predicting what comes next, finding what object is missing, and describing a pattern, are all important skills that will be used many times. Indeed they are essentially what mathematics is all about.

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. As the sessions in this unit focus on simple 2-element patterns it is more likely that ways to extend students may be needed. Ways to extend students include:

  • introducing a third colour to the daisy pattern in session 1
  • adding a third flower to the pattern in session 3
  • increasing the size of the “cloche” in session 4 so that it covers a larger part of the pattern.

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

  • using native birds or animals instead of flowers and vegetables. For example, tūī, pīwakwaka (fantail), tuatara
  • using recreational or sporting objects. For example, scooters and bicycles, netballs and rugby balls.
  • the learning in this unit could be linked to the context of creating a school or community garden, or the context of looking at a pre-existing garden (e.g. the Botanical gardens, the garden at a marae).

Te reo Māori vocabulary terms such as tauira (pattern), as well as counting from tahi ki tekau (one to 10) could be introduced in this unit and used throughout other mathematical learning. Other te reo Maori that could be useful in this unit are colours (such as kōwhai and ma), puaka (flower), and huawhenua (vegetables).

Required Resource Materials
  • Nursery rhyme card "Mary, Mary Quite Contrary" (This is available as part of the Ready to Read series, and is easily found online)
  • Coloured paper petals to construct flowers
  • Magnetic backed paper flowers and magnetic board
  • Vegetable cut outs
  • Flower game cards
Activity

Session 1

This session explores simple 2-element patterns around the theme of a daisy.

  1. Read and/or listen to the nursery rhyme "Mary, Mary Quite Contrary". Consider using this poem in your literacy teaching to enhance its relevance.
  2. Talk about what might be in Mary’s garden. Name some flowers and talk about them. If possible show the students a daisy – note the petals.
  3. Using the cut petals and a centre circle, the teacher partially constructs a "daisy" with a regular 2-element pattern using coloured petals. The pattern could be yellow, white, yellow, white, …
  4. Can you read my pattern?
    What will the next petal be?
    How do you know?
  5. Students explore and create their own "daisies".
  6. Students share and describe their daisy pattern with the class.

Session 2

Using the same nursery rhyme theme again, explore patterns with flowers.

  1. Reread the nursery rhyme.
  2. Mary likes to keep her garden neat and tidy. She plants flowers in patterns.
    Model this idea using magnetic backed coloured flowers on a magnetic board.
  3. Can anyone continue my pattern?
  4. Select a student to complete the pattern of coloured flowers.
  5. Invite two or three students to create a flower pattern in front of the class using the magnetic flowers.
  6. What is the pattern here?
    Can we read this pattern?
    What will come next?
    How do you know?
  7. Students construct their own garden flower patterns using the flower cut outs. Move around the students and discuss what they are doing.
    Tell me your pattern.
    What will come next?
    How do you know?"

Session 3

Simple patterns are again explored but this time using a card game.

Use the copymaster to make a set of cards. Now create baseboards with ten squares. Attach two flower cards to the first two squares to form the beginning of a pattern:

Picture of a purple flower card.Picture of a red flower card.        
  1. Students work in pairs. They each select a baseboard that has the outline of a pattern.
  2. The students take it in turns to take a card from the pile. If it is part of their pattern they place it in the correct place on the baseboard. If not needed the card is put at the bottom of the pile of cards.
  3. Repeat with the same baseboard and with different baseboards.
  4. Move around the students and discuss what they are doing.
    Tell me your pattern.
    What will come next?
    How do you know?

Session 4

Instead of using flowers we now use vegetables to make 2-element and even 3-element patterns.

  1. Tell the following story:
    Mary likes to grow vegetables. In her garden she grows carrots, tomatoes, pumpkins and kūmara. She grows her vegetables in patterns.
  2. Model a 2-element vegetable pattern for the class, for example, carrot, carrot, tomato, carrot, carrot, tomato...
  3. The class reads and predicts the pattern.
  4. Explain how gardeners sometimes use cloches (mini glasshouses) to protect plants as they are growing. 
    Mary often uses these in her vegetable garden.
  5. The teacher covers part of her pattern with a "cloche".
  6. Can you tell me what is hidden inside the cloche?
    How do you know?"
  7. Students construct vegetable gardens and cover part of their "garden" with a cloche. Working with a partner they try to predict which vegetables are hidden.
  8. More able students can move to constructing a vegetable garden using 3 different vegetables.

Session 5

The students guess the missing members of a vegetable pattern where more than 1 vegetable has been "eaten".

  1. Make a vegetable pattern like the ones in the last session. But this time some vegetables are missing from the row. Tell the students that rabbits have got into Mary’s garden and eaten some of the vegetables. Start with just one eaten vegetable and gradually increase the number eaten to 3.
  2. The students have to decide which vegetables have been eaten and place these in the correct places.
  3. Are the vegetables in the right place? How do you know?
  4. In pairs the students play the same game with their partner. They take turns forming the pattern and removing some of the vegetables.
Attachments

Matariki - Level 1

Purpose

This unit consists of mathematical learning, at Level 1 of the New Zealand Curriculum, focused around celebrations of Matariki, the Māori New Year. The sessions provide meaningful contexts that highlight Māori culture and provide powerful learning opportunities that connect different strands of mathematics.

Specific Learning Outcomes
  • Assemble parts of a shape to form the whole.
  • Create symmetrical figures (reflection and rotation).
  • Calculate the number of direct ancestors they have.
  • Use fractions to create rhythmic percussion patterns.
  • Order events.
  • Describe the likelihood of outcomes using the language of chance.
  • Measures quantities to follow a recipe.
Description of Mathematics

In this unit the students will apply different mathematical and statistical ideas, such as the properties of symmetry. In this, they will demonstrate understanding of the features of a shape that change and remain invariant under translation, reflection and rotation.

Table showing features of shapes that change and remain invariant under translation, reflection and rotation.

Students also apply simple probability. For example, given this set of cards, what is the chance of getting a bright star if you choose one card at random? Random means that each card has the same chance of selection.

Image showing four cards. One has a picture of a cloud, one has a dull star, and two have bright stars.

The set of all possible outcomes contains four possibilities. Two of those possible outcomes are selecting a bright star card. The chances of getting a bright star are two out of four or one half. There is a one quarter chance of getting a fuzzy star and the same chance of getting a rainy cloud.

Opportunities for Adaptation and Differentiation

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

  • explicitly modelling the key mathematical processes that students are required to apply in each session (e.g. measuring, identifying fractions)
  • supporting the use of specific counting and addition and subtraction strategies in reflection of your students’ strengths and strategy knowledge
  • modifying the numbers utilised in each session to suit the needs of your students
  • grouping students to encourage tuakana-teina (peer learning) and mahi-tahi (collaboration).

Although the context of Matariki should be engaging, and relevant, for the majority of your learners, it may be appropriate to frame the learning in these sessions around another significant time of year (e.g. Chinese New Year, Samoan language week). This context offers opportunities to make links between home and school. Consider asking family and community members to help with the different lessons. For example, members of your local marae may be able to share local stories and traditions of Matariki with your class.

Te reo Māori language is embedded throughout this unit. Relevant mathematical vocabulary that could be introduced in this unit and used throughout other learning include āhua (shape), shape names (e.g. whetū - star), hangarite (symmetry, symmetrical), whakaata (reflect, reflection), huri (rotate, rotation), tātai (calculate, calculation), tāpiri (add, addition), hautau (fraction), raupapa (sequence, order), tūponotanga (chance, probability), and ine (measure).

Required Resource Materials
Activity

Lesson One

  1. Introduce Matariki, The Māori New Year, to your class. There are many picture books and online videos that could be used to introduce this context. Matariki begins with the rising of the Matariki star cluster, (Pleiades in Greek), in late May or June. For the previous three months the Matariki cluster is below the horizon so it cannot be seen. The rising signals the turn of the seasons and sets the calendar for the rest of the year.
  2. Show your students the first few slides on PowerPoint 1. Discuss what stars are and how our sun is an example.
    What shape is a star?
    Today we are going to make some stars to display using shapes.
  3. For each slide discuss how the left-hand star is made then built onto to form the right star. Encourage your students to use correct names for the composing shapes, such as triangle, square, hexagon, trapezium. If necessary, provide a chart of the shapes and their names for students to refer to. Using a set of virtual or hard-copy pattern blocks, support students to make the stars on slides three and four by copying the pattern. Model this for students (especially if using virtual pattern-blocks). It may also be beneficial for students to work collaboratively (mahi-tahi) during this task.
  4. Encourage students to use the blocks to create their own stars. Slide 6 is a blank canvas of pattern blocks. With the slide in edit rather than display mode, you can use the blocks to form other patterns.
  5. Copymaster 1 provides two different puzzles for your students. They cut out the pieces to form a star. Glue sticks or blue-tack can be used to fasten the parts in place.
  6. Other Activities with Stars
    • Most star designs have mirror symmetry. That means that a mirror can be placed within the star, so the star appears complete. The reflection provides the missing half of the star. Demonstrate to your students how that works. Copymaster 2 provides four different star patterns. Give students small mirrors and ask them to find the places where a mirror can go so the whole star is seen. You could also demonstrate this on a PowerPoint, or using an online tool. An internet search for “online symmetry drawing tool” reveals a number of websites that could be used. Note that Star Four has no mirror symmetry so it is a non-example. Star Four does have rotational symmetry so it can map onto itself by rotation.
    • Copymaster 2 also has half stars on page two. Ask your students to complete the whole star. Be aware that attending to symmetry is harder when the mirror line is not vertical or horizontal. Can your students attend to perpendicular (at right angle) distance from the mirror line in recreating the other half?
  7. Creating stars by envelopes
    • The diagonals of some polygons create beautiful star patterns. The most famous pattern is the Mystic Pentagram that is created within a regular pentagon. Video 1 shows how to get started and leaves students to complete the pattern. The exercise is good for their motor skills as well as their attendance to pattern and structure. Copymaster 3 has other shapes to draw the diagonals inside. Note that a diagonal need not be to the corner directly opposite, it can also go to any corner that it does not share a side with.
    • Nice questions to ask are:
      How do you know that you have got all the diagonals? (Students might notice that the same number of diagonals come from each corner)
      Does the star have mirror lines? How do you know?

Lesson Two

In this lesson your students explore family trees, working out the number of people in their direct whakapapa. This may be a sensitive topic for some students. Thinking about our relatives who are no longer with us, or have just arrived, is a traditional part of Matariki, the Māori New Year. According to legend, Matariki is the time when Taramainuku, captain of Te Waka O Rangi, and gatherer of souls, releases the souls of the departed from the great net. The souls ascend into the sky to become stars.

  1. Begin by playing a video or reading a book about Ranginui (Sky Father) and Papatuanuku (Earth Mother), the mother and father of Māori Gods. 
  2. Ask: How many parents (matua) do you have?
    That question needs to be treated sensitively but the focus is on biological parents, usually a father and mother. You might personalise the answer by telling your students the names of your mother and father. Draw a diagram like this, or use an online tool to create the diagram:
    Image of part of a family tree showing two parents and their child.
  3. Ask:
    My mother and father had parents too. What are your parents' parents called?
    How many grandparents (koroua) do you have?
    Students may have different ways to establish the number of grandparents, such as just knowing, visualising the tree and counting in ones, or doubling (double two),
  4. Extend the whakapapa tree further.
    Image of part of a family tree showing two parents and their child.
  5. Ask: What do we call your grandparent’s parents? (Great grandparents, koroua rangatira)
    Nowadays, many students will still have living great grandparents. You might personalise the idea using your whakapapa.
    What do we call the parents of your great grandparents?
    Now I want you to solve this problem. How many great great grandparents do you have?
  6. Encourage students to work in small groups. Provide materials like counters or cubes to support students. Ask students to draw the whakapapa diagram to four layers and record their strategy as much as they can. After an appropriate time, share strategies.
  7. Discuss the efficiency of counting based strategies, counting by ones and skip counting in twos. Highlight more efficient methods such as doubling, e.g. 2 + 2 = 4, 4 + 4 = 8, 8 + 8 = 16.
  8. Ask: Now let’s just think about our parents. If three children in this class invited their parents along, how many parents would that be?
    Use the context as a vehicle for introducing even numbers (multiples of two), Act out three children getting their parents (other students) and bringing them to school. Change the number of students and work out the total number of parents. Find a way to highlight the numbers that come up, such as shading the numbers on a virtual Hundreds Board.
  9. Ask: Can anyone see a pattern in the numbers of parents?
    Students might notice that even numbers occur in the 0, 2, 4, 6, 8 columns of the hundreds board.
  10. Introduce a challenge: If everyone in this class brought their parents along, how many parents would that be?
  11. Ask the students to work in small teams with materials. Providing transparent counters and individual Hundred Boards will be useful but provide a range of options. Watch for your students to:
    • structure their model as "two parents for every one student"
    • deploy materials in an organised way to represent the whole class
    • use efficient counting strategies, to systematically find the number of parents
    • use recording to organise their thinking, particularly the use of number symbols.
  12. Share the strategies students used with a focus on the points above. Depending on the current achievement of your students you might extend the problems. For example:
    • Ten parents came along. How many students brought them?
    • How big would our class be if 100 parents came along?
    • If every student in another class brought two parents along, could there be 54 parents? What about 53 parents? Etc.
    • If students in our class brought all their grandparents along, how many grandparents would that be?
    • If we had to provide a Matariki celebration for our grandparents, what food and drink would we need?
    • How much of each food and drink would we need?

Lesson Three

Matariki is a time for cultural activities, such as story-telling, music, and games. Titi Rakau is a traditional game that involves hitting and throwing sticks, usually to a rhythmic chant. It was used to enhance the hand-eye coordination of children and warriors. Rakau can be used as a vehicle for fractions and musical notation, as well as physical coordination. You can make the tasks below as simple or as difficult as you like.

  1. Look at slide 1 of PowerPoint 2
    What fractions has the bar been broken into? (Quarters)
    Each of these notes (crotchet) is one quarter of a bar in this music.
  2. Find a piece of music online with a clear 4/4 time signature. That means there are four crochet (quarter) beats to the bar. This timing is very common in popular music. “Tahi” released by Moana and the Moa Hunters in 1994 is a good example that is easily found online. Ask your students to clap in steady 1, 2, 3, 4, … time with a consistent time between claps as the music plays.
  3. Introduce rākau, made from rolled up magazines taped together with duct tape. Students might practise hitting the ground with the ends of the sticks on every beat of the 4/4 time. This can be changed to beat one on the ground, and beat two ‘clapping’ the sticks together in the air, beat three on the ground, and beat four in the air, etc.
  4. Introduce the rest symbol using slide 2 of PowerPoint Two. In 4/4 time the rest is for one beat. So the rhythm is ‘clap, clap, clap, rest, clap, clap, clap, rest…” as is used in “We will rock you,” by Queen. Slide 3 has a bar with two rests. See if the students can maintain that rhythm.
  5. Slides 4 and 5 introduce the quaver which is a one-eighth note in 4/4 time. See if students can manage the two different rhythms, including the beamed (joined) quavers. Copymaster 4 can be made into cards, or cut out as is, to create different rhythmic bars in 4/4  time. Note that the semibreve (circular note) denotes the whole of four beats, and the minim (stemmed hollow note) denotes one half of a bar. A minim is equivalent to two crotchets.
  6. Let your students make up a single bar using the cards. Encourage them to experiment with possible rhythms by trailing them with Rakau. Rests are usually part of Rakau to allow movement of the sticks from one position, e.g. floor, to another, e.g. chest. The rhythm a student creates can be played by another using Rakau.
  7. Look for your students to:
    • Apply their knowledge of fractions, such as one half and two quarters make one whole (bar)
    • Recognise equivalence, such as two quarters make one whole or two eighths make one quarter.
  8. Share the bar patterns that students create and play them with Rakau. Rhythms can also be checked by finding an online music composer for children and entering the notes. The software usually has playback.
  9. Natural extensions of the task are:
    • Explore different time signatures. Many Māori action songs are in Waltz time (3/4) meaning that there are three crotchet beats to a bar. A crotchet is one third of a bar in that time signature and a quaver is one sixth of a bar.
      The popular chant associated with Ti Rākau (E Papa Waiari - available on YouTube) is in 6/8 time meaning there are six quaver beats to a bar. If you watch a video of a performance with Rākau the sticks are often hit on the ground on the first and fourth beats, or clicked together on the second, third, fifth and sixth beats.
    • Try to work out and record the rhythm of pieces of music, using the cards. Choose a difficulty that suits your students. For example, E rere taku poi, is in 4/4 time and is the tune to “My Girl.”  Kiri Te Kanawa’s recording of Te Tarahiki in 1999 features a six quaver rhythm in 3/4  time. 

Lesson Four

The rising of Matariki, in late May or June, signals to Māori that it is the start of a new year. It is appropriate for students to reflect on the passage of time. For young students there are important landmarks in the development of time, including:

  • Recalling and sequencing events that occurred in their past.
  • Anticipating events that might occur in the future.
  • Recognising that time is independent of events, it progresses no matter what is occurring.

Cooking in a hāngī

In the first part of the lesson students work with the first two ideas, recalling the past and anticipating the future.

  1. Show students a video about preparing and cooking a hāngī. There are many examples online. Before viewing the video prompt your students:
    Watch carefully. At the end of the video I will ask you about how to make a hāngī.
  2. At times pause the video to discuss what might be occurring. Use the pause as an opportunity to introduce important language, like hāngī stones, kai (food), prepare, cover, serve, etc.
  3. Give each pair or trio of students a copy of the first six pictures of Copymaster 5
    I want you to put the pictures in the order that they happened. Put them in a line. Be ready to explain why you put the pictures in that order.
  4. You might allow groups to send out a ‘spy’ to check the order that other groups are using. After a suitable time let the groups ‘tour’ the lines that other groups have created and change their own line if they want to. Bring the class together to discuss the order of events.
    Why does this happen before this?
    Why does this happen after this?
  5. Do your students recognise the consequential effect of order? e.g. The fire cannot be lit until the hole is dug and there is somewhere to put it.
  6. Can the students recognise what events occurred between two events? e.g. Covering the food with soil and waiting four hours occurred between putting the food and stones in the hole and taking the cooked food out.
  7. Discuss:
    What might have happened before the hole was dug?
    What might have happened after the food was served?
  8. Ask students to draw and caption an event that occurred before the sequence of pictures, and another event that happened after. You could also provide a graphic organiser for students to use. For example, the food must be prepared before or while the hole is dug. It must be bought or gathered before it can be prepared. After the food is served it will be eaten. Copymaster 5, pictures 7 and 8 are before and after pictures.
  9. Add students’ before and after pictures to the collection from Copymaster 5. You might create a wall display. Some before and after pictures might need to be sequenced. Picture 9 is an event (uncovering the hole) that occurs between two of the six events. Where does it go? Why?

Chances of a good year

In former times, tohunga, wise people of the village, looked at the sky before dawn to watch the rising of Matariki. They used the clarity of the stars to predict what the new year would bring. A clear sky with the stars of Matariki shining brightly signalled a good season for weather and the growing and harvesting of crops. A cloudy sky signalled bad luck.

  1. At the rising of Matariki, some stars shine brightly while others do not. Each star has a special job. Use PowerPoint 3 to introduce the stars and their jobs. Play a game with Copymaster 6. The first page is a game board. Use the second page to make a set of 12 cards (bright stars, fuzzy stars, and clouds). The second page can be used to make three sets of the cards.
  2. Put the gameboard down and spread the cards face down on the floor. Mix the cards up while students close their eyes. Students select cards one at a time to cover each of the seven stars. For example, Matariki might be covered by the card for a fuzzy star. Slide 2 of PowerPoint 3 shows a completed gameboard (click through it to place the cards).
    If you saw this, what would you predict?
  3. Students should make comments like:
    There will be plenty of rain but not too much, and the crops will grow well.
    It is going to be a bit windy.
    There will be lots of food in the rivers, lakes and sea.
  4. Let students play their own game of predicting the upcoming year. Look to see whether students consider what is on the set of cards in predicting what card might come next.
  5. After playing the game discuss:
    • Is it possible to have a year where every star shines brightly? (No. There are six bright star cards and seven stars of Matariki)
    • What is the worst year you can have? (All two clouds and four fuzzy stars come up)
    • How likely is it that you will have a good year? (Quite likely since half the cards are bright stars and one third of the cards are fuzzy stars)

Lesson Five

This lesson involves making rēwena paraoa (potato bread). The process of making it takes three stages; preparing the ‘bug’, mixing and baking, then serving. Therefore, it is not a continuous lesson. Preparation and serving food are important activities for Matariki celebrations. It would be beneficial to invite older students, or community members, in to help with this session.

  1. Explain: In the next three days we are going to make rēwena bread from potatoes. Why is the bread you buy at the supermarket so light and fluffy?
  2. Some students may have made bread with their parents or grandparents and can talk about yeast as the ‘leavening’ agent. Play an online video of breadmaking and discuss what each ingredient contributes.
  3. In rēwena bread the natural yeast from potatoes is used to raise the dough. The best potatoes are older taewa (Māori potatoes) which are small and knobbly, but any medium sized aged potato will do. One medium sized potato is needed per recipe (for three students).
  4. Weighing the potatoes on kitchen scales is a good opportunity to introduce the students to the gram as a unit of mass. Can your students predict the weight of each potato? You might have a potato peeling competition, using proper peelers (not knives). Focus on peeling slowly, with control, as opposed to quickly and without control. The student who gets the longest peel wins. Naturally, you will need to measure the lengths of the peels and come up with a class winner.
  5. To make one batch of ‘the bug’ cut up the potatoes into smaller bits and boil them in clean water (no salt) until they are soft. You might time how long that takes. Let the potatoes cool and don’t drain the water. Mash the potatoes, water included. Add in (for each recipe):
    2 cups of flour
    1 teaspoon of sugar
    Up to one cup of luke-warm water (as needed to maintain a paste-like consistency)
  6. After you have made a bulk lot of ‘the bug’ put it into clean glass jars to ferment. Fill each jar to one third as the mixture will expand. Cover the jar with greaseproof paper and fix it with a rubber band. Over three of four days the mixture will ferment. Feed it daily with a mix of one teaspoon of sugar dissolved in half a cup of potato water. Your students will be intrigued by the foaming concoction that develops.
  7. After ‘the bug’ has developed, let your students create their own batch of rēwena bread by following the recipe (PowerPoint 4). This is a good exercise in interpreting procedural language. Read the instructions to the class if necessary or use your most competent readers.
  8. Once the bread is made it needs to be cut into slices.
    How many slices should we make?
    How thick will the slices be?
    How many cuts will we make?
  9. You might explore sharing slices equally among different numbers of students. Naming the equal parts will introduce fractions. You might explore the different ways to cut a slice in half or quarters.

Printed from https://nzmaths.co.nz/user/75803/planning-space/early-level-1-plan-term-2 at 11:10am on the 21st July 2024