Late level 1 plan (term 3)

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
Geometry and Measurement
Units of Work
In this unit students participate in a variety of art based activities to develop their knowledge of 2-dimensional shapes. They use their own language to describe their works and the shapes they have used.
  • Name 2-dimensional shapes: triangle, square, oblong (non-square rectangle), circle, oval and diamond.
  • Describe shape attributes in their own language.
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 the place value structure of the numbers from ten to twenty.
  • Instantly recognise patterns for teen numbers.
  • Make groups of ten and represent teen numbers with materials.
  • Recognise and record words and symbols for teen numbers.
  • Understand that in a teen number the 1 represents one group of ten.
  • Expand teen number notation and understand simple place...
Resource logo
Level One
Geometry and Measurement
Units of Work
This unit involves the students directly comparing the weight (mass) of two or more objects.
  • Compare two objects by weight.
  • Order three or more objects by weight.
  • Describe the weight of objects using comparative language, for example, heavier, lighter.
Resource logo
Level One
Number and Algebra
Units of Work
This unit explores early multiplication where students are encouraged to skip count to solve story problems, rather than counting all. For example "John has 3 ponds and there are 2 fish in each pond. How many fish are there altogether?" Students will be encouraged to solve this problem by going 2, 4...
  • Skip count in twos and fives.
  • Skip count to solve simple multiplication problems with a sum of up to 20.
  • Solve simple multiplication problems in various ways and talk about how they found the answer.
Resource logo
Level One
Number and Algebra
Units of Work
In this unit we explore linear patterns using snakes as the context. We examine, construct and record snakes of different patterns. We also put scarves on our snakes and ask others to predict what is hidden.
  • Record patterns on grid paper.
  • Make predictions about ‘missing’ sections of a pattern.
  • Use words to describe linear patterns.
Source URL: https://nzmaths.co.nz/user/75803/planning-space/late-level-1-plan-term-3

Arty Shapes

Purpose

In this unit students participate in a variety of art based activities to develop their knowledge of 2-dimensional shapes. They use their own language to describe their works and the shapes they have used.

Achievement Objectives
GM1-2: Sort objects by their appearance.
Specific Learning Outcomes
  • Name 2-dimensional shapes: triangle, square, oblong (non-square rectangle), circle, oval and diamond.
  • Describe shape attributes in their own language.
Description of Mathematics

This unit begins an exploration of basic 2D shapes, their properties and the mathematical language associated with them. There is a progression from the way the students think of and see these objects to the more formal mathematical ideas and descriptions. In order to be able to communicate on any topic, there is a need for a common language. This unit takes the initial steps in the formulation of this common language.

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 the tasks include:  

  • In session 1, provide students with cut-out shapes if they have difficulty cutting them from paper.
  • In session 1, ask the students to suggest objects that they could create with the shapes available.

The contexts for the geometric pictures used in this unit can be adapted to the interests and experiences of your students. In session 1 there is an opportunity for students to identify the object that they want to create from the available shapes. It is also possible to enrich the unit by identifying the shapes being investigated in the school and classroom environment.

Required Resource Materials
  • Examples of Mondrian art. These can be found by doing an online image search.
  • Session One: Black paper, colour copies of the Shape Sheet in a variety of sizes, scissors, glue.
  • Session Two: Paper for each student, shallow containers of PVA glue, paint or food colouring to colour PVA (optional), string.
  • Session Three: Paper for each student, large stencils made of thick card in a variety of shapes, crayons and dye.
  • Session Four: Salt, flour and water to make salt dough, rolling pins, biscuit cutters in a variety of shapes, drinking straws, coat hangers or similar to hang shapes from, access to an oven to dry salt dough shapes, paint and string.
Activity

Throughout each session encourage the students to talk about what they are making and the features of the shapes they are using. Discuss the similarities and differences in shapes and encourage a wide use of a range of terms. Counting the numbers of sides and the numbers of corners each shape has is also a good way to get students to focus on shapes.

Terms: sides, corners, curved and straight lines, edges, pointed

Questions to use:

  • Do you see any ways that these shapes that are alike? How are they alike?
  • Can you see any shapes that are different? How are they different?
  • What do these shapes have in common?
  • What are some of the things you notice about the shapes you are using?
  • Do you know what we call these shapes?
  • What can you tell me about that shape?
  • Why have you chosen to use that shape?
  • Are all the sides the same? Are all the corners the same?

Session 1: Shape collage

  1. Begin the session by looking at some of Piet Mondrian’s primary coloured and cubist art works. Have students identify the shapes they can see and describe these.
    • What shapes has the artist used in their painting?
    • Can you see where the artist has used corners?
    • Where are the straight lines in this art work?
    • How would you describe the shapes the artist has used?
  2. Provide students with one sheet of black paper each, a variety of shapes in different sizes and a pair of scissors.
  3. Have students colour in and cut out a variety of shapes and arrange them in interesting ways to make a picture, this may be abstract or a familiar object such as a car or a person.
  4. Encourage students to discuss their work and the works of others and to change their designs as their ideas develop.
  5. Once they are satisfied with their pictures, students glue the shapes in place.

Session 2: String shapes with PVA

  1. Provide each student with a sheet of paper, strings of varying lengths and access to a shallow container of PVA. PVA may be coloured using food colouring or paint if desired.
  2. Students dip pieces of string into the PVA and place them onto their pictures, making a variety of shapes in their work.
  3. Encourage students to discuss their work and the works of others and to change their designs as their ideas develop.
  4. Once designs are dry they can be use as a block to create crayon rubbings if desired.

Session 3: Shape stencils in crayon and dye

  1. Provide each student with a piece of paper, some large stencils made of thick card in a variety of shapes and some crayons.
  2. Students trace around the stencils in a variety of different colour crayons, overlapping shapes to create an interesting effect.
  3. Encourage students to discuss their work and the works of others.
  4. When shapes are complete students can paint over shapes with dye to enhance their work.

Session 4: Shape mobiles

  1. Mix salt dough using equal quantities of salt and flour with enough water to form dough with good consistency.
  2. Provide students with dough and cutters.
  3. Students flatten dough using rolling pins and cut a variety of shapes using biscuit cutters. Each shape needs a hole at the top to enable it to be hung with string. This can be made using a small piece of drinking straw.
  4. Encourage students to discuss their work and the works of others.
  5. Place shapes in the oven at 100°C for 1 - 2 hours to dry out.
  6. Once shapes are dry they can be painted and hung onto a coat hanger with string to create a mobile.

Session 5

In this session students reflect on one of their art works made in the previous sessions, discuss and describe it and write about their work.

Their writing could then be published and displayed, either in a classroom display or in a large book for the book corner.

Attachments

Teen numbers (building with ten)

Purpose

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

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

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

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

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

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

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

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

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

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

Links to the Number Framework

Stages 2-4

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 the tasks include:  

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

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

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

Session 1

SLOs:

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

Activity 1

  1. Show the students single tens frames. Have them show the same number of fingers as the number of dots, say and write the number with their finger in the air or one the mat.
     
  2. Show two tens frames, one of ten and the other of a number less than ten, together making a teen number. Have students ‘write’ with their finger how many dots they see. For example:
        13
    Repeat with several teen numbers.
     
  3. Write the numbers 11 – 19 in symbols and words on chart paper, highlighting the inconsistencies of the language and exploring for fun alternative forms of some of the teen numbers, for example, eleven (oneteen), twelve (twoteen), thirteen (threeteen), fifteen (fiveteen). For each word, as appropriate, underline teen in the word, practice saying it and hearing the final consonant, ‘n’. Make the connection between this ‘teen’ word and ‘ten’. Retain this chart to add to later.
     
  4. Ask what the students notice about all of these numbers. (They all have teen at the end and are ten and ‘something’). They are known as teen numbers.

Activity 2

Have the students work in pairs to play Teen Pairs.
(Purpose: to recognise and match teen number representations and the words ‘ ten and ____’)

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

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

For example:
   

Activity 3

  1. Have students now work to ‘make’ their own group of ten. Give each pair forty nursery or ice-block sticks, two elastic hair ties, pens and chart paper.
     
  2. Have each student choose and write in symbols a number from eleven to nineteen and take that many sticks. Have them count out and make one bundle of ten using the hair tie, then write and draw what they have. For example:
      
    12 is ten and two 
  3. Have them unbundle and return their sticks to the centre then repeat with another teen number making use of spare sticks as required.
     
  4. Ask the students to return to the whole group with their drawings, keeping them hidden. Have the students take turns to describe to the class/group what they have drawn, and ask a classmate to say what number it is. The drawing is then shown.
     
  5. The teacher concludes by recording the ‘ten and _________’ words beside each of the teen numbers on the class chart begun in the earlier activity. Also consider exploring together the Place Value nursery sticks animation, available from https://e-ako.nzmaths.co.nz/modules/PVanimations/

Session 2

SLOs:

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

Activity 1

  1. Have students sit with a partner. Tell them that each pair is going to be making teen numbers on their fingers and ask them to discuss how they will do this. Look and listen for those students who immediately identify that one of their pair will be the ‘ten person’, holding up ten fingers each time.
     
  2. Hold up a mixture of cards with number names in words, symbols and those reading ‘ten and ___’. (Attachment 2). Each time, give the card to the first pair to achieve the cooperative representation on their fingers.
     
  3. The teacher makes a teen number from nursery or ice block sticks, having the students count to ten as the ten bundle is made.

    Hold up the ten bundle and ask, “Do I still have ten sticks here?” (yes) “How many bundles of ten do I have?” (1). Record on the chart, for example, I have fifteen. 15 is ten and five. 15 is 1 ten and 5 ones. Discuss the language of ‘ones’ and that sometimes ‘ones’ can be called ‘units’.
     
  4. Model one more example then have the students individually draw and write about three of their favourite teen numbers. For example "12 is 1 ten and two ones".

Activity 2

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

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

Activity 3

  1. Return to the class chart started in Session 1. Record Māori words for teen numbers, highlighting ‘tekau ma’ is ‘ten and’, connecting this mathematics language with the other expressions already recorded.
     
  2. In small groups, using BSM 9-1-48 cards, students play Teen Teams (purpose: to match word, pictorial and symbol representations of teen numbers).
    Students deal out 7 cards each. The remaining pile of cards is placed in the centre of the group. Students take turns to ask one other player for a card needed to complete a set of 5 teen family cards. If the other player does not have the card sought the requesting player takes one from the pile. As sets are complete, students place these in front of them.
    The winner is the player with the most complete sets.

Session 3

SLOs:

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

Activity 1

  1. Display the chart started in Session 1. Record beside the numbers 11 – 19 the description ‘1 ten and x ones’ for each of the numbers.
     
  2. Using enlarged arrow cards demonstrate and discuss the place value notation that we use, highlighting tens and ones language.
              
     
  3. Introduce students to plastic beans and containers. Have them work in pairs to make up containers with ten beans in each and discuss what the containers will be called. (a container is ‘one ten’ or ‘a ten’). Have the students discuss the similarities between the sticks they have been using and the beans.

    NB. The container for the beans looks different from the ones, but can still be unpacked. This is a subtle and important shift. Also consider exploring together as a group or class the place value beans animation, available from https://e-ako.nzmaths.co.nz/modules/PVanimations/
  4. Give students time to become familiar with the beans and the arrow cards. Have them make and model at least three teen numbers with the equipment, explaining this to their partner.
     
  5. Have each student complete a think board sheet (Attachment 3) or a mini poster about one of their favourite teen numbers. Display these.

Activity 2

Students play Go Teen in pairs.
(Purpose: to use ten ones to make one group of ten when adding add two single-digit numbers.)

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

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

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

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

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

Session 4

SLOs:

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

Activity 1

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

    A problem is posed in which the number being subtracted requires the ten to be ‘unpacked’ or decomposed:
    “Here are the beans Gardener Gavin is going to plant. He plants 9 in the first row. How many beans are left to plant in the second row? How can we work this out?”
    The students discuss strategies for subtracting 9 and suggest what they can do with the materials. The teacher models this and one more example is explored together.
     
  2. Students are provided with place value materials and each is given at least two subtraction problems to solve with decomposition (Attachment 4). Students should record with pictures, words and an equation what they did and what their result is.
     
  3. Share as a class/group and discuss. The language of making ten (composing) and breaking ten (decomposing) can be introduced.

Activity 2

  1. The teacher asks a student to model twenty using place value material. Discuss what this represents: two tens is the same as twenty.
     
  2. Have the students play in pairs or small groups First to twenty.
    (Purpose: to understand how to compose and decompose a ten.)
    Students have beans and containers, numeral cards 11- 14, a set of playing cards 2 – 5, a dice with a + or – symbol marked on each of the six faces. Numeral cards are spread out face down.
    Each student selects a card and makes that number using place value equipment.
    Players take turns to roll the dice and turn over a playing card. They follow the instruction, either adding or subtracting from their materials. Each time the student has a turn they are required to write the equation.
    The winner is the first student who has two containers of ten beans (twenty).
    For example: a student turns over and models 13, rolls + and 3, and makes 16.
    At their next turn the student may have to – 4, followed on the next turn by – 3. This will requires the student to decompose the ten.
    The student will have recorded for the three turns so far:
    13 + 3 = 16
    16 – 4 = 12
    12 – 3 = 9
     
  3. Conclude the lesson with a focus on the words, ‘place value’. The teacher writes ‘place value’ on a chart and asks the students what this could mean. They are encouraged to look at all the recording of teen numbers completed throughout these lessons. Accept all responses, but conclude by highlighting and recording that “the place of a numeral in a number tells us what it is worth or its value.’’ Show the enlarged arrow cards drawing attention to the words tens and ones.
Attachments

Seesaws

Purpose

This unit involves the students directly comparing the weight (mass) of two or more objects.

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 two objects by weight.
  • Order three or more objects by weight.
  • Describe the weight of objects using comparative language, for example, heavier, lighter.
Description of Mathematics

Weight is a measure of the force of gravity on an object.  Mass is the amount of matter in an object and a measure of the force needed to accelerate it. This means that the mass of the object on the moon is the same as its mass on earth, but its weight is lighter on the moon.  For practical purposes, the mass and weight of an object on earth are the same and the terms are used interchangeably,

An important early goal in measurement is for students to understand the attribute they are going to measure.  Comparison activities help students develop an understanding of the attribute that is being measured.  In the case of mass, the most personal experience is comparing the weights of two objects by holding one in each hand and feeling which has the greatest downward pull. This personal experience can then be transferred to the use of balance and spring scales.

Young students are influenced by what they see. The shape or the size of an object can easily deceive them. For example, students who do not yet conserve the property of mass will think that if the shape of an object changes then so does its mass. In one of the stations, in this unit, the students change the shape of a piece of plasticene and then weigh it to see that the weight has stayed the same.

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 provide more support include:  

  • Comparing the weight of objects using hands and outstretched arms (as described above) to further develop a student’s conceptual understanding of weight. 
  • Instead of using stations where students are left to work with partners, convert the stations to daily sessions, offering a more supported experience.  

The objects weighed in unit can be selected to suit the interests and experiences of your students. For example, the students could bring small objects from home or objects that they can collect from around the school playground (e.g. stones, cones, berries or shells).

Required Resource Materials
  • Station 1: Soft drink cans, shoe box lids (cut to about 10 cm in width), plasticene, small toys (plastic vehicles and animals from BSM)
  • Station 2: Plasticene, homemade "seesaw"
  • Station 3: Balance scales, toys
  • Station 4: Balance scales, toys
  • Station 5: Hat elastic, bull-dog clip, toys, paper, crayon
Activity

Station One: See-saws

In this station we work with a partner to make a see-saw using a soft-drink can and a shoe box lid. We then use the see-saw to find objects that are the same weight.

  1. First make a see-saw.
    Stop the soft drink can from rolling by fixing it to the table with tape or put plasticene rolls on each side.
  2. Now see if the students can balance the lid on the can when it is empty.
  3. Now use the cars and animals to see if you can find things that make the see-saw balance.
  4. Draw a picture to show some of the things that balanced.
  5. As the students work ask questions that focus on the way that things balance
    How did you make your see-saw?
    What are some things you found that balance? Show me.
    Have you ever been on a see-saw? What happens?

Station Two: Weighing balls and worms

In this station the students, in pairs, experiment with plasticene or play dough to find that changes in an object’s shape does not change its weight.

  1. Give each student a ball of plasticene. Tell them that they need to work with a partner.
  2. Ask them to check that their "balls" are the same weight by using their see-saws.
  3. If they are different ask them to make them the same by removing some of the play dough.
  4. Ask the students to make a cat using their plasticene.
    Will your cats be the same weight? Why /Why not?
    Check on the balance scales.
  5. Ask the students to remake their "cat" into the longest worm they can.
    Whose worm is longest?
    Whose worm is heaviest? Check?
    Why are they the same weight?
  6. Ask the students to make their "worm" into different sized balls.
    Whose has made the most balls?
    Which ball is the heaviest? Check?
    If you both put all your balls together on the seesaw what do you think will happen?
    What do you notice? Why is the seesaw balanced?
  7. Ask the students to draw a picture of what they found out.

Station Three: What balances Freddy Frog?

In this station the students experiment to find items that balance Freddy Frog (or an alternative object). The students paste their solutions onto a class chart.

  1. Set up the balance scales with Freddy Frog in one of the balance buckets.
  2. Have a collection of different objects at the table for the students to experiment with, for example, linking cubes, pattern blocks, counters, small toys, buttons.
  3. Ask that the students put their solutions with their name on the chart paper.
  4. Ask questions that focus on their use of the balance scale.
    What happens on the scales when Freddy is heavier?
    Do you think that this "car" will be lighter or heavier? Why do you think that? Were you right?
    What are some of the things that you found that were the same weight as Freddy Frog?

Station Four

In this station we line objects up in order of weight so that we can work out who goes where in our "tower". We need to have the heaviest at the bottom and the lightest at the top.

  1. Give the students four toys and ask them to put them in order of weight.
  2. Before using the balance scales ask the students to hold the toys and guess the lightest and heaviest.
  3. Check guesses with the balance scales.
    Were your guesses correct?
    Tell me how you put the toys in order?
  4. Ask the students to find another toy or object, which is lighter than the four toys they have ordered.
    Did you find a lighter toy on your first guess?
    How did you check your guess?
  5. Ask them to find another toy or object which is heavier than the 5 they now have ordered.

Station Five: Bungees

In this station students use a simple piece of elastic as a bungee and measure how far the elastic stretches to compare the weight of different objects.

  1. Set up a bungee by tying a piece of elastic onto a bull-clip or a clothes peg. The top of the bungee will need to be attached to something it can hang from, a string suspended tight across the classroom or a metre ruler suspended across two desks would be ideal. There also needs to be a piece of paper behind the bungee, which the students can use to mark how far down the wall the bungee extends
  2. Have students take one object at a time and attach it to the clip. They then let the objects go, wait till the elastic comes to rest and mark on the paper how far down the object falls.
  3. Students repeat for all objects and then decide which is heaviest.

Skip it to multiply it

Purpose

This unit explores early multiplication where students are encouraged to skip count to solve story problems, rather than counting all.  For example "John has 3 ponds and there are 2 fish in each pond.  How many fish are there altogether?"  Students will be encouraged to solve this problem by going 2, 4, 6.  "There are 6 fish altogether."

Achievement Objectives
NA1-1: Use a range of counting, grouping, and equal-sharing strategies with whole numbers and fractions.
NA1-5: Generalise that the next counting number gives the result of adding one object to a set and that counting the number of objects in a set tells how many.
Specific Learning Outcomes
  • Skip count in twos and fives.
  • Skip count to solve simple multiplication problems with a sum of up to 20.
  • Solve simple multiplication problems in various ways and talk about how they found the answer.
Description of Mathematics

This unit develops the skill of skip counting to find the total of several equal sets. At Level One students are expected to use a range of counting strategies such as counting on, counting back, skip counting, etc. Both conceptual understanding and procedural fluency are important to counting. Skip counting involves understanding that a set can be treated as a composite unit. The last number counted tells how many objects are in the set. Composites can be combined whether they are equal or not, but skip counting (e.g. 5, 10, 15, 20) can be used particularly when the sets are equal. The procedural fluency students need to enact skip counting is knowledge of the skip counting sequences. Ideally learning word and numeral sequences, like 2, 4, 6, 8… is learned in conjunction with quantity. That way students realise that the next number is the result of adding two more objects to what is already there.

As well as knowing skip counting sequences, students need fluency in tracking the number of counts. Initially they may use fingers to do that. For example, the fingers in four hands might be skip counted 5, 10, 15, 20, while the number of hands is tracked 1, 2, 3, 4.

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 the tasks include:  

  • Increasing the difficulty by asking the students to extend the number of skips in the pattern.  For example, ask the students to extend the pattern to 10 or more skips.
  • Reduce the difficulty by focusing on skips of 2 until students are secure in their understanding. 

The contexts for this skip patterns used in this unit can be adapted to suit the interests and experiences of your students. For example:

  • Instead of horses in stables, count tui in kōwhai trees or geckos on rocks.
  • Ask the students to suggest the contexts for the skip counting activities.
Activity

Each of the following sessions is designed to take 20 to 25 minutes. This series of session can be used in whole class or small group situations.  The first session develops students’ ability to skip count in a variety of ways.

Session 1 – Skip Counting

  1. Begin by counting in twos.  Get students to slap their knees and whisper the number 1.  Then get them to push their arms out to the side (or click fingers) and say 2 in a bigger voice.  Continue the sequence 1 (whisper) 2 (big voice) 3 (whisper) 4 (big voice) etc. 
  2. Choose different odd numbers to start from.  Don’t always start from 1. 
    Encourage the students to continue counting while you record the numbers they are saying in a loud voice on the board.  Then stop and talk about the number sequence and the patterns they can see. 
    What can you tell me about the big voice numbers?
    What patterns can you see?
  3. Tie a weighted object to a piece of string and swing it from side to side.  Get the students to count as the pendulum swings. Then omit the odd numbers. This will enable the students to focus on counting in twos.
  4. You might use Animation 1A to connect the spoken words to numerals on the Hundreds Board or Animation 1B to connect numerals to putting counters on a Slavonic Abacus. Animation 1C and 1D deal with skip counting in fives. Links to animations are in the list of required resources.
  5. Challenge students to see if they can count backwards in twos from 10. Animation 1E - 1H use the Hundreds Board and Slavonic Abacus to count backwards by twos and fives.
  6. Counting circles - put students in different sized groups of up to eight students.  Each group sits in a circle.  Students skip count around the circle. One or two students have an individual piece of paper. When the counting reaches them, they record the number they say as a numeral, e.g. 25.  Students continue to count around the circle as far as they can.  Get the students to bring their numbers back to share with the whole class. Place the numbers on the mat.
    What patterns did you see?
    What numbers are missing from the pattern?
  7. Use puppets - have 2, 3, 4 or 5 puppets, students come to the front of the class and count using the puppets.  E.g. Using 3 puppets - puppet 1 says 1, puppet 2 says 2, puppet 3 says 3, puppet 1 says 4, puppet 2 says 5, …
    What do you think puppet 2 is going to say when it his turn next?
    What will she say the next turn?
  8. Encourage students to count up and predict.

Session 2 Horses and Stables

  1. Begin the session by choosing one of the skip-counting activities from Session 1 as a warm up exercise.
  2. Seat students in a circle.  Place four ice cream containers upside down in the middle of the circle.  
    Here are four horse stables.
    Place two horses under each stable. 
    There are two horses in each stable (uncovering the collections and hiding them sequentially). How many horses are there altogether?
  3. Give the students some time to think about the problem.  Encourage students to share their answers and come into the circle to demonstrate what they did.
    Try to record their responses e.g.  Len thought 1, 2, 3, 4, 5, 6, 7, 8; Tom went 1 2, 3 4, 5 6, 7 8; Hemi went 2, 4, 6, 8; and Kelly went 4 + 4 = 8 (note that this is an additive, not counting, response).
  4. Continue to pose several other similar problems.
    For example, “Now there are 5 stables at John’s farm down the road.  He has 5 horses in each stable how many horses are there altogether?” Encourage students to explain how they got their answer. 
  5. Change the bolded numbers in the problem to alter the complexity of the task. Be aware that increasing the number of stables encourages skip counting by making one by one counting inefficient. Changing the number of horses to other multiples such as 3 and 4 greatly increases difficulty, especially if students do not know the skip counting sequence. Using ten animals each stable supports place value development.
  6. Pair up students and give them a series of counters to represent horses and some ice cream containers, or cups to represent stables.  The students take turns to hide the same number of horses under each stable while their partner hides their eyes or turns around.  When the student turns back, their partner says "There are 2 horses under each of these stables.  How many are there altogether?"  Their partner then works out how many horses there are altogether.

Session 3 – Fish in Fishponds

  1. Start the session by choosing one of the skip-counting activities from Session 1 as a warm up exercise. Include the skip counting sequence in fives.
  2. Set up the scenario for this session by seating the students in a large circle. In the middle of the circle make 4 fishponds using four pieces of string joined up to make them look like ponds.  Give each student 1 fish (Copymaster One). 
  3. Ask five students to put their fish in one of the ponds, then another five students to put their fish in another pond.  Continue until all the ponds have five fish. 
    How many fish are there altogether?
    How can we work it out without counting the fish one by one?
  4. Talk about how you might be able to work it out without individually counting each fish.  Give the students some time to work the answer out and then encourage individuals to share their strategies.
    Did anyone do it a different way?
  5. With the skip counting by five sequence students may use additive knowledge, e.g. 5 + 5 = 10, 10 + 10= 20. Thinking like that should be encouraged. Record students’ strategies using numbers and operation signs. Include the multiplication notation 4 x 5 = 20, asking students to explain what the 4, 5, and 20 represent.
  6. Choose a student to be a fisherperson.  Ask them to take a fish out of each pond. 
    Is there a quick way to work out how many fish there are left?
  7. Change the equation to 4 x 4 = □. Do your students use these strategies?
  8. Skip count in twos, i.e., 4, 6, …, 16, 18, 20.
  9. Take away from 4 x 5 = 20, 20 – 4 = 16.
  10. Go back to 4 x 5 = 20. What if someone (student) puts one more fish in each pond? How many fish will there be altogether, then?
  11. Continue to pose similar problems.  Increase the number of ponds and the number of fish put in each pond with awareness of the difficulty level of the problems, and the skip counting knowledge of your students.
  12. Copymaster Two is an activity sheet with further pond and fish problems.  The starting problems are closed but the later problems are open so you or students can add the missing information.

Session 4 – Cartons and Eggs

  1. Begin the session by repeating a skip-counting activity from Session 1.
  2. Discuss how many eggs are usually in a packet. Have dozen and half dozen packets available and larger trays if they are accessible.
  3. Put down three half dozen packets.
    How many eggs are there altogether? (You might have cubes, ping pong balls, or other objects as the make-believe eggs).
  4. Look for students to explain their strategies. Some may count in ones. Others may use skip counting in twos or threes. Some may use addition, such as 6 + 6 = 12 and count on the last six.
    Sixes are hard to count with, so we are going to use smaller packets today.
  5. Set up problems such as “Here are five packets with three eggs each. How many eggs are there altogether?” You might write 5 x 3 = __ to model the equation form. Mask the packets at first but be prepared to uncover them if students need support with image making. Discuss their strategies and the efficiency of count by ones, composites or just knowing facts.
  6. For independent work give small groups of students many egg packets of the same size (Twos, threes, fours and fives) and make-believe eggs.
    I want you to make problems for each other using the same sized packets.
    You might like to record your strategies using numbers. That is up to you.
    Be ready to share your problem with the whole class at the end.
  7. Wander the room. Are students setting problems with equal sets? Are students using non-count-by-ones strategies when they have the available skip counting or addition knowledge.
  8. Gather the class to share their favourite problems. Encourage your students to reflect on what is the same and what is different about the problems (equal sets, different numbers of sets, different set between problems).
  9. Pose problems like this, “Four cartons of five eggs and two extra eggs. How many eggs altogether?” Extras or missing eggs in a packet requires students to adapt skip counting, e.g. 5, 10, 15, 20, 21, 22.

Session 5

  1. Use the context of legs on animals to set problems for the students. Remember to challenge the students to think of quick ways to solve the problems.  Try to encourage them not to count by ones.
  2. Copymaster Three provides some open problems where the number of the legs on each animal is given but the number of animals is left open. Using nursery sticks or iceblock sticks the students can physically model each problem by giving the animals “legs”. They then use whatever strategies they have available to anticipate the number of “legs” that are needed.
  3. You might photocopy and laminate pictures of the ‘legless’ animals to use in problem posing. Students to create their own skip counting problems using outs of the animals’ legs.  Share these with the class.
  4. Finally challenge the class with these problems.
    How many legs would be on five goldfish? Do students still realise that the problem can be written and solved, 5 x 0 = 0? 
    How many legs would be on 10, 50, 100 goldfish?” What is always true?
  5. You might do the same with kiwi with one leg.
    How many legs would be on 10, 50, 100 1-legged kiwi? What is always true?

Snakes and Scarves

Purpose

In this unit we explore linear patterns using snakes as the context. We examine, construct and record snakes of different patterns. We also put scarves on our snakes and ask others to predict what is hidden.

Achievement Objectives
NA1-6: Create and continue sequential patterns.
Specific Learning Outcomes
  • Record patterns on grid paper.
  • Make predictions about ‘missing’ sections of a pattern.
  • Use words to describe linear patterns.
Description of Mathematics

The main idea behind this unit is for students to develop basic concepts relating to pattern by exploring simple patterns in a novel situation. So they will use multi-link cubes masquerading as snakes. The snakes have patterned ‘skin’. The students play with a variety of snakes, both inventing their own and investigating other students’. In the process, they should begin to see that (i) patterns are made up of repeating sections of coloured cubes; (ii) they can continue a pattern by adding on more cubes of the right colours; and (ii) they can predict parts of a pattern that are missing.

Pattern is an important idea both in mathematics generally and as a precursor to algebra. For instance, discovering patterns enables us to predict events. By knowing how the tides work we can predict when high tide will be and when will be a good time to go fishing. This pattern concept generalises in secondary school to finding results that work again and again. 

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 the tasks include:  

  • Actively supporting students, as needed, to record their snakes on the grid paper.
  • Ensuring that students are confident with patterns of two colours before introducing 3 colour patterns.

The snake context used in this unit could be adapted to use worms or eels, although it would require a little more imagination as neither are multi-coloured or patterned.  The simple counts and primary colours used in the unit provide an opportunity to use te reo and Pasifika words alongside English.

Required Resource Materials
  • Multi-link cubes
  • Pieces of fabric for the scarves
  • Prepared snakes (made with multi-link cubes)
  • Snakes with scarves booklets
  • Strips of cubed paper for recording
  • Crayons or felt pens
Activity

Getting Started

Today we investigate snakes with special patterns. We think about what would come next as we increase the length of our snakes. We also think about what happens when we cover part of our snake with a scarf.

  1. This week we are going to investigate patterns. Does anyone know what a pattern is?
    Share ideas about patterns. Encourage the students to look around the classroom for examples of patterns.
  2. I am going to make a snake for you out of these multi-link cubes. Watch carefully to see if you can guess what kind of snake I am making.
    [Make a snake with a blue, red, blue, red, blue pattern.]
    Who knows what colour comes next in our snake?
    How did you know?
  3. Let the students have turns adding cubes to the snake.
  4. Ask if anyone could think of a way of describing the snake to someone who can’t see it. This could be someone who rings to find out what you have been doing in class today.
  5. As a class read the pattern “red, blue, red, blue, red, blue…”
  6. Record the pattern on strips of grid paper one cube wide.
  7. Repeat the process of constructing and examining a snake, finding its pattern and then extending the pattern. This time use a snake that is made of three repeating single colours.
    Who knows what colour comes next?
    How did you know? 
  8. Now wrap a scarf around the snake and ask the students to predict what colour cubes are hidden. Make the scarf about 3 cubes wide.
    What cubes are hidden?
    How did you know?
  9. Take the scarf off and check.
  10. Continue with this activity until you feel that the students are ready to explore pattern snakes independently.

Exploring

Over the next 2-3 days we examine, construct and record the patterns on our snakes.  We cover parts of our snakes with scarves and play ‘guessing games’ with other students.

  1. Let each child (or pair of students) select a pattern snake from the ‘basket of snakes’. Alternatively you could give each pair of students a collection of prepared snakes. Also give each pair a supply of cubes that they can use to extend the patterns and plain grid paper strips for recording.
  2. As the students examine the snake ask questions that focus on their search for a pattern.
    Can you ‘read’ me your snake?
    What colour cubes is your snake made of?
    Can you see a pattern in your snake?
  3. When the students have discovered the pattern, ask them to extend it using the supply of cubes. Let the students decide on the length of their snakes.
  4. Ask the students to record their completed snakes on the recording strips.
  5. As the snake recordings are completed they could be displayed on a line at the front of the class for others to see.
  6. Alternatively the students could make snakes-in-scarves pages for a class booklet.  These pages have a grid to record the snake and a ‘flap’ to cover part of the snake.
  7. The process is repeated as the students select new snakes to investigate.  You may also wish to have a basket for the students to put their snakes in. Other students can then examine them.
  8. At the end of each session look at the snakes displayed and select a couple to put ‘scarves’ on.
    With all the students gathered together ask:
    What cubes do you think are hidden under the scarf?
    How do you know?

Reflecting

We conclude the unit by sharing the pattern snakes that we have made. We look for snakes that are alike.

  1. Give each child one of the recorded snakes from the previous days’ exploration.
  2. Ask one of the students to display their snake to the rest of the class. Together ‘read’ the pattern of the snake.
  3. Ask if anyone else has a snake that has a pattern that is the same as, or similar to, the one being displayed.
  4. How are they alike?
  5. The snakes may be alike in a number of different ways. Accept all the possibilities and then focus the students on the snakes that have exactly the same pattern.
  6. Which snakes have the same pattern as this one?
  7. Sort the snakes on the display line according to patterns
  8. Repeat by asking a child with a different snake to come to the front of the class. Continue to sort the snakes according to their patterns.

Printed from https://nzmaths.co.nz/user/75803/planning-space/late-level-1-plan-term-3 at 1:08pm on the 21st January 2022