Whilst this unit is presented as sequence of five sessions, more sessions than this will be required between sessions 3 and 4. It is also expected that any session may extend beyond one teaching period.
Session 1
This session is about playing a familiar game and evaluating its health benefits and safety considerations.
Students of this age may be challenged to accurately measure their pulse rate. Therefore these lessons use an alternative ‘indicator’ of the effects of exercise: that is that the intensity of worthwhile exercise should prevent you from singing, but should not prevent you from talking.
SLOs:
 Understand how running a distance contributes to fitness and wellbeing.
 Create a personal benchmark for 1 metre.
 Accurately use three measuring devices to measure a distance of more than 3 metres.
 Correctly record length measurements using abbreviations.
 Understand how many metres are in one kilometre.
 Establish a person benchmark for 1 kilometre.
Activity 1
Begin the lesson with singing a favourite song that has a more challenging vocal range.
Activity 2
 Explain to the students that they will be undertaking their regular fitness run (a distance of up to half a kilometre). Ask what are the effects/benefits of this, and elicit specific statements that should include: “We get puffed”, “Our heart beat/pulse speeds up”, “It’s good for us”. In response, explain that the increase of heartbeats per minute (hpm) is because their body physically needs to circulate oxygen more quickly as they exercise. Science has shown this is good for us.
Explain that today, when they each return from their run they should (individually) immediately sing the first verse of the song from 1 (above), and then talk to a classmate about their run.
 Have students complete their run and this task.
 Ask: ‘Who was able to sing the song immediately?’
‘Who was able to talk to their classmate?’
Count the responses for each and record these on the class chart. Discuss the results, explaining that being unable to sing immediately shows that they exercised well and their bodies will benefit.
Activity 3
Ask, “How far did you run today?” and “How can we find out?”
Make available 1 centimetre cubes, meter rulers, a 10 metre + tape measure and a measuring wheel.
Have the students tell what they know about the metre ruler. Establish that it is called a metre ruler. It is 1 metre long. (If centimetres have already been introduced and used, have students line up 1 cm cubes along the ruler to confirm that 1 metre = 100 centimetres).
Activity 4
Develop a personal benchmark by asking: “Who can jump 1 metre?”
Have student pairs measure a 1 metre length on the carpet/floor, marking this with chalk.
Highlight that the measure begins at 0 and ends at 100. Discuss the ‘extra’ space at each end of the ruler.
Have student pairs check if each person can each jump 1 metre.
Agree that when we think about how big 1 metre is, we can think of it as one big personal jump.
Activity 5
 Introduce the tape measure and measuring wheel, explaining and showing how each measures 1 metre and multiples of 1 metre.
Highlight the 1 metre personal benchmark by asking:
If the tape measure is 10 metres, about how many of your jumps is that?
If we measured 100 metres with the wheel, about how many of your jumps is that?
 Write ‘standard measure’ on the class chart and ask what it means. Elicit responses and point out that standard units have been created to allow consistency and communication of measures. We understand each other’s measurements if we use the same measures.
Explain that the standard units used in New Zealand, and in most countries in the world, are metric units.
 Write centimetre, metre and kilometre on the class chart. Explain that when we write them often, we want a quick way to record them. Model cm, m and km abbreviations.
Activity 6
Have a student model both the correct and an incorrect way to measure using a metre ruler. Highlight how to mark the beginning and end of the measure and how to correctly replace the metre ruler, when measuring a distance greater than 1 metre.
Have several students measure a length that is more than a metre, read the measure aloud, and record this on the class chart.
Activity 7
Explain that student pairs will participate in two measuring tasks to become familiar with the measuring tools. Emphasise that their recording should use the correct abbreviations.
 Show and have students make a recording sheet, for example:
Measurement
from ... to 
Metre ruler 
Measuring tape 



Have them measure at least three different lengths around the classroom, hall, or other designated area, using a metre ruler and a measuring tape, checking that they get the same measure using each tool.
 Clarify the exact fitness course route, the start and end points, and set relevant boundaries. Have student pairs take turns using the measuring wheel to measure the distance around the course and to then record the result.
Activity 8
Conclude the session by sharing measurement results and reviewing the fitness course distance. Discuss how many metres in 1 kilometre. Estimate and calculate together the number of times they would need to run around the fitness course to cover a 1 kilometre distance. Establish a rough benchmark for 1 kilometre. (For example, 1 kilometre is 5 times around the fitness course.)
Session 2
This session is about recognising that rules that address fairness and safety, help to ensure that a PE activity is enjoyable. As students design a PE activity, they learn more about accurately measuring outdoor spaces.
SLOs:
 Understand that rules are designed to ensure fairness and safety.
 Pose an investigative question.
 Create and write instructions for a PE game, giving consideration to fitness, safety and enjoyment.
 Accurately measure and record the length of a given outdoor space.
Activity 1
Begin with a fitness run.
Activity 2
Explain that the class is going to play a favourite PE game (for example: Tunnel ball, Scatter Ball). Together, list the rules on the class chart.
Ask: Which of the rules are about making the game fair? Write F beside these. Discuss that fairness makes the game more enjoyable for everyone.
Ask: Which of the rules are about making the game safe? Write S beside these. Discuss any anomalies. If there are no safety rules, list at least 3.
Activity 3
Return to the class, review the enjoyment of the game and ask if playing the game will make them fit. Discuss why/why not. Refer to original “talk/sing measure” from 4 above.
(The response may be, “No, because it didn’t make me puff and I could sing.”)
Review the list of rules and confirm the fairness (F) and safety (S) decisions made earlier.
Highlight the importance of games and activities being safe and enjoyable. Ask if any other safety rules should be added and why.
Activity 4
 List on the class chart, the words ‘enjoyment, fitness and safety’.
 Suggest that student pairs will create their own games/activities and that the class will conduct an investigation. Through discussion, lead students to pose an investigative question. For example:
‘Can we design a game or activity that keeps us fit, is enjoyable and is safe?’
Record this on the class chart/modeling book.
 Explain that students will be using an outdoor space with suitable boundaries, for example, the school tennis courts. Large balls and small balls will be made available. (Make available other equipment, for example hockey sticks, if skills have been taught.)
 Clarify the task. Students will work in pairs or small groups to:
 Measure and record the size of the designated outdoor space (using skills learned in Session 1.)
 Invent a simple team game or activity that the class can play.
 Write down clear instructions and rules, checking for safety and fairness.
 Set time limits and clarify expectations. Have students complete the task.
Activity 5
Have two student pairs swap game instructions. Have them read, critique, seek clarification and suggest refinements or improvements to the other’s game design.
Give time for these adjustments to be made.
Activity 6
Review pair measurements for the outdoor space. (Tennis courts are 23.77m x 8.23m) Review 1000m = 1 km. Estimate together the number of times the length of the court would need to be run to achieve the length of 1 kilometre. (eg. Round up to 25m. 25m x 40 = 1000m) Together calculate the number of lengths of the tennis court = 1km.
Students may use this as a 1 kilometre benchmark.
Session 3
This session is about creating a simple questionnaire to evaluate each pair’s activity, and learning about dot plots.
SLOs:
 Plan data collection.
 Collect data by trialling and evaluating an activity on its fitness, safety and enjoyment values.
Activity 1
Begin with a fitness run.
Activity 2
 Review the investigation question recorded on the chart in Session 2.
Ask the students how they should gather the data to answer the question. Guide discussion and agree on a simple evaluation form to be completed by the class after playing each pairlead activity. For example:
The name of the game: ________________________________
Circle for each: 1 (not so good) 2, 3, 4 or 5 (excellent),
Enjoyment: 1 2 3 4 5
Fitness: 1 2 3 4 5
Safety: 1 2 3 4 5
 Print off the evaluation or have students copy this and practice using it by completing an evaluation for the game played in Session 2: 2 and 3.
Activity 3
Together collate and present the data using three dot plots. For example:
Discuss the dot plot features, the results, and draw conclusions.
Activity 4
For the remainder of the session, and for sessions to follow, have students participate in and evaluate each other’s games. Each pair of students will collect the data for their game to analyse and present in Session 4.
Session 4
This session is about student pairs sorting the data from their classmate’s evaluations of their activity and presenting the findings.
SLOs:
 Sort and display category data.
 Answer an investigative question.
Activity 1
Begin with a fitness run.
Activity 2
Make available pencils, paper, and sets of data for each pair activity.
Have students work in pairs to sort their data and to discuss their findings. Each student should create three dot plots to present their data, record their own findings and should answer the investigative question in their own way.
As students work, have them record on a small poster, their knowledge of centimetres, metres and kilometres, the relationship between them, and explain why we have standard measures.
Session 5
This session is about communicating investigation findings to others and sharing their understanding of standard measures of length.
SLOs:
 Present findings.
 Review and reflect on the investigative process.
 Review and reflect upon measurement learning.
 Discuss the need for small units of length measure and introduce millimetres.
Activity 1
Begin with a fitness run.
Activity 2
Have each student present to a partner (not the person with whom they developed the game) their dot plots, their findings, and the measurement posters. Have them critique each other’s work and give feedback.
Activity 3
 Have selected students communicate the findings about their game with the class.
 Together, as a class:
 Summarise on the class chart conclusions about safety, enjoyment, and fitness.
 Reflect on the investigation process and suggest ways it could have been improved.
Activity 4
Arrange the length measurement tools in front of the students.
Have individual students share their learning about each of the tools.
Ask which tool would be used to measure small lengths.
Introduce the millimetre measure for tiny lengths.
Conclude by reviewing personal benchmarks for (1cm), 1m and 1km.
Fun and fitness
The purpose of this unit is to have students design a PE game, use standard measures of length, and conduct a statistical investigation into the safety factors and the health benefits of their game.
This unit of work assumes prerequisite knowledge gained at level one: the student can recognise the attribute of length, knows that measurement units are countable and that they can be partitioned and combined. When measuring length they realise that there should be no gaps or overlaps.
In these lessons the student is developing an understanding of a linear scale, and recognising that it is made up of units of equal size that are known as ‘standard units’, because they are understood by everyone.
They are learning to accurately reposition a metre ruler when required to measure a length longer than the ruler. In becoming familiar with metre and centimetre units of measure, the student is learning to express parts of metres as centimetres and to use the abbreviations m and cm when recording length measures. Students come to understand that 1000 metres are equal to 1 kilometre, and develop a personal benchmark for one metre and one kilometre measurements.
Further to the development of measurement skills and knowledge, the student participates in planning and collecting appropriate data to answer a question that has been composed with the support of the teacher (as required). The student sorts the data and presents these using a dot plot, at the same time refining key understandings of the investigative process. They can answer the investigative question and can suggest consequences of their findings.
Associated Achievement Objectives
Health and Physical Education
Positive attitudes
Safety management
This unit can be differentiated by varying the scaffolding or altering the difficulty of the tasks to make the learning opportunities accessible to a range of learners. For example:
The focus of this unit is designing a fitness game. Encourage students to consider their friends and classmates when planning, and to create a game that will appeal to them and be fun to play. This could be achieved by incorporating favourite elements from other games, or items of current interest.
Whilst this unit is presented as sequence of five sessions, more sessions than this will be required between sessions 3 and 4. It is also expected that any session may extend beyond one teaching period.
Session 1
This session is about playing a familiar game and evaluating its health benefits and safety considerations.
Students of this age may be challenged to accurately measure their pulse rate. Therefore these lessons use an alternative ‘indicator’ of the effects of exercise: that is that the intensity of worthwhile exercise should prevent you from singing, but should not prevent you from talking.
SLOs:
Activity 1
Begin the lesson with singing a favourite song that has a more challenging vocal range.
Activity 2
Explain that today, when they each return from their run they should (individually) immediately sing the first verse of the song from 1 (above), and then talk to a classmate about their run.
‘Who was able to talk to their classmate?’
Count the responses for each and record these on the class chart. Discuss the results, explaining that being unable to sing immediately shows that they exercised well and their bodies will benefit.
Activity 3
Ask, “How far did you run today?” and “How can we find out?”
Make available 1 centimetre cubes, meter rulers, a 10 metre + tape measure and a measuring wheel.
Have the students tell what they know about the metre ruler. Establish that it is called a metre ruler. It is 1 metre long. (If centimetres have already been introduced and used, have students line up 1 cm cubes along the ruler to confirm that 1 metre = 100 centimetres).
Activity 4
Develop a personal benchmark by asking: “Who can jump 1 metre?”
Have student pairs measure a 1 metre length on the carpet/floor, marking this with chalk.
Highlight that the measure begins at 0 and ends at 100. Discuss the ‘extra’ space at each end of the ruler.
Have student pairs check if each person can each jump 1 metre.
Agree that when we think about how big 1 metre is, we can think of it as one big personal jump.
Activity 5
Highlight the 1 metre personal benchmark by asking:
If the tape measure is 10 metres, about how many of your jumps is that?
If we measured 100 metres with the wheel, about how many of your jumps is that?
Explain that the standard units used in New Zealand, and in most countries in the world, are metric units.
Activity 6
Have a student model both the correct and an incorrect way to measure using a metre ruler. Highlight how to mark the beginning and end of the measure and how to correctly replace the metre ruler, when measuring a distance greater than 1 metre.
Have several students measure a length that is more than a metre, read the measure aloud, and record this on the class chart.
Activity 7
Explain that student pairs will participate in two measuring tasks to become familiar with the measuring tools. Emphasise that their recording should use the correct abbreviations.
from ... to
Have them measure at least three different lengths around the classroom, hall, or other designated area, using a metre ruler and a measuring tape, checking that they get the same measure using each tool.
Activity 8
Conclude the session by sharing measurement results and reviewing the fitness course distance. Discuss how many metres in 1 kilometre. Estimate and calculate together the number of times they would need to run around the fitness course to cover a 1 kilometre distance. Establish a rough benchmark for 1 kilometre. (For example, 1 kilometre is 5 times around the fitness course.)
Session 2
This session is about recognising that rules that address fairness and safety, help to ensure that a PE activity is enjoyable. As students design a PE activity, they learn more about accurately measuring outdoor spaces.
SLOs:
Activity 1
Begin with a fitness run.
Activity 2
Explain that the class is going to play a favourite PE game (for example: Tunnel ball, Scatter Ball). Together, list the rules on the class chart.
Ask: Which of the rules are about making the game fair? Write F beside these. Discuss that fairness makes the game more enjoyable for everyone.
Ask: Which of the rules are about making the game safe? Write S beside these. Discuss any anomalies. If there are no safety rules, list at least 3.
Activity 3
Return to the class, review the enjoyment of the game and ask if playing the game will make them fit. Discuss why/why not. Refer to original “talk/sing measure” from 4 above.
(The response may be, “No, because it didn’t make me puff and I could sing.”)
Review the list of rules and confirm the fairness (F) and safety (S) decisions made earlier.
Highlight the importance of games and activities being safe and enjoyable. Ask if any other safety rules should be added and why.
Activity 4
‘Can we design a game or activity that keeps us fit, is enjoyable and is safe?’
Record this on the class chart/modeling book.
Activity 5
Have two student pairs swap game instructions. Have them read, critique, seek clarification and suggest refinements or improvements to the other’s game design.
Give time for these adjustments to be made.
Activity 6
Review pair measurements for the outdoor space. (Tennis courts are 23.77m x 8.23m) Review 1000m = 1 km. Estimate together the number of times the length of the court would need to be run to achieve the length of 1 kilometre. (eg. Round up to 25m. 25m x 40 = 1000m) Together calculate the number of lengths of the tennis court = 1km.
Students may use this as a 1 kilometre benchmark.
Session 3
This session is about creating a simple questionnaire to evaluate each pair’s activity, and learning about dot plots.
SLOs:
Activity 1
Begin with a fitness run.
Activity 2
Ask the students how they should gather the data to answer the question. Guide discussion and agree on a simple evaluation form to be completed by the class after playing each pairlead activity. For example:
The name of the game: ________________________________
Circle for each: 1 (not so good) 2, 3, 4 or 5 (excellent),
Enjoyment: 1 2 3 4 5
Fitness: 1 2 3 4 5
Safety: 1 2 3 4 5
Activity 3
Together collate and present the data using three dot plots. For example:
Discuss the dot plot features, the results, and draw conclusions.
Activity 4
For the remainder of the session, and for sessions to follow, have students participate in and evaluate each other’s games. Each pair of students will collect the data for their game to analyse and present in Session 4.
Session 4
This session is about student pairs sorting the data from their classmate’s evaluations of their activity and presenting the findings.
SLOs:
Activity 1
Begin with a fitness run.
Activity 2
Make available pencils, paper, and sets of data for each pair activity.
Have students work in pairs to sort their data and to discuss their findings. Each student should create three dot plots to present their data, record their own findings and should answer the investigative question in their own way.
As students work, have them record on a small poster, their knowledge of centimetres, metres and kilometres, the relationship between them, and explain why we have standard measures.
Session 5
This session is about communicating investigation findings to others and sharing their understanding of standard measures of length.
SLOs:
Activity 1
Begin with a fitness run.
Activity 2
Have each student present to a partner (not the person with whom they developed the game) their dot plots, their findings, and the measurement posters. Have them critique each other’s work and give feedback.
Activity 3
Activity 4
Arrange the length measurement tools in front of the students.
Have individual students share their learning about each of the tools.
Ask which tool would be used to measure small lengths.
Introduce the millimetre measure for tiny lengths.
Conclude by reviewing personal benchmarks for (1cm), 1m and 1km.
Dear parents and whānau,
In mathematics we have been measuring distances and learning about metres and kilometres in particular. Ask your child to show how big a centimetre and a metre is, and to tell you about how big a kilometre is.
Please take opportunities to talk about and use these measurements: for example, measure and mark in pencil on a door frame, the height in metres and centimetres of each family member, or, when you are next travelling in the car, point out the speedometer and explain to your child how you know when the car has travelled 1 kilometre.
Thank you.
Letter patterns
In this unit we look at the number patterns we get from letters and numbers. We keep track of the numbers involved by drawing up a table of values. It’s important here to look for the pattern and see how the number of tiles changes from letter to letter.
Patterns are an important part of mathematics. They are one of the overriding themes of the subject. It is always valuable to be able to tell the relation between two things in order to predict what will happen and understand how they interrelate.
Patterns also provide an introduction to algebra proper as the rules for simple patterns can be first discovered in words and then be written using algebraic notation.
Links to Numeracy
This unit provides an opportunity to develop number knowledge in the area of Number Sequence and Order, in particular development of knowledge of skip counting patterns.
Help students focus on the number patterns by discussing the tables showing the numbers of tiles used in each successive letter pattern. Look at those patterns that are made by adding a constant number of tiles onto each successive letter. Highlighting numbers on a hundreds board or using a number line may also be helpful.
Questions to develop strategic thinking:
Which number comes next in this pattern?
How do you know?
Which number will be before 36 in this pattern? (or another number as appropriate)
How do you know?
What is the largest number you can think of in this pattern? How did you work it out?
Could you make a letter T with 34 tiles? How do you know?
This unit can be differentiated by altering the difficulty of the tasks to make the learning opportunities accessible to a range of learners. Specifically, some students may explore the patterns and describe how the shape and number patterns are growing, but may not be ready to predict the next number in the pattern, or how many tiles would be needed to make the nth shape in the pattern.
The context of letter patterns can be adapted to recognise diversity and student interests to encourage engagement. Support students to identify and explore other growing patterns in their environment. For example, tukutuku patterns on the walls of the wharenui, or the number of seats on the bus that are occupied as students get onto the bus in pairs.
Getting started
Starting with a simple pattern we build up the level of difficulty and see that it’s necessary to use a table to keep track of what is happening.
How many tiles do we need for the first ‘I’? The second? The third?
Who can tell me how many tiles we’ll need for the fourth ‘I’?
Can someone come and show us how to make the fifth ‘I’?
How many tiles will we need for the tenth ‘I’? Make it.
What is the number pattern that we are getting?
If we had 11 tiles, which numbered ‘I’ could we make?
Repeat the questions from the last ‘I’ problem.
How many tiles do we need for the first ‘I’? The second? The third?
Who can tell me how many tiles we’ll need for the fourth ‘I’?
Can someone come and show us how to make the fifth ‘I’?
How many tiles will we need for the tenth ‘I’? Make it.
What is the number pattern that we are getting?
How many tiles do we add on at each step?
If we had 11 tiles, which numbered ‘I’ could we make?
Work them around to the idea of a table.
‘I’ number
1
2
3
4
5
Number of tiles
1
2
3
4
5
What would the table look like where we added two tiles at a time?
Draw up the table with help from the students.
How did you know how many tiles to use on the fourth ‘L’?
What is the pattern here?
Which ‘L’ in the sequence will use 27 tiles?
Tell me what numbers you used to fill the table. (Check that they are correct by counting the tiles.)
What patterns can you see here?
How did you get the number of tiles for one ‘L’ from the one before?
How many tiles would you need for the 10th ‘L’?
If you had 23 tiles, what numbered ‘L’ could you make?
Exploring
For the next three days the students work at various stations continuing different number patterns and building up the corresponding tables. Notice that there are three series of stations here. In the first station, the students have to do a similar problem to the one that was done in ‘Getting Started’. In the second station the students have to find a missing shape in the pattern sequence. Finally in the third station they have to make their own pattern that fits the given table of values. When the class seems to have finished most of the task, bring them back together to discuss their answers. Ask them the kind of questions that were used in ‘Getting Started’. Use the table to discuss the pattern involved and what the relation is between successive numbers in the sequence.
Day 1
The material for these stations is on Copymasters 1.1, 1.2, 1.3, 1.4. The students continue the pattern and complete the table.
Day 2
The material for these stations is on Copymasters 2.1, 2.2, 2.3, 2.4. The students find the missing element of the pattern and complete the table.
Day 3
The material for these stations is on Copymasters 3.1, 3.2, 3.3, 3.4. The students make up their own pattern to fit the values in the table.
Reflecting
On the final day let the students make up their own patterns using numbers instead of letters. Some students might want to leave gaps in the pictures of their shapes. Let the students share their patterns with the whole class. In the discussion, point out the importance of the table in seeing what the number pattern is.
Dear parents and whānau,
This week in maths we have been exploring number patterns that come from letters and numbers. Work with your child to fill in the table below for the plus sign shape in the diagram.
‘+’number
1
2
3
4
5
6
7
number of tiles
How many tiles would there be in the 4th ‘plus’ shape?
How about the 10th ‘plus’ shape?
Which ‘plus’ in the sequence would you be able to make with 25 tiles?
Exploring and understanding patterns is an important and interesting part of maths. We hope you enjoyed this. Thank you for your help.
Figure it Out Links
Some links from the Figure It Out series which you may find useful are:
Voting vitality
In this unit, which explores the context of voting, students will become familiar with and apply the five keys steps of carrying out a statistical investigation.
In this unit which explores the context of voting, students will become familiar with and apply the five keys steps of carrying out a statistical investigation:
These five are closely linked as what data is collected can dictate the way that it is displayed and the conclusions that can be reached from the investigation. On the other hand, if some restrictions have been placed on the means of display, only certain types of data collection may be relevant.
At Level 2 you can expect students to be posing (with teacher support) a greater range of questions, including investigative questions and survey questions. They will also be helped to understand some of the issues involved in conducting surveys and learn new methods for collecting data. While at Level 1 students collected data and chose their own ways to display their findings, at Level 2 they will be introduced to pictographs, tally charts and bar charts. More emphasis here will also be placed on describing the data and the making of sensible statements from both the student’s own displays and the displays of others.
Investigative questions
At Level 2 students should be generating broad ideas to investigate and the teacher works with the students to refine their ideas into an investigative question that can be answered with data. Investigative summary questions are about the class or other whole group. The variables are categorical or whole numbers. Investigative questions are the questions we ask of the data.
The investigative question development is led by the teacher, and through questioning of the students identifies the variable of interest and the group the investigative question is about. The teacher still forms the investigative question but with student input.
Associated Achievement Objective
Social sciences AO2: understand that people make choices to meet their needs and wants.
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:
The context for this unit can be adapted to suit the interests and experiences of your students. For example, instead of class captains you could vote on a game to play at the end of the week, or a class treat for the end of term. The favourite example can be adapted to explore any favourites.
This teaching sequence is designed for teachers to take students through the five key stages of a statistical investigation. The context used is voting for the class captain, however school house captains could be an alternative context. At the end of this unit other possible statistical investigations are provided as examples of what students might further investigate in pairs or small groups. This would then allow for the unit to be extended beyond a week.
Session 1
It’s that time again where we need to vote for the class captains. The hunt is on to find the most suitable boy and girl to lead our class.
Session 2
This session is about going through the voting process and collecting the data in a systematic way.
Session 3
In this session students will see how a strip graph can be transformed into a bar graph.
What would be an appropriate title for our graph?
What labels could you use for this graph and where would you write them?
Is this a helpful way of presenting this information?
It is easier to make statements from a bar graph or from a strip graph?
Which completed graph shows our results most clearly?
The questions could be asked in a whole class situation or students could complete a bus stop activity with the questions being posed on the top of a large piece of paper and students visiting each station to record their ideas. Small groups would also be a valuable way for ideas and responses to the questions to be discussed and explored.
Ask the students what they notice about the information shown on the bar graph. Use the prompt “I notice…” to start the discussion. These “noticings” could be recorded as "speech" bubbles around the bar graph.
Session 4
What are the class’s favourite pastimes?
What should we spend the fundraising money on?
What class pet should we get?
Dear parents and whānau,
In maths we have been voting for class captains and using this information to make strip graphs and bar graphs. We have also developed our own statistical investigations.
Please talk with your child about what they have been doing in maths and take any opportunities that arise to discuss with them any simple statistical information that may be presented in the newspaper or on television.
Thank you.
Fraction bits and parts
This unit explores the beginnings of proportional thinking by introducing fractions and associated language. The purpose for this unit is to make, name, and recognise wholes, halves, third parts, fourth parts and fifth parts of a variety of objects.
This unit is based on the work of Richard Skemp. His ideas for teaching fractions can be used successfully with year 2 students, and also with students up to year 8 who are having difficulty understanding fractions. Skemp’s use of the word ‘parts’ is deliberate in that he uses it to refer to ‘equal parts’ whereas bits refers to non equal parts.
The use of two different physical representations, the whole and parts of a whole, are used to develop the concept of a fraction. Language also plays an important role. Being able to count in fractions helps students understand that you can have 5 thirds or 6 halves.
Using denominators that are the same, students need to know:
This unit supports teaching and learning activities in the Student Fractions eako 1 and 2 and complements the learning activities in Book 7 Teaching Fractions, Decimals and Percentages.
This unit can be differentiated by varying the scaffolding provided and altering the difficulty of the tasks to make the learning opportunities accessible to a range of learners. For example:
The context of equal shares can be adapted to recognise diversity and student interests to encourage engagement. Support students to identify and explore other situations in their lives where equal sharing occurs. For example, sharing kai at home or sharing cards to play a game (the pack of cards represents one whole).
Prior Experiences
Although the unit is planned around 5 sessions it can be extended over a longer period of time.
Session 1
The purpose of this session is to develop students' understanding of equal parts (the denominator).
Resources
Hoepo and his brothers and sisters are at their Poua’s tangi and although they are sad they are looking forward to the hakari because eel is always on the menu.
Hoepo is planning to go early to the marquee because he wants one eel all to himself. He is given one whole eel. Hoepo doesn’t know it but he is going to be one sick boy!
The twins appear and they are told they have to share one eel evenly between the two of them. There are now two half parts.
The triplets come next and Aunty Wai says we will have to cut another eel into three equal parts. There are now three third parts.
Hoepo’s sister has come with her three friends. Aunty Wai says that they will have to cut the eel into four equal parts. There are now four fourth parts. Aunty Wai says they are also known as quarters.
Hoepo’s five baby cousins are only allowed to eat small portions so Aunty Wai cuts the last eel into five equal parts. There are now five fifth parts.
I want you to look at one of the third parts and one of the fifth parts. Which is bigger?
Have the students take one of each of the equal parts and put them on another blank board.
Order the equal parts from smallest to biggest.
Let’s say the names.
Students should order from 1/5 – 1
Put them back on the original board.
How many halves are equal to the whole?
How many fourths are equal to the whole?
How many thirds are equal to a whole?
How many wholes are equal to a whole?
Depending on the age of the students symbolic notation can be introduced, using the terms like 1/2 and one half part interchangeably.
Session 2
The purpose of this session to develop the idea that parts of the same kind may not look alike. In Activity 1 this arose from the use of different objects. Here we see that this can be so, even with the same object.
Resources
Revise knowledge about equal parts.
What can we remember from yesterday? Write students’ comments in your modelling book.
The three straightforward ways are:
Session 3
The purpose of this session is to consolidate the concepts formed in Sessions 1 and 2, moving onto a pictorial representation.
Resources
Rules of the Game
This game is best played by groups of 24 people.
Session 4
The purpose of this session is to develop students' understanding of a number of like parts (the numerator).
This is the next step towards the concept of a fraction. It is much more straightforward than that of session 1 3 which involved (i) separating a single object into part objects (ii) of a given number (iii) all of the same amount. Here we only have to put together a given number of these parts and to recognise and name the combination
Resources
Warm up
1/2, 2/2, 3/2, 4/2, 5/2, 6/2 (be prepared for students to carry on counting and not realise that 6/2 is equal to 3).
How many halves did we count (six halves = three wholes, write on the board)
How many halves do you think would equal 6? Write on the board
How many halves do you think would equal 9? Write on the board
A Number of Like Parts
This is an activity for up to six students working in two teams. Its purpose is to introduce the concept described above.
Note that the eels, slabs, and hay should be of standard sizes.
Note also that the eels, after their head and tails are removed, resemble the eels in a cylinder shape and the slabs of meat and hay are oblongs.
Session 5
So far we have covered denominator and numerator without mentioning their names. Students need to understand that the denominator names the equal parts and numerator names the number of like parts.
Resources
Revise some of the ideas from sessions 14, selecting from these activities:
I want you to give me one fourth + one fourth (write on the board). Can anyone give me cards that mean the same but are written in a different way? (1/4 + 1/4)
I want you to find one fifth and one fifth and one fifth. How many fifths are there? Can anyone give me cards that mean the same but are written in a different way? (1/5 + 1/5 + 1/5)
What happens if we had to feed 5 giraffes and they were allowed 1/3 of a bale of hay each?
What happens if we had to feed 5 rhinos and they are allowed 1/2 a bale of hay each?
What happens if we had to feed 6 zebras and they are allowed 1/4 of a bale of hay each?
To conclude the session, ask the students to work in pairs and complete a think board (Copymaster 7 provides a blank think board and Copymaster 8 shows a completed example.) Suitable fractions for think boards include 2 halves, 3 fourth parts, 2 fifth parts, 4 third parts, 2 quarters. Show them the example of a completed think board for 3/5.
Dear family and whānau,
This week we have been learning about dividing things into equal parts so people get fair shares. Please draw your child's attention to any fractions you use over the week in cooking or when sharing kai or meals. For example if you are having pizza show them how it is sliced into 4 or 6 or 8 equal sliced parts. Ask them to help share out food when dishing up dinner or making lunches. They can draw pictures of the things you talk about and bring these to class to share.
In the garden
This unit uses the context of a garden to explore Level 2 symmetry and transformation concepts (translation, reflection and rotation).
Three important ideas about symmetry are covered in this unit:
This unit can be differentiated by varying the scaffolding provided or altering the difficulty of the tasks to make the learning opportunities accessible to a range of learners. For example:
The context in this unit can be adapted to recognise diversity and student interests to encourage engagement. For example create a classroom display of a skate park instead of a garden. Symmetrical people, dogs, and skateboards could be created, and tessellating paths and walls drawn.
It would be helpful to introduce this work by reading a book to the students that includes a garden setting. The overall aim of the unit is to make a classroom display about a garden using the activities as starting points. Be as creative as you can!
Session 1: Up the garden path
In this session students will explore shapes that tessellate or repeat to cover the plane without gaps or overlaps. Although the students will only be covering a strip (path) any covering of a path can be used to tessellate the plane simply by putting paths together.
Create garden designs around the paths.
Session 2: Bugs, Beetles and Butterflies
In this session students will be investigating line symmetry by making butterflies out of coloured paper.
Session 3: Butterfly Painting
In this session students will make symmetrical butterflies with paint.
Session 4: The Flower Garden
In this session students will be introduced to making symmetrical patterns with shape blocks. The theme for this lesson is flowers for the garden. Sunflowers would be a great example of this. Show students pictures of sunflowers or read the story "The Sunflower That Went Flop" by Joy Cowley) which can be accessed on YouTube if it is not readily available.
Session 5: The Garden Wall
In this session introduce students to the idea of translation. Students will be making tiles for the garden wall. Introduce the activity by showing them examples of some wall tiles.
Session 6: Wind Catcher in the Garden
In this session students will make a wind catcher, which illustrates rotation, as an ornament for the garden .
Cut along lines in first image
Teaching Notes:
The wind catcher has rotational symmetry but not reflective symmetry. This is because it can be rotated around onto itself but it doesn't have a line of symmetry in the plane.
Session 7: Making Scarecrows
Ask students to draw a scarecrow on a piece of paper. Fold the piece of paper down the middle of the scarecrow. Cut down this middle line. Students then give their scarecrow to a buddy who has to draw the other half of the scarecrow making sure that the drawing is symmetrical. Stick one half of the scarecrow onto a piece of paper. A buddy draws on the other half. Finished scarecrows could be stuck onto sticks and displayed in the garden.
Other Ideas
This week in maths we have been doing a unit on symmetry using things that we might find in a garden. We identified objects that had reflective symmetry by finding the line or lines of symmetry in the object.
At home this week I would like your child to find three things outside that have a line or lines of symmetry and to draw a picture of these to share at school.
Figure it Out Links
Some links from the Figure It Out series which you may find useful are: