This unit is run as a series of stations over four days with students rotating around the stations in groups. The final session is run as a class activity with all students working on the same task in groups. Consider grouping together students with mixed mathematical abilities in order to encourage collaboration (mahi tahi) and tuakana-teina (peer supported learning).
The four stations involve the students looking for objects that they estimate to be a certain length. You will need to set appropriate boundaries for their search, e.g. the classroom or the playground.
As students work, the teacher can circulate amongst the groups. Points to reinforce in your discussions with students include:
- There are 100 centimetres in a metre.
How many 1 cm lengths in a metre?
How many 10 cm lengths in a metre?
Why is 50 cm sometimes called half a metre?
What is another name for a metre? - Estimation can involve the use of personal benchmarks e.g. knowledge that your fingernail is 1cm long or the length of your stride is 1m can help you estimate these lengths more accurately.
- To measure accurately, one end of the object being measured must be aligned with zero on the ruler.
- The meaning of the unmarked gradations on the ruler may need to be considered. Measurement to the nearest cm often requires identification of the number closest to the end of the object being measured.
Introduce the concept of a scavenger hunt, and model how to complete the tasks at each station. Depending on the needs of your students, it may also be appropriate to model how to accurately measure items with a ruler. This modelling could be used to create a class chart or set of guidelines for measuring. In turn, this could be used to support students in practising accurate modelling skills throughout the session.
Station One
Students work in pairs or small groups to find items that they estimate to be 1cm long. They check their estimates by measuring.
Student Instructions (Copymaster 1)
Go on a Scavenger Hunt!
- Use a ruler to find out how long 1 cm is. Take a good look!
- Find ten objects that you estimate to be 1cm long.
- Record your objects on the table below.
- Check your estimations using a ruler to measure the length of the objects accurately.
Object with estimated length 1cm | Measured length |
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How accurate were your estimates?
Were your estimates too long or too short?
What would be a good way to try and remember how long 1cm is?
Station Two
Students work in pairs or small groups to find items that they estimate to be 10cm long. They check their estimates by measuring.
Student Instructions (Copymaster 2)
Go on a Scavenger Hunt!
- Use a ruler to find out how long 10cm cm is. Take a good look!
- Find ten objects that you estimate to be 10cm long.
- Record your objects on the table below.
- Check your estimations using a ruler to measure the length of the objects accurately.
Object with estimated length 10cm | Measured length |
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How accurate were your estimates?
Were your estimates too long or too short?
What would be a good way to try and remember how long 10cm is?
Station Three
Students work in pairs or small groups to find items that they estimate to be 50cm long. They check their estimates by measuring.
Student Instructions (Copymaster 3)
Go on a Scavenger Hunt!
- Use a ruler to find out how long 50cm is. Take a good look! This length is also known as half a metre. Why?
- Find ten objects that you estimate to be 50cm long.
- Record your objects on the table below.
- Check your estimations using a ruler to measure the length of the objects accurately.
Object with estimated length 50cm | Measured length | Difference between estimated and measured length |
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How accurate were your estimates?
Were your estimates too long or too short?
What would be a good way to try and remember how long 50cm is?
Station Four
Students work in pairs or small groups to find items that they estimate to be 1metre long. They check their estimates by measuring.
Student Instructions (Copymaster 4)
Go on a Scavenger Hunt!
- Use a ruler to find out how long 1 metre is. Take a good look! What is another name for this length?
- Find ten objects that you estimate to be 1 metre long.
- Record your objects on the table below.
- Check your estimations using a ruler to measure the length of the objects accurately.
Object with estimated length 50cm | Measured length | Difference between estimated and measured length |
| | |
| | |
| | |
How accurate were your estimates?
Were your estimates too long or too short?
What would be a good way to try and remember how long 1 metre is?
Reflecting – Class activity
- Before the session, set up six activity stations around the room. At each station put a selection of paper strips in a variety of lengths. Ensure that at each station there are strips with a length of 1cm, 10cm, 50 cm and 1 metre. Label the strips at each station with letters.
- Tell the students they will be participating in the ultimate estimation challenge. Have the students rotate around the stations identifying the strips they believe to be 1cm, 10 cm, 50 cm and 1 metre long. They record their results on recording sheets (Copymaster Five).
At the conclusion of the session reveal the correct letters for the 1cm, 10cm, 50 cm and 1 metre lengths. Students check their answers and have a chance to measure the strips they chose as required.
Extension
Students who finish the activity early could estimate and measure the lengths of the other paper strips at the stations.
Maps
In this unit ākonga are introduced to using maps. They use maps to locate landmarks, identify views from different locations, and give directions using left and right turns, and distances.
Maps provide a two dimensional representation of the real world. By looking at a map ākonga can anticipate the landmarks they will see from a given location and in which direction (N, S, E, W) those landmarks will be seen. By using maps of their kura or local area, ākonga will be able to check their thinking by matching the map with the real world.
Ākonga will begin to use maps to help them follow and give directions. They will start to use directions involving left and right turns and use landmarks to clarify pathways. Ākonga will begin to use distances in whole numbers of metres.
This unit can be differentiated by varying the scaffolding of the tasks or altering expectations to make the learning opportunities accessible to a range of learners. For example:
Some activities in this unit can be adapted to use contexts and materials that are familiar and engaging for ākonga. In particular, the choice of maps to use will depend on the interests of your class. Some ākonga may respond best to maps of familiar areas, (for example, marae, beach access or playground) while others may be more engaged by an imaginative context. You could work as a class (mahi tahi model) to create maps of a favourite story, or the location of a movie.
Te reo Māori vocabulary terms such as map (mahere), North (raki), South (tonga), East (rāwhiti), West (uru), left (mauī) and right (matau) could be introduced in this unit and used throughout other mathematical learning.
Session 1
In this session ākonga are introduced to using a map to locate landmarks and identify views from different locations.
Which classroom has the best view of the marae?
What building can you see from the field?
What building can you see out the library windows?
Session 2
In this session ākonga use the kura map to describe pathways from locations.
Session 3
In this session ākonga use a local or imaginative map to describe different views they can see from different locations. They use compass directions to give the direction of landmarks from given locations. The map below is available as Copymaster 1.
How many whare have a direct view of the marae?
What can the children see from the playcentre?
What can the doctor see out the window?
If you sat in the doctor’s carpark what could you see?
Colour in a whare that has a view of the playcentre, the dairy, and the hall?
What building is east of the café?
What building is north of the hall?
What building is south of the chemist?
What direction is the playcentre from the church?
What direction is the marae from the doctors?
How many whare are south of the hall?
From which building can you look west to see the church?
Session 4
In this session ākonga give a set of directions between two locations using distances and quarter turns to the left and right.
Session 5
In this session ākonga learn about pathways and apply this to creating a fire escape plan for their whare.
Dear family and whānau,
This week your child has been using maps to describe views and pathways from locations. Your child has started to draw a plan of your whare and is finishing it by marking the escape routes out of each room in case of a fire. Please help them to complete the activity. You may wish to complete the Fire Escape Plan on the NZ Fire Service website - https://www.escapemyhouse.co.nz
Figure it out
Some links from the Figure It Out series which you may find useful are:
Staircases
In this unit ākonga look for and describe patterns they see in different types of staircases and other patterns.
In much of early pattern work, the numbers involved can be compiled in tables like the one below:
Two relationships can be seen:
In practice, recurrence relationships are easier to identify than functional ones.
This unit can be differentiated by varying the scaffolding of the tasks or altering the difficulty of the tasks to make the learning opportunities accessible to a range of learners. For example:
The materials used in this unit can be adapted to recognise diversity and ākonga interests to encourage engagement. Instead of creating patterns with classroom blocks or cubes, ākonga could be encouraged to make the patterns using environmental materials such as pebbles, shells, or daisies from the school lawn. Be sure to discuss patterns that your ākonga know about from their personal experience, for example, staircases at home or at the local library, ladders in the kura playground and patterns they have seen at marae or in the community garden.
Te reo Māori vocabulary terms such as tauira (pattern) and the phrase, e hia? (how many) could be introduced in this unit and used throughout other mathematical learning.
Getting Started
Today we explore up-and-down staircases to find the pattern in the number of blocks they are made from.
Begin the session by telling ākonga about up-and-down staircases. This type of staircase can be likened to traditional lattice poutama which can be found on tukutuku panels in many marae.
How many blocks are in the staircase?
How many blocks do you think would be in a 3-step up-and-down staircase?
How could you work it out?
Get ākonga to build more staircases. As they do, ask them about any patterns they see.
Some may recognise the horizontal layers as being the sequence of odd numbers. Some may see the vertical stacks.
Some may see that square numbers of blocks are always involved. This can be checked by rearranging the blocks to make square numbers (see the diagram below). This is an important discovery. Let them make it. This may require some careful scaffolding on your part. Ask ākonga to make several squares and look for patterns. The first square is 1 block, then the next square is 1 + 3 followed by 4 + 5. The square term is a number raised to the second power (n2 e.g., 2 x 2 = 4). Using blocks to build some squares and then asking ākonga to draw three more builds a good understanding of square numbers.
Exploring
Over the next 2-3 days, ākonga work in pairs or individually to solve the following problems (Copymaster of problems). A tuakana/teina model could work well here. Show ākonga how to use grid paper to draw the patterns and continue them. They could also use materials. As ākonga complete the problems, ask them about any patterns they see and encourage ākonga to record these observations with the patterns on the graph paper or by building the patterns with materials. Ākonga can also record their patterns using a table. The teacher will need to demonstrate how to do this and potentially provide blank tables for ākonga to use. For example:
Problem 1: Straight up the stairs
How many blocks are in this 4-step-up staircase?
How many blocks would there be in a 5-step-up staircase?
How many blocks would there be in a 6-step-up staircase?
How many blocks in a 10-step-up staircase?
How many more blocks will an 11-step-up staircase need?
What is the largest up staircase that you can tell us about?
Note: the numbers of blocks in this pattern are the triangular numbers, see Algebra Information.
Problem 2: Climbing ladders
How many pieces of wood have we used in this 1-rung ladder?
How many pieces of wood have we used in this 2-rung ladder?
How many pieces of wood would there be in a 4-rung ladder?
How many pieces of wood would there be in a 6-rung ladder?
What is the largest ladder that you can tell us about?
How many pieces of wood will you need to add to a 7-rung ladder to get an 8-rung ladder?
Note: the number of pieces of wood is three times the number of rungs.
Ice-block sticks could be used to create ladders.
Problem 3: Small steps
Watch out! You need to take small steps to walk up and down these little stairs.
How many blocks are in the 4-step staircase?
How many blocks are in the 6-step staircase?
What is the largest staircase that you could tell us about?
Does this remind you of something you have done before?
Note: the count here is the same as that in Problem 1.
Problem 4: Star patterns
How many blocks are in a 4-star?
How many blocks are in a 5-star?
What do you notice about the stars?
How many blocks do you need to add to a 7-star to make an 8-star?
What is the largest star that you could tell us about?
Note: the pattern here is 1, 5, 9, 13, … At each stage you add on 4 blocks. To make a 100-star you need to have 99 lots of 4 plus one block for the centre.
Problem 5: L-shapes
How many blocks are in a 4-L?
How many blocks are in a 5-L?
What do you notice about the pattern in the L’s?
What is the largest L that you could tell us about?
Note: to make a 100-L you need 100 + 100 – 1 = 199 blocks.
Reflecting
In this session we share our findings and solutions to the problems of the previous days. We listen and look carefully as the patterns are explained. We then make some block patterns of our own which we give to our classmates to continue.
Dear parents and whānau,
In maths this week we have explored different block patterns.
Discuss the pattern with your child and see if they can continue the pattern. You may want to find some objects your child could make this pattern out of, for example, pebbles or coins.
Figure it Out Links
A link from the Figure It Out series which you may find useful is:
Data cards: Level 2
This unit introduces the students to a way of looking at information from a group of individuals, i.e. a data set.
A "data card" is simply a square piece of paper containing information about an individual person or thing. At this level, the data card is divided into three areas with the same category information in the same location on each card. In this unit, the terms data and information are used to mean the same thing and are interchanged throughout. Because several pieces of information about individuals are on each data card, different categories can be looked at simply by rearranging the cards.
This unit focuses on sorting and organising data sets, i.e. collections of information from a group of individuals. As the data set is looked at, questions or interesting things arise. This is different from starting with an investigative question then collecting data to answer the investigative question.
Understanding the difference between individual data and group data is central to the unit. The goal is to move students from “that is Jo’s data and that is me” to making statements about the group in general. Increasing students' ability to accurately describe aspects of a data set, including developing statistical vocabulary, is part of the unit. As students become comfortable with making statements and describing data, more precise vocabulary is to be encouraged. The meaning and usage of words like; same, similar, exactly and almost need to be explored during the unit along with the importance of using numerical descriptions, e.g. 2 more than, when describing or comparing data.
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.
Data collection or survey questions
Data collection or survey questions are the questions we ask to collect the data to answer the investigative question. For example, if our investigative question was; “What native birds do the students in our class like?” a corresponding data collection or survey question might be “What is your favourite native bird?”
As with the investigative question, data collection or survey question development is led by the teacher, and through questioning of the students, suitable data collection or survey questions are developed.
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. This can happen easily in Session 4 and 5.
The te reo Māori vocabulary term pātai (question) could be introduced in this unit and used throughout other mathematical learning.
pīwakawaka, tūī or kererū?
Session One
What could “tūī” mean? What could “reading” mean? What could “Even date” mean?
Does anyone in the class fit this data card?
Do you know someone that fits this data card that is not in this class?
How many different people could this data card be correct for?
What would a data card about you look like?
Session Two
Initially encourage the students to look at one category at a time then, encourage students to look for categories within other categories, e.g. What favourite subject (reading, writing or maths) is most popular with students who like tūī?
Session Three
What do you think we will find out about our class?
Will it be mainly different or similar to the group looked at in Session Two?
Session Four
Today the students, in pairs (tuakana/teina model could work well here), will design and collect their own data using data cards. Each pair of students needs to design three data collection questions to ask other students in the class.
Sample data collection questions:
Session Five
In pairs the students are to sort and organise their data cards to look for other interesting things about the class and to see if the statements they made about the class were correct.
After a set time each pair reports what they found out about the class. This could be in the form of a written report with some sentences about what they found out, a conference with their teacher or an oral presentation to the class.
Dear whānau,
At school we have been learning about data collection. You could support your child to write 3-4 questions to survey your whānau on. These questions should have a ‘yes’ or ‘no’ answer or 2-3 options for an answer. For example, What is your favourite native bird - kererū, tūī or pīwakawaka? Ask your child to say or write some concluding statements about the data s/he collects. For example, All the people in my whānau like tūī.
Getting partial
In this unit we explore fractions of regions as well as fractions of sets. We look for, and develop understanding of, the connection between fractions and division.
Fractions are one of the first departures from whole numbers that students will see. This unit introduces a number of important concepts relating to fractions. The first of these is that fractions represent parts of one whole, and can be represented in a variety of ways including regions and sets. This makes them useful in a large variety of situations where whole numbers by themselves are inadequate.
The second useful concept is that a given number can be represented as a fraction in many ways. Knowing that fractions such as ½ can be disguised as 2/4 or 3/6, etc is important both for recognition purposes and for use in calculations.
Finally, students should know that fractions can be represented both as one whole number divided by another whole number and as points on the number line. Having a knowledge of the different representations of fractions provides connections across mathematics for students and so increases their level of understanding.
In this unit we also introduce the idea of a fraction of 100. This lays the groundwork for the decimal representation of fractions at Level 3, and percentages at Level 4. These ideas are developed further in the units Getting the Point, Level 3 and Getting Percentible, Level 4. Facility with fractions is also an important precursor for algebra. Algebraic fractions have a wide range of uses. Without a good understanding of how fractions work, students will be restricted in their work at higher levels when fractions occur in algebraic settings.
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 for this unit can be adapted to recognise diversity and student interests to encourage engagement. Consider making links between the learning in these sessions and relevant learning from other curriculum areas (e.g. number of children competing in different events at the School Athletics championship, numbers of different native birds observed in a week). For example:
Te reo Māori vocabulary terms such as hautau (fraction), haurua (half), hauwhā (quarter), haurima (fifth), hauwaru (eighth) and hautekau (tenth) as well as numbers in Māori could be introduced in this unit and used throughout other mathematical learning.
Session 1
Here we look at different representations of 1/2.
Session 2
Here we look at fractions other than 1/2 and consider ways to represent these fractions that involve 100.
Session 3
This session involves fractions in problem situations.
Session 4
Another way to represent numbers is the number line. Here we use the number line to show the relative positions and sizes of fractions.
These problems will highlight students’ knowledge of the relative size of fractions. For example, a student might find half of the distance between 0 and 1/5 to see where 1/10 should be or half the distance between 1/2 and 1 to see the location of 3/4 . The problems will also highlight their understanding of the role of the numerator (top number) as the selector of the number of parts and the role of the denominator (bottom number) as nominating how many equal parts the whole is separated into.
Session 5
Here we try to link the concepts of fractions in length and sets by dividing up a big worm.
The worm was 18 cubes long. Each bird got three cubes of worm. How many birds were there?
Dear family and whānau,
This week we have been thinking about fractions. Ask your child to explore some fractions with you. For example: take a newspaper or magazine and ask them to find the longest word that they can. How many letters does it have? Now find some words that are half that length or a third of the length or a quarter of that length. Ask your child to record the words they find and the fractions you talk about.
How many pages does the paper or magazine have? What is half that number and a quarter of that number?
We would be glad if the answers could be brought back to class so that we can discuss them.
Figure it Out Links
Some links from the Figure It Out series which you may find useful are:
Scavenger hunt
In this unit students participate in a series of scavenger hunts to develop their own personal benchmarks for measures of 1cm, 10cm, 50cm and one metre. An understanding of the relationship between centimetres and metres is also developed.
Children need to recognise the need to move from using non standard to standard measures of length. The motivation for this arises out of students comparing differences in the lengths of different objects (e.g. in the length of their hand spans). From this the need for standard measurement becomes evident.
Students also need to develop personal benchmarks with which they can measure various objects in their daily lives. Their personal benchmarks need to gradually relate more to standard measures such as metres and 1/2 metres.
Ultimately, students should able to choose appropriately from a range of strategies including estimation, knowledge of benchmarks, and knowledge of standard measures to approach various measuring tasks with confidence and accuracy.
This unit can be differentiated by varying the scaffolding of the tasks or altering the difficulty of the tasks to make the learning opportunities accessible to a range of learners. For example:
This unit can be adapted to acknowledge student interests and contexts encouraging engagement. For example:
Te reo Māori vocabulary terms such as ine (measure), mita (metre), mitarau (centimetre), whakatau tata (estimate), and paerewa (benchmark) could be introduced in this unit and used throughout other mathematical learning.
This unit is run as a series of stations over four days with students rotating around the stations in groups. The final session is run as a class activity with all students working on the same task in groups. Consider grouping together students with mixed mathematical abilities in order to encourage collaboration (mahi tahi) and tuakana-teina (peer supported learning).
The four stations involve the students looking for objects that they estimate to be a certain length. You will need to set appropriate boundaries for their search, e.g. the classroom or the playground.
As students work, the teacher can circulate amongst the groups. Points to reinforce in your discussions with students include:
How many 1 cm lengths in a metre?
How many 10 cm lengths in a metre?
Why is 50 cm sometimes called half a metre?
What is another name for a metre?
Introduce the concept of a scavenger hunt, and model how to complete the tasks at each station. Depending on the needs of your students, it may also be appropriate to model how to accurately measure items with a ruler. This modelling could be used to create a class chart or set of guidelines for measuring. In turn, this could be used to support students in practising accurate modelling skills throughout the session.
Station One
Students work in pairs or small groups to find items that they estimate to be 1cm long. They check their estimates by measuring.
Student Instructions (Copymaster 1)
Go on a Scavenger Hunt!
How accurate were your estimates?
Were your estimates too long or too short?
What would be a good way to try and remember how long 1cm is?
Station Two
Students work in pairs or small groups to find items that they estimate to be 10cm long. They check their estimates by measuring.
Student Instructions (Copymaster 2)
Go on a Scavenger Hunt!
How accurate were your estimates?
Were your estimates too long or too short?
What would be a good way to try and remember how long 10cm is?
Station Three
Students work in pairs or small groups to find items that they estimate to be 50cm long. They check their estimates by measuring.
Student Instructions (Copymaster 3)
Go on a Scavenger Hunt!
How accurate were your estimates?
Were your estimates too long or too short?
What would be a good way to try and remember how long 50cm is?
Station Four
Students work in pairs or small groups to find items that they estimate to be 1metre long. They check their estimates by measuring.
Student Instructions (Copymaster 4)
Go on a Scavenger Hunt!
How accurate were your estimates?
Were your estimates too long or too short?
What would be a good way to try and remember how long 1 metre is?
Reflecting – Class activity
At the conclusion of the session reveal the correct letters for the 1cm, 10cm, 50 cm and 1 metre lengths. Students check their answers and have a chance to measure the strips they chose as required.
Extension
Students who finish the activity early could estimate and measure the lengths of the other paper strips at the stations.
Dear parents and whānau,
This week in maths we are working on estimating lengths of up to a metre. Please help your child find any objects at home that they estimate to be 1cm, 10 cm, half a metre, and 1 m long. They can record the names of the objects and the estimations in their book. Ask them to choose one object to bring to school so we can measure it carefully to check their estimation.