Purpose
This unit is based around a series of activities in which students explore aspects of measurement. This is explored through making predictions and using non standard units to answer a 'how many' question.
Specific Learning Outcomes
- Use a counting on strategy to keep track of a series of additions.
- Explore the concepts of length, volume and area.
Description of Mathematics
This unit develops understanding of non-standard units as students learn that some form of unit needs to be used to answer a question such as "how much longer is your pencil than mine?". Non-standard units are ordinary objects which are used because they are known to students and are readily available, for example, paces for length, books for area and cups for volume. Experience measuring with these introduces students to the potential for quantifying a measured outcome, for example, the desk is 4 hand spans across. Therefore, students should be provided with many opportunities to measure using these kinds of non-standard units. Many of the principles associated with measurement are introduced through the use of non-standard units:
- Measures are expressed by counting the total number of units used
- The unit must not change during a measurement activity,
- Units of measure are not absolute but are chosen for appropriateness. For example, the length of the room could be measured by hand spans but a pace is more appropriate.
Students need to realise that non-standard units tend to be personal and are not the most suitable for communication. For example, one student's hands will be smaller than another's, so measuring using hand span is not always useful or accurate.
Opportunities for Adaptation and Differentiation
The learning opportunities in this unit can be differentiated by providing or removing support to students and by varying the task requirements. Ways to differentiate include:
- supporting students that have difficulty with the measuring aspect of the task. It is important that they realise that each measure must be the same, for example, each cup full and level
- modelling correct methods of measuring for each station
- varying the sizes of the containers and cups students are asked to use in each session
- providing opportunities for students to work in pairs and small groups in order to encourage peer learning, scaffolding, extension, and the sharing and questioning of ideas
- working alongside individual students (or groups of students) who require further support with specific area of knowledge or activities.
The activities in this unit can be adapted to make them more interesting and meaningful for students by adapting them to reflect familiar contexts. For example, rather than measure an arbitrary distance, measure how many steps it is from the door of the classroom to the playground. Perhaps you could think of a potential link to students' cultural backgrounds (e.g. how many steps does it take to walk across the wharenui at our local marae) or a link to learning from other curriculum areas (e.g. how many steps would a moa have to take to cross the classroom?).
Te reo Māori kupu such as ine (measure) and tatau (count) could be introduced in this unit and used throughout other mathematical learning.
Required Resource Materials
- Dice (at least one per pair of students)
- Measuring spoons
- Rice
- Measuring cups
- Measuring bowls
- Hundreds board and/or a number line
- Ink pad or trays of paint
- Paper or card
- Copymaster of instructions
Activity
Session 1
In this session the class is introduced to a game where they have to guess how many spoons of rice it will take to fill a cup. They play a game, first as a class, then in pairs to find out how many spoonfuls of rice will fit in a cup. You could sand or water if you feel the use of food is not appropriate. Note that rice can easily be repurposed as a material for making items such as rhythm shakers, juggling balls, and stress balls. Initially, choose cups/spoons/containers that will allow the container or cup to be filled with approximately 30 spoons of rice. This number (and therefore, the size of the measurement utensils) can be varied to change the difficulty of the measurement tasks.
- Show the whole class a large spoon and a cup.
- Ask students to predict how many spoons of rice it will take to fill the cup.
- Record the predictions on the board.
- Select one student to come forward. That student should roll a die, show the result to the class, and say what number they have rolled.
- If they are correct, they should scoop that number of spoons of rice into the cup counting, one, two, three, four...
- Ask: Is the cup full yet?
- Select another student to take a turn rolling the die. This time, once they have identified the number rolled, they should add that many spoons of rice to the cup, continuing the count from where the previous student finished. The count can be tracked on a number line or on a 100s board/frame.
- Some support may be required for students still operating at stage 3 of the Number Framework. Ask questions such as:
How many spoonfuls are in the cup so far?
What is the number after that?
How many spoonfuls will there be if we put one more in? - Ask: Is the cup full yet?
- Continue to select students until the cup is full.
- Ask: How many spoons of rice fit in the cup? Were your predictions close?
- If necessary, repeat with a slightly different sized cup or spoon to allow more students the chance to participate.
- When all students understand how the game works put them into pairs (small groups will also work) and give each pair a die, a cup, a spoon, and a container of rice to play the game on their own.
- As they play ensure that you circulate around the room reinforcing sensible predictions and correct counting-on, and supporting those students that require it.
Exploring (Sessions 2-4)
In Sessions 2-4 students move around five stations playing variations on the game played in Session 1.
- Remind students of the game they played in the previous session. If necessary play a game to refresh their memories.
- Explain that they will now play the same type of game but with different types of things to predict.
- The games should be played in the same way as the game in the previous session, with students predicting “how many" and then taking it in turns to roll a die and add that many to the total count. You could construct a class chart of "how many" and use this to record students' discoveries.
- Introduce the games that you will be using at your stations. There are 5 described below, for which instructions are provided as a Copymaster. However, you may want to create more of your own, or exclude some of those suggested, depending on your class and on resources available. It may be advisable to start with only a couple of versions on the first day so there is less for students to think about and introduce more on the following days.
- As an alternative you may wish to play one game each day, introducing it to the class and then splitting into pairs to play.
Station 1: How many cups?
In this activity students predict how many cups (small measuring cup) of rice will fit into a bowl.
Station 2: How many bowls?
In this activity students predict how many bowls of water will fit into a bucket. This activity will need to be carried out either outside or over a sink area. Alternatively, a sandpit could be used.
Station 3: How many ladybird steps?
In this activity students predict how many ladybird steps (steps taken with the heel of the foot touching the toe of the previous foot) it takes to travel a given distance. You will need to teach students how to take ladybird steps, and practise the action as a class. Set up a start and finish line approximately 30 foot lengths apart.
Station 4: How many giant steps?
In this activity students predict how many giant steps (steps taken as long as possible) it takes to go the length of a tennis court (or other suitable distance). You will need to teach students how to take giant steps, and practice the action as a class.
Station 5: How many thumbprints?
In this activity students are given a piece of paper or card (around ¼ of an A4 sheet) and asked to predict how many thumbprints it will take to cover it. They could use either an inkpad or trays of paint to produce the thumbprints. A demonstration should be given so that students understand that they should put their thumbprints side by side in a grid rather than trying to cover every spot of white on the page!
Session 5
In this session we discuss the games and activities that have been explored over the last four days and play a new game as a class.
- Ask students to talk about the games/activities they have explored over the last 4 sessions.
Which was your favourite?
Which were your predictions closest for?
Why did some people get different answers for the same games? - Introduce the new game: How many sheets of paper will it take to cover the mat? As previously, choose a size of paper and an area to give a correct answer of around 30.
- Record and discuss the students’ predictions.
- Play the game as a class.
- Discuss:
How close were our predictions?
Why are our predictions not always right?
Extension
As an extension you may wish to allow students to suggest their own ‘how many’ games that they could play. Pairs of students could, with supervision, write the instructions for a game using those they have played over the last sessions as a model. Then pairs could swap games with another pair and play each other’s games. Ensure that students make games which have a reasonable answer (within the range 10 – 50 or so).
Home Link
Family and whānau,
This week in maths we are playing measuring games. You could play at home by using dice or cut up pieces of paper with the numbers 1-6 and put them in an envelope or ice cream container to draw out. Using a cup and a bowl, have your child predict how many cups of water it will take to fill the bowl. Have your child then roll the die or select a card, add that many cups of water to the bowl, then roll the die again and count on from the first number. Repeat this till the bowl is full and have your child check to see if their prediction was close.
Your child will enjoy showing you how to play.
Tricky Bags
This unit comprises 5 stations, which involve ākonga developing an awareness of the attributes of volume and mass. The focus is on development of the language of measurement.
Early experiences must develop an awareness of what mass is, and of the range of words that can be used to describe it. A mass needs to be brought to the attention of many ākonga attention as it is not an attribute that can be seen. They should learn to pick up and pull objects to feel their heaviness. Initially, young ākonga might describe objects as heavy or not heavy. They should gradually learn to compare and use more meaningful terms (e.g. lighter and heavier).
As with other measures, ākonga require practical experience to begin forming the concept of an object taking up space. This can be developed through lots of experience with filling and emptying containers with sand and water. Pouring experiences that make use of containers of similar shapes and different capacities (and vice versa), are also important at this stage. They also need to fill containers with objects and build structures with blocks. The use of language such as: it’s full it’s empty! There’s no space left! It can hold more! focus attention on the attribute of volume. The awareness of the attribute of volume is extended as comparisons of volume are made at the next stage.
The stations may be taken as whole class activities (fostering mahi tahi - collaboration) or they may be set up as group stations for ākonga to explore (fostering tuakana-teina - peer learning). We expect that many young ākonga will already be aware of the attributes of volume and mass. For them, these may be useful learning-through-play activities.
The learning opportunities in this unit can be differentiated by providing more support or challenge to ākonga. For example:
The measuring activities in this unit can be adapted to use objects that are part of your ākonga everyday life. For example:
Te reo Māori vocabulary terms such as papatipu (mass), kahaoro (volume), taumaha (heavy) and taimāmā (light) could be introduced in this unit and used throughout other mathematical learning.
Session 1: Tricky bags
In this activity we investigate bags that look the same, but one is empty and the others are filled with books.
Are these bags the same or different?
How do you know?
Are you sure?
Can you guess by just looking, which is heavy?
Session 2: Push and Pull
In this activity we push and pull objects to see which feels heavier.
Are these cartons the same or different?
How do you know?
Are you sure?
How could you find out?
The cartons are too large for you to lift safely. Can you think of another way of finding out how heavy they are?
Do you think they are the same?
Why? Why not?
Which carton is heavier? How do you know?
Session 3: Popcorn containers
In this activity we make popcorn containers for the Three Bears. Any other picture book that describes a quantity of something (e.g. an amount of food) could be used in this session.
What size popcorn would Father Bear want?
What size popcorn would Mother Bear want?
What size popcorn would Baby Bear want?
How could we check if Father Bear's cone holds the most?
Session 4: Fill it up
In this activity we pour water (or beans) between containers and guess how high up the water or beans will go.
What do you think will happen if I pour the beans into the ice-cream container?
How far will it fill up?
Did you guess correctly?
Is the container full?
Is it empty?
Session 5: Book corner
In this activity we look at some picture books that could be read to ākonga or enjoyed independently by ākonga, to reinforce measuring language associated with volume and mass.
More titles and measurement specific activities are available on the Level 1 Measurement Picture Books page.
Dear family and whānau,
This week in maths, we have been exploring activities that develop an awareness of volume and mass (weight). We have been using words like: heavy, light, full and empty to describe objects.
Support your child to look around your home or local area, and find objects that they would describe as being light and objects they would describe as being heavy. Take a photo of these objects or draw pictures of them so your child can share their findings with us at kura.
The Three Bears
In this unit we compare the volumes of containers using the context of Goldilocks and the Three Bears.
In this unit we compare the volumes of a number of different containers by pouring the contents from one to the other. We use this direct comparison to order containers from those that hold the least to the most.
We also explore the conservation of volume by looking at how two different shaped objects can have the same capacity.
The learning opportunities in this unit can be differentiated by providing or removing support to students and by varying the task requirements. Ways to differentiate include:
The activities in this unit can be adapted to make them more interesting by adding contexts that are familiar to them, for example, you may prefer to use three class toys, three teachers, three characters from a culturally relevant story, three animals etc. Consider what links could be made here to students' interests, cultural backgrounds, and to their learning from other curriculum areas. You might use a story other than Goldilocks and the Three Bears to frame this unit - perhaps one focused around native birds filling their nest with twigs or around a lake or river being filled with water.
Te reo Māori kupu such as rōrahi (volume) could be introduced in this unit and used throughout other mathematical learning.
Getting Started
We introduce this unit by reading Goldilocks and the Three Bears (or another relevant story). The story provides a good starting point for the comparison of different sized containers.
Which bowl do you think has the most rice bubbles in it?
Why do you think that one?
How could we find out which bowl holds the most rice bubbles?
Which cup do you think has the most drink in it?
Why do you think that one?
How could you check?
Exploring
In the following days we are going to continue to compare and order volumes of containers that might belong to the Three Bears. Each day question students about what they are doing.
During the week, students may find containers that look very different even though they hold the same amount. Question them about this.
Ideas for exploration:
Today the bears are going for a walk and need to take water with them. Find out which bottle belongs to which bear.
Today the bears are going for a picnic and each pack lunch into their lunch box. In groups of three, the students could investigate their own lunch boxes (emptied) and decide which box is the largest and which is the smallest.
The students are given a variety of small containers that could hold the bears "secret treasures". They need to work out which holds the most, ordering 3 containers from least to greatest volume.
Reflecting
In this session the Bears invite Goldilocks to their house for breakfast. As the students make decisions about the bowl, cup, spoon and bottle reflect on the fact that some containers might hold the same amount even though they are very different shapes (conservation of volume). You may have touched on this concept during the week but this session reinforces it for all students.
Which bottle do you think will hold the most drink? Why?
How could we find out which holds the most drink?
Which bottle holds the most?
Which bottle did you think would hold the most? Why?
What is different about these bottles?
What is the same about these bottles?
Dear families and whānau,
At school this week we have compared the volumes of a number of different containers by pouring from one to the other. We have found that some containers, which look very different, can have the same volume.
At home this week your child is to try to find two containers that look different but hold similar amounts of water. Your child will then ask family members to guess which holds the most and see if anyone is “tricked".
Dino Cylinders
In this unit the students use a small plastic dinosaur as the unit with which to measure the capacity of containers. They apply their counting strategies and discover that a number of different shaped containers can contain the same number of dinosaurs.
Measurement provides a context for the further development and reinforcement of number skills. Students can measure without the use of numbers up to the stage of indirect comparison. However as soon as they repeatedly use a unit to measure an object they need numbers to keep track of the repetitions.
This unit is also designed to allow students to practice their one-to-one counting as they calculate the capacity of containers filled with plastic dinosaurs.
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:
Session 1
In this session we measure the capacity of containers by counting the number of dinosaurs they hold.
How many dinosaurs do you think would fit in this container?
How can we check?
One, two, three, four...
How many dinosaurs does this container hold?
Which container holds the most dinosaurs?
How do you know? (This will reinforce the order and sequence of numbers.)
Do these containers hold the same number or dinosaurs? (check).
Are they the same?
Session 2
In the following sessions the students create cylinders to contain a given number of dinosaurs. The challenge is to create a cylinder that contains exactly the given number of dinosaurs. The activities give students the opportunity to practice counting objects in ones, and to order and compare numbers using objects. This is a good opportunity for your students to practice counting in te reo Māori.
How many dinosaurs do you think it would hold exactly? (Discuss that exactly means that no more dinosaurs could fit into the cylinder.)
Please count your dinosaurs to me.
Does your cylinder fit exactly 10 dinosaurs?
Can you fit any more dinosaurs in your cylinder?
Are cylinders a good container for dinosaurs? Why or why not?
Could you make a cylinder for 20 dinosaurs? What would it be like?
What do you notice about the cylinder?
Can you see any cylinders which are exactly the same?
What do you think that a cylinder for 20 dinosaurs would look like?
Sessions 3-4
In these sessions the students continue their exploration of the capacity of cylinders by constructing cylinders for a given number of dinosaurs. As the containers are created they are displayed in order of capacity. Many opportunities are provided for one-to-one counting and sequenceing of numbers in English and te reo Māori.
Where does your cylinder belong?
How do you know it comes after __?
Which cylinder will come after your one?
How many dinosaurs does this one hold?
Which one holds one (2, 3..) more? How do you know?
Which one holds one (2, 3..) less? How do you know?
Which cylinders look the biggest?
Do they hold the most dinosaurs?
Session 5
In today’s session each student makes a cylinder. We then use the cylinder to see how many objects (cubes, dinos, etc) can fit exactly into our cylinder.
Family and whānau,
In maths this week we have been practising counting objects up to 20 as part measuring how much a container can hold. As part of our experiences we have constructed cylinders to fit certain numbers of toy dinosaurs. Our home task this week is to make a paper or cardboard cylinder that fits 20 small objects (for example; pebbles, toothpicks or milk lids). Your child will need paper or light card (the side of an old cereal box would be good), scissors and tape and they will be keen to show you what to do.
Counting on Measurement
This unit is based around a series of activities in which students explore aspects of measurement. This is explored through making predictions and using non standard units to answer a 'how many' question.
This unit develops understanding of non-standard units as students learn that some form of unit needs to be used to answer a question such as "how much longer is your pencil than mine?". Non-standard units are ordinary objects which are used because they are known to students and are readily available, for example, paces for length, books for area and cups for volume. Experience measuring with these introduces students to the potential for quantifying a measured outcome, for example, the desk is 4 hand spans across. Therefore, students should be provided with many opportunities to measure using these kinds of non-standard units. Many of the principles associated with measurement are introduced through the use of non-standard units:
Students need to realise that non-standard units tend to be personal and are not the most suitable for communication. For example, one student's hands will be smaller than another's, so measuring using hand span is not always useful or accurate.
The learning opportunities in this unit can be differentiated by providing or removing support to students and by varying the task requirements. Ways to differentiate include:
The activities in this unit can be adapted to make them more interesting and meaningful for students by adapting them to reflect familiar contexts. For example, rather than measure an arbitrary distance, measure how many steps it is from the door of the classroom to the playground. Perhaps you could think of a potential link to students' cultural backgrounds (e.g. how many steps does it take to walk across the wharenui at our local marae) or a link to learning from other curriculum areas (e.g. how many steps would a moa have to take to cross the classroom?).
Te reo Māori kupu such as ine (measure) and tatau (count) could be introduced in this unit and used throughout other mathematical learning.
Session 1
In this session the class is introduced to a game where they have to guess how many spoons of rice it will take to fill a cup. They play a game, first as a class, then in pairs to find out how many spoonfuls of rice will fit in a cup. You could sand or water if you feel the use of food is not appropriate. Note that rice can easily be repurposed as a material for making items such as rhythm shakers, juggling balls, and stress balls. Initially, choose cups/spoons/containers that will allow the container or cup to be filled with approximately 30 spoons of rice. This number (and therefore, the size of the measurement utensils) can be varied to change the difficulty of the measurement tasks.
How many spoonfuls are in the cup so far?
What is the number after that?
How many spoonfuls will there be if we put one more in?
Exploring (Sessions 2-4)
In Sessions 2-4 students move around five stations playing variations on the game played in Session 1.
Station 1: How many cups?
In this activity students predict how many cups (small measuring cup) of rice will fit into a bowl.
Station 2: How many bowls?
In this activity students predict how many bowls of water will fit into a bucket. This activity will need to be carried out either outside or over a sink area. Alternatively, a sandpit could be used.
Station 3: How many ladybird steps?
In this activity students predict how many ladybird steps (steps taken with the heel of the foot touching the toe of the previous foot) it takes to travel a given distance. You will need to teach students how to take ladybird steps, and practise the action as a class. Set up a start and finish line approximately 30 foot lengths apart.
Station 4: How many giant steps?
In this activity students predict how many giant steps (steps taken as long as possible) it takes to go the length of a tennis court (or other suitable distance). You will need to teach students how to take giant steps, and practice the action as a class.
Station 5: How many thumbprints?
In this activity students are given a piece of paper or card (around ¼ of an A4 sheet) and asked to predict how many thumbprints it will take to cover it. They could use either an inkpad or trays of paint to produce the thumbprints. A demonstration should be given so that students understand that they should put their thumbprints side by side in a grid rather than trying to cover every spot of white on the page!
Session 5
In this session we discuss the games and activities that have been explored over the last four days and play a new game as a class.
Which was your favourite?
Which were your predictions closest for?
Why did some people get different answers for the same games?
How close were our predictions?
Why are our predictions not always right?
Extension
As an extension you may wish to allow students to suggest their own ‘how many’ games that they could play. Pairs of students could, with supervision, write the instructions for a game using those they have played over the last sessions as a model. Then pairs could swap games with another pair and play each other’s games. Ensure that students make games which have a reasonable answer (within the range 10 – 50 or so).
Family and whānau,
This week in maths we are playing measuring games. You could play at home by using dice or cut up pieces of paper with the numbers 1-6 and put them in an envelope or ice cream container to draw out. Using a cup and a bowl, have your child predict how many cups of water it will take to fill the bowl. Have your child then roll the die or select a card, add that many cups of water to the bowl, then roll the die again and count on from the first number. Repeat this till the bowl is full and have your child check to see if their prediction was close.
Your child will enjoy showing you how to play.
Make a measurement maths trail
In this unit students pose measurement questions, make estimates and carry out practical measuring tasks using appropriate metric units. They first complete a trail devised by the teacher and then devise and complete a maths trail of their own.
The maths trail can be made to accommodate any level of measurement expertise and any range of measurement topics. To make a maths trail (which can be inside the classroom or school buildings or outside, or a combination of both), the steps are:
Comments on questions
Suggestions for Measurement Questions (Of course, questions do not need to be all measurement)
The learning opportunities in this unit can be differentiated by providing or removing support to students and by varying the task requirements. Ways to differentiate include:
The context for this unit is open. Choose contexts that are of relevance to your students. The school or a site of interest, such as a local park with playground, are idea sites. You might use a local marae if permission is given by elders and protocols are observed. Develop challenges around topics that interest your students. If they are interested in sport, then activities like ball throwing or kicking, can generate challenges. If they are interested in animals, you might integrate the measurement trail with an investigation of the local rock pools, pond, or stream. Small creatures as ideal for learning about small units if measure, such as millimetres. Students are usually interested in themselves so measurement tasks based on setting Guiness Book records for tasks make excellent challenges.
Session 1
(Mark out the maths trail in advance)
Session 2
Which questions were most difficult?
Which questions were most interesting?
Were any questions too easy?
Session 3
Session 4
Session 5
Groups complete the maths trail as in Session 1, then come together to discuss answers and strategies and to comment on the idea of a maths trail.
Extension
Some students may wish to make a new maths trail for a younger class to complete, which may include number and space.
Family and whānau,
At school this week we have been using maths trails to practice our measurement skills. Your child is going to set up a maths 5 stop trail for you to try out at home. We hope you have fun together answering the measurement questions at each station on the trail. Please write a comment in your child's book about their maths trail. For example: what was the trickiest question? what one was the most fun? was the trail well organised?