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.
About this resource
Specific learning outcomes:
- Use a counting-on strategy to keep track of a series of additions.
- Explore the concepts of length, volume, and area.
Counting on measurement
Achievement objectives
GM1-1: Order and compare objects or events by length, area, volume and capacity, weight (mass), turn (angle), temperature, and time by direct comparison and/or counting whole numbers of units.
Supplementary achievement objectives
NA1-2: Know the forward and backward counting sequences of whole numbers to 100.
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 that are used because they are known to students and 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 handspans, 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 for 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 must be full and level
- modelling the 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 areas 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 measuring an arbitrary distance, measure how many steps there are 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 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
See Materials that come with this resource to download:
- Counting on measurement activity (.pdf)
Activity
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 use 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, or 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.
1.
Show the whole class a large spoon and a cup.
2.
Ask students to predict how many spoons of rice it will take to fill the cup.
3.
Record the predictions on the board.
4.
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.
5.
If they are correct, they should scoop that number of spoons of rice into the cup, counting: one, two, three, four...
6.
Ask,
- Is the cup full yet?
7.
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 or frame.
8.
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?
9.
Ask,
- Is the cup full yet?
10.
Continue to select students until the cup is full.
11.
Ask,
- How many spoons of rice fit in the cup?
- Were your predictions close?
12.
If necessary, repeat with a slightly different-sized cup or spoon to give more students the chance to participate.
13.
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.
14.
As they play, ensure that you circulate around the room, reinforcing sensible predictions and correct counting-on, and supporting those students that require it.
In Sessions 2–4, students move around five stations, playing variations on the game played in Session 1.
1.
Remind students of the game they played in the previous session. If necessary, play a game to refresh their memories.
2.
Explain that they will now play the same type of game but with different types of things to predict.
3.
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.
4.
Introduce the games that you will be using at your stations. There are 5 described below, for which instructions are provided as a Counting on measurement activity. However, you may want to create more of your own or exclude some of those suggested, depending on your class and the 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.
5.
As an alternative, you may wish to play one game each day, introduce it to the class, and then split into pairs to play.
Station 1: How many cups?
In this activity, students predict how many cups (a 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 practice the action as a class. Set up a start and finish line approximately 30 feet 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!
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.
1.
Ask students to talk about the games and activities they have explored over the last four sessions.
- Which was your favourite?
- Which were your predictions closest for?
- Why did some people get different answers for the same games?
2.
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.
3.
Record and discuss the students’ predictions.
4.
Play the game as a class.
5.
Discuss:
- How close were our predictions?
- Why are our predictions not always right?
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 few sessions as a model. Then pairs could swap games with another pair and play each other’s games. Ensure that students make games that have a reasonable answer (within the range of 10–50 or so).
Home link
Dear parents and whānau,
This week in maths, we are playing measuring games. You could play at home by using dice or cutting up pieces of paper with the numbers 1–6 and putting 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 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.
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