Counting on Measurement
This unit is based around a series of activities in which students explore aspects of measurement using non standard units to answer a 'how many' question. They make predictions and work in pairs over 4 to 5 sessions.
- use a counting on strategy to keep track of a series of additions
- explore the concepts of length, volume and area
Some form of unit needs to be used if a question such as "How much longer is your pencil than mine?" is asked. 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. Students should be provided with many opportunities to measure using these kinds of non-standard units. Non-standard units introduce the students to the use of units to provide numbers that quantify a measure outcome, for example, the desk is 4 hand spans across. Non-standard units introduce most of the principles associated with measurement:
- 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.
Prior to introducing standard units, students need to realise that non-standard units tend to be personal and are not the most suitable for communication. For example, my hands are smaller than yours, so telling me to measure a piece of cloth three hands wide may not be useful.
measure, how many, different, same, predict, prediction, counting on, total count
tahi, rua, toru, what, rima, ono, whitu, waru, iwa, tekau.......tasi, lua, tolu, fa, lima, ono, fitu, valu, iva, sefulu.........
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.
- Show the whole class a large spoon and a cup (these should be chosen so that the cup can be filled with approximately 30 spoons of rice).
- 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....tahi, rua, toru, wha....tasi, lua, tolu, fa........
- 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 numberline 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.
In Sessions 2-4 students move around 5 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 for the next three maths lessons they will be playing 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.
- Introduce the games that you will be using at your stations. There are 5 described below, and for which copymasters are provided, but 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.
a. How many cups?
In this activity students predict how many cups (small measuring cup) of rice will fit into a bowl. Try to pick containers so that the answer is around 30.
b. How many bowls?
In this activity students predict how many bowls of water will fit into a bucket. Try to pick containers so that the answer is around 30. This activity will need to be carried out either outside or over a sink area. A sandpit would be an alternative if one is available.
c. 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 probably practice as a class. Set up a start and finish line approximately 30 foot lengths apart.
d. 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 probably practice as a class.
e. How many thumbprints?
In this activity students are given a sheet of paper (around ¼ A4) 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 we have been playing over the last four days and play a new game as a class.
- Ask students to talk about the games they have played 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.
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 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).