In this unit we take, estimate, and compare measurements of ourselves and our peers. We store these in a time capsule to be opened and used later in the year.

- Compare the length of two objects.
- Select objects which are about the same length as a given object.
- Order three or more objects by length.
- Estimate measurements using personal benchmarks and knowledge of non-standard units.

In this unit students use lengths of string to represent the lengths of different parts of the body. This enables them to compare and order different students' heights, arm lengths, etc. The comparisons can be made indirectly by (i) putting the strings, representing the same body parts, next to each other, and by (ii) putting the strings next to the body parts. This should show the advantage of indirect comparisons, especially with regards to things such as waist measurements, which are extremely difficult to compare directly.

Although comparing occurs at the early stages of the measurement learning framework, adults will often measure things by estimating and/or by using non-standard units. It is often useful to have an estimate of the size of an answer, as this helps us to ensure the accuracy of calculations. The comparisons of lengths in this unit lay the foundation for estimates in area and volume, and for estimates generally.

This unit is also valuable in cementing the idea of conservation of length. For instance, the string’s length is unchanged no matter where it is in the classroom and no matter how much it is rolled up. It is the conservation property that allows the students' height, represented by a given string length, to be identified.

In comparing three lengths, students implicitly recognise the transitive nature of length. Hence if string A is longer than string B and string B is longer than string C, then string A is automatically longer than string C. There is no need to compare the lengths of A and C. The difference in length follows from the first two comparisons. This ordering ability is a valuable property of numbers and has many uses throughout mathematics.

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:

- altering the range and complexity of body measurements required
- having students work in pairs or small groups to help each other with measurements. Strategically organise these groups to encourage peer extension and scaffolding
- working alongside students during measurement tasks
- providing opportunities for students to stop, share, and check their measurements with a partner
- suggesting ways to make measurements easier. For example, for some body parts it may be easier to mark the length on a piece of paper first and then cut the string to that length.

The context for this unit requires students to think about themselves and should therefore be engaging. You may want to consider including measurements of other people (e.g. sports people, students' family members, teachers, community members and leaders, notable public figures) that are of particular interest to your class, so that they compare themselves.

Te reo Māori kupu such as ine (measure), estimate (whakatau tata), tāroaroa (height (of a person), tall), poto (short), and kauwhata (graph) could be introduced in this unit and used throughout other mathematical learning. You could also encourage students, who speak a language other than English at home, to share the words related to measurement that they use at home.

- String
- One large piece of card for each student (large enough for students to draw a picture of their face and write their name) with five holes punched out (A4 is a good size)
- One small piece of card for each student with two holes punched out at even intervals
- Class list
- Tape
- Scissors
- Graph making resources (e.g. A3 graphing template)
- Shoebox

#### Getting Started

We begin the lesson with a game focused on height. We measure students' heights using string and order the heights.

- Explain the purpose of the unit to students.
*We are going to measure ourselves and then put these measurements in a time capsule to be opened later on in the year.*You might read a book or watch a video about a time capsule, or tell students about a time when a time capsule was opened in your local community. - Split the class into two groups. Have each group form a line ready to play "shorts". To play, the students from the front of each line stand together and the class decides who is shorter. The shorter student takes the other student back to the end of their group’s line. Repeat the process with the two students who are now at the front of the lines. Emphasise that there are no winners or losers in this game - the aim is to see if we, as a class, can correctly order the heights or students in our class.
- Explain to the class:
*We are now going to measure our heights with string. We are going to create***measurement cards.**

Have the students work in pairs to help each other cut a piece of string to match their heights. Give them the opportunity to work out how they might do this. (Lying down works well.) After deciding on a method together, model this for the class to ensure they know what to do. You might also model some incorrect methods of string measurement (e.g. not measuring with a straight string, starting the string measurement at a child's knees instead of at their feet, using two separate bits of string with gaps and/or overlaps). Emphasise to students that they should make their measurement**1 finger length longer**than the actual measurement. This extra string will be taped to the card in the next step. - Distribute pieces of card, with five holes punched in each, to students. Have them draw a picture of their face and write a title on their card (e.g. Tane's Measurement Card). Have them thread the string through the first hole. They should tape down the extra finger-length piece of string to the back of the card (to keep the string in place). Have them write "height" next to the hole which they have inserted the heigh-measurement string through. Model this process for students.
- Provide time for students to create their measurement cards. Students ready for extension could estimate what other things they think they are the same height as (e.g. items in the classroom, animals, plants etc.), and then (if possible), compare their string measurements to these things (e.g. the whiteboard). They could draw pictures of these things on their measurement card under the heading "what do I think I am the same height as?" Use this as an opportunity to support students with the process of creating their measurement cards.
- Order the measurement cards as a whole class. Students can take turns to put their strings in place.
*Where are you going to place your string?**Why do you think it goes there?**Who are you taller/shorter than?**Who is the tallest?**Who is the shortest?**Who is about the same height as (name)?*

#### Exploring

Over the following days have students take **three **other measurements of themselves using new measuring strings. These strings should be attached to each student's measurement card and labelled appropriately (e.g. waist, leg, arm etc.). As in the previous session, students can be extended by being asked to estimate and compare these measurements to things in their environment. Students could also be extended by comparing their measurements to the measurements of a notable person (e.g. a teacher, a world record holder, olympians etc.) Support students to measure accurately. Compare the string measurements taken at the end of each day, with either the whole class or in pairs and/or small groups. Display all measurement cards at the end of the week. At the end of the week these measurements can be placed in the time capsule (shoebox).

Body parts that can be measured and labelled include

- length of smallest finger/foot/handspan
- length of hair
- distance around head/neck/wrist/ankle (avoid measuring distance around waist)

If you use the home link activity to collect height information about your students' whānau members, ensure you provide time for students to add these measurements to their cards.

You could also spend a day exploring the following questions, which require the students to make comparisons between their own measurements.

- Which is longer – your hand or your foot?
- Which is longer – around your wrist or around your ankle?
- Which is shorter – around your head or the length of your foot?
- Find measurements that are close to being the same

You might use a writing session to help students write a few sentences about the measurements they have taken. Within this, you could also ask students to **estimate **what measurements they think will have changed, and how, at the time when they open the time capsule.

For further whole-class extension, use the measurement strings to create a shared graph. Ask students to measure a particular body part such as their right foot and then glue the strings vertically along an x axis. This creates an instant graph of everyone's foot size.

#### Reflecting

- On the fifth day, students apply their measurement skills to search for a mystery student. The students try to find who belongs to two particular string lengths. In preparation, you will need to cut two lots of string for all the class. These strings represent the height, and another body measurement, of one of the students in the class.
- Give each student the two lengths of string. Together, decide what parts of the body the two lengths will represent (e.g. height and head circumference).
- Have students cut their string lengths to fit the specified body parts. Look for students to measure accurately. Have them tape these string lengths to a small piece of card. Have the students give their cards to you, one at a time. Write a number on each student's card, and record the number beside each child's name on a class list. Wrap the strings around each card (to avoid any tangles) and place the cards inside a special container (e.g. hat, bag etc.)
- Pick out a string card. Tell the students that they have to find the student whose body lengths are represented by the string. They can do this by comparing string lengths with different students' heights, etc or by comparing string lengths with string lengths on display in the classroom.
- The students report to you when they think they know to whom the string belongs. For those students who finish early you might ask them to see if any other student has the same dimensions. Consult your class list and tell the class if they have correctly found the mystery student.
- Conclude the week’s activity by displaying your graph (if created) and small measurement cards from the "mystery student" activities. Store the large measurement cards in a time capsule (e.g. box) to be opened later in the year. When you open the time capsule, compare the changes in students' body measurements, reflect on students' estimates, and on any new learning (e.g.
*now we can measure in centimetres!).*

Dear families and whānau,

At school this week we have taken measurements of ourselves using pieces of string. We have used these measurements to create measurement cards which will be stored in a time capsule. Later on in the year we will open our capsule to see how much we have grown.

At home this week please help your child take height measurements using string for the people who live in your home. Label the strings with a piece of tape or paper with the person's name. The strings can come to school to be put into the capsule with your child's other measurements. At the end of the year we'll check to see who has grown the most in your family.