Making benchmarks: Length

Purpose

This unit explores how benchmarks for 1 metre, 1/2 metre, and 1 centimetre can be used to aid in the estimation of length for given objects.

Achievement Objectives
GM2-1: Create and use appropriate units and devices to measure length, area, volume and capacity, weight (mass), turn (angle), temperature, and time.
Specific Learning Outcomes
  • Demonstrate a personal benchmark for 1 metre, 1/2 metre, and 1 centimetre.
  • Identify and use external benchmarks to carry out practical measuring tasks.
  • Demonstrate the need for having and using standard measures of length.
  • Make sensible estimates about the lengths of given objects.
Description of Mathematics

Students need to be motivated to progress from using non-standard to standard units in the measurement of length. This motivation can develop from experiences in which students come to realise the necessity of standard measurement. An example of this is tasks that require students to compare differences (e.g. the differing length of their hand spans and feet size).

Students also need opportunities to develop personal benchmarks with which they can measure objects from their daily lives. These personal benchmarks need to gradually relate more to standard measures such as metres, 1/2 metres.

The ultimate aim is for students to be able to choose appropriately from a range of strategies including estimation, knowledge of benchmarks, and knowledge of standard measures in order approach various measuring tasks with confidence and accuracy.

Opportunities for Adaptation and Differentiation

The learning opportunities in this unit can be differentiated by providing or removing support to students and varying the task requirements. Ways to support students include:

  • providing regular opportunities for students to practise estimating the lengths of objects while working in other curriculum areas.
  • providing opportunities for individual, grouped, and paired work. Organise these groups strategically to be composed of students with varying levels of mathematical knowledge and confidence to enable peer learning, scaffolding, and extension
  • working alongside individual students (or groups of students) who require further support with specific area of knowledge or activities.

The context for this unit can be adapted to suit the interests and experiences of your students. For example:

  • Discuss why carpenters use mm when building and the different rulers/tapes/lasers they use. Who else would use similar measurements and tools?
  • Māori taiaha measured between 1.5 and 1.8m. Explore reasons for the difference in length and compare with a metre ruler
  • Identify Māori body parts used for measurement. Shorter measures were based on the hand and arm: Pakihiwi – full length of the arm, from shoulder to fingertips, Tuke – length from the elbow to the fingertips (cubit), Kōiti – length of the little finger, Ringa – width of the hand.
  • Provide opportunities for students to measure and estimate the length of items that are relevant to their learning in other curriculum areas.

Te reo Māori kupu such as ine (measure), mita (metre), mitarau (centimetre), rūri (ruler), and taura ine (tape measure) 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.

Required Resource Materials
  • Rulers, tape measures
  • Metre stick
  • Various non standard measuring equipment e.g unfix cubes, Cuisenaire rods etc
Activity

Session 1

  1. Show students a strip of paper or a piece of masking tape stuck to the carpet that is one metre in length. 
    Ask the students: how long do you think this strip of paper/tape is? Why?. 
    Challenge students to think about how they can come up with an estimate.
    E.g. is there something that you know the length of that might be similar in length to this strip?
  2. Organise students into groups of four. Have them discuss and record their estimations in an appropriate format (e.g. list, brainstorm, table, shared digital document) and report their estimates back to the class. Compile a class list of strategies used as well as the estimates given.
  3. Ask the students how they could check the accuracy of their estimates.
    With the equipment we have in our room, which method will provide us with the most accurate answer? 
    Encourage students to see that a metre stick or ruler will provide them with an accurate, consistent, quick measurement.
  4. Measure the strip of paper/tape using the metre stick/ruler. Model accurate measurement. You might ask students to tell you how to measure properly (e.g. start at the baseline, no gaps or overlaps) or teach them directly and record a chart of the steps shown.
  5. Now ask students to think about what they could do if they didn’t have access to a standard measuring tool such as a ruler or a metre stick. This discussion should focus on the importance of students developing personal benchmarks for measuring lengths. Pose prompts such as how could we use parts of our body to show 1 metre in length?
  6. Have students get back into their groups of four. Provide each group with a metre length of paper or string. They will use this to experiment, finding 1 metre lengths on their bodies that could be used as personal benchmarks.
  7. Once students have recorded a number of possible personal benchmarks for 1 metre have them try to find as many objects in the room/playground/school that are 1 metre in length (e.g. the length of two desk tops, the height of a computer table), using their newly-developed benchmark knowledge. Have them record the objects they find that they estimate to be 1 metre in length. Work alongside groups of individuals to ensure they are measuring accurately. Students ready for extension could explore what objects are twice, or half, the length of their benchmark, or could create a chart listing some of the objects they found throughout their exploration. 

Session 2

Over the next three days students will develop further benchmarks around 1/2 a metre and 1 cm. Students will then use standard measuring devices to check their estimations of length.

  1. Pose the questions having a metre benchmark is handy when you need to measure what kinds of things? 
    What other personal benchmarks do you think would be useful to have?
  2. Brainstorm possibilities. Ensure that students recognise benchmarks as a few key measurements that can aid in estimating the lengths of various objects. 
  3. Point to items around the room and ask the students to decide which of their benchmarks they will use to help them estimate its height. Ask them to justify their decision. Have them repeat this task in pairs, before discussing the different benchmarks used as a class. You could record this in a table or have students write their benchmarks and justifications on sticky notes.
    What personal benchmark would you use to estimate the length of:
    • whiteboard duster?
    • the desk?
    • the art trolley?
    • the tree outside?
    • my earring?
  4. Have students work in pairs to create benchmarks for half a metre, one centimetre and maybe one other of their choice.
  5. Provide students with a list of the various objects from around the room. Have them identify which benchmark they think would be most useful to use in estimating the length of the objects, and then use the benchmark to make an actual estimate. This activity could be turned into a measurement trail, where students rotate or move around the trail of items to be measured.

Session 3

  1. Begin the session with a problem like How far is it from one end of the mat to the other end of the mat?  The problem should illustrate a distance between 2 objects anywhere between 4-8 metres. Encourage students to record how they would estimate the length.
  2. Ask students to share their estimates, solutions, and strategies. Draw attention to any strategies not shared in discussion but evidenced in students' work. For example:
    • Some may have acted it out and used their metre benchmark as a non standard unit of measure.
    • Some may have looked at the distance, visualised a metre and estimated the distance.
    • Some may have estimated the length of one carpet tile and multiplied it by the number of tiles from one side of the mat to the other.
    • Some may have known that the length of 2 desks was a metre and visualised the number of desks it would take to get from one end of the mat to the other.
  3. Summarise the discussion by saying that we have benchmarks that include body parts but there are other benchmarks that we can use, for example visualising the length of a 30 cm ruler.
  4. Organise students into groups of 3 or 4 to discuss other possible benchmarks that may be useful to add to your benchmark ‘belt’. Allow students 2-3 minutes to discuss and record other possibilities. Record the responses under the heading ‘other possible benchmarks’. For example students may come up with ideas like visualising a 30 centimetre ruler, knowing the length of a new pencil is 20cm.
  5. Test out students' benchmarks by asking them to work out the length of an item using them new benchmarks and newly-developed strategies.

Session 4

In this session students apply their knowledge of measurement to a practical task.

  1. Provide groups of students with metre rulers, tape measures and 30 cm rulers.
  2. Have students select five to ten items that are visible around the room. The items must include things more than a metre, approximately a metre and less than a metre. They should record the names and lengths of these items on a sheet of paper (their answer sheet - you might provide a graphic organiser to keep this structured), and then create a sheet with only the names of the items and a space for the recorded estimation and measurement of each item (the quiz sheets). Keep the answer sheets in a safe place. Shuffle the quiz sheets and hand them out to groups of students - ensuring that every group receives a quiz sheet created by a different group.
  3. Have students work through the following process in a set time period:
  • Decide which benchmark they are going to use to help aid in their estimation.
  • Record their estimation and use the correct units (m, cm).
  • Measure the item using a standard measurement tool to see how close their estimation was to the actual length.
  1. At the end of the set time period distribute the answer sheets back to the students that wrote them, and have groups give their quiz sheets to the group that wrote the quiz sheet. Have each group mark the quiz sheets and return them to the students that completed the quiz. Provide time for students, in their groups, to discuss any discrepancies in the answers given and measured.
  2. Gather the class together and discuss any differences in measurement and what the cause of these may be. Refer back to students' personal benchmarks and have them discuss which benchmarks the measured lengths are close to. Conclude by sharing the strategies that students feel that they can now use to work out the length of given items.
    What are the key benchmarks you now know to use use when measuring different items? 

Printed from https://nzmaths.co.nz/resource/making-benchmarks-length at 3:06am on the 30th March 2024