Making benchmarks: Length

Purpose

In this unit we will explore the idea of having benchmarks of 1 metre, 1/2 metre, and 1 centimetre to aid in estimating the length of given objects.

Specific Learning Outcomes
  • Demonstrate a personal benchmark (e.g.1 stride – 1 metre, arm span - 1/2 metre) for 1 metre, 1/2 metre.
  • Identify and use external benchmarks ( e.g. visualising 3 x 30cm ruler lengths for 1 metre) 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 able to see the need to move from using non standard measures of length to standard measures of length. The motivation for this will arise out of students comparing differences in the length of their hand spans etc. From this the need for standard measurement will become evident.

Students also need to develop personal benchmarks with which to measure various objects in their daily lives. Their 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 standards measures in order approach various measuring tasks with confidence and accuracy.

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

Getting Started

Begin the session by showing students a strip of paper or a piece of masking tape stuck to the carpet that is a metre in length. Ask the students “How long do think this strip of paper/tape is?” “Why?”. Challenge students to think about how they come up with their estimate.

  1. Students get into groups of four to discuss and record their estimations. As a class, have groups report back on their estimates. Emphasise the strategies used to make their estimates. Compile a class list of strategies used as well as the estimates given.
  2. Ask the students how they could check the accuracy of their estimates. Ask students “With the equipment we have in our room, which method will provide us with the most accurate answer?” (Students should be encouraged to see that a metre stick or ruler will provide them with an accurate, consistent, quick measurement.)
  3. Measure the strip of paper/tape using the metre stick/ ruler.
  4. Now ask students to think about what you could do if you 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. Your questioning may need to be more specific by posing prompts such as “How could we use parts of our body to show 1 metre in length?”
  5. 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.
  6. Once students have recorded a number of possible personal benchmarks for 1 metre that could be used have them try to use it to find as many objects in the room/ playground/ school that are 1 metre long (e.g. the length of two desk tops, the height of a computer table). Have them record the objects they find that they estimate to be 1 metre in length.

Exploring

For the next three days students will spend time experimenting and finding personal and external benchmarks for carry out practical measuring tasks. This will be followed by students using standard measuring devices to check their estimated lengths of given objects.

Session 2

  1. Make the statement “Having a metre benchmark is handy when you need to measure what kinds of things?” The aim of this next lesson is to equip students with other key benchmarks like 1/2 a metre and 1 cm so that they can estimate the lengths of objects that are a lot smaller than 1 metre in length.
  2. Ask students the following question “What other personal benchmarks do you think would be useful to have?” Brainstorm possibilities ensuring that benchmarks are just that - a few key measurements to aid in estimating lengths of various objects. Discuss the importance of not having too many.
  3. Now point to items around the room and say don’t estimate the length tell your partner what benchmark you would use to estimate the length of that particular object. For example point to the door, and ask the students to decide which of their benchmarks they will use to help them estimate it’s height. Ask them to justify their decision.

What personal benchmark would you use to estimate the length of;

  • whiteboard duster
  • the desk
  • the art trolley
  • the tree outside
  • my earring
  1. Send the students off in pairs to create benchmarks for half a metre, one centimetre and maybe one other of their choice.
  2. Provide students with a list of the various objects from around the room to firstly acknowledge which bench mark they think would be most useful to use in estimating the length of given objects and then using the benchmark to make an actual estimate. Obviously the items to be recorded will vary according to the resources and features within your own school. 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?". (It could be 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 and solution strategies for example:
  • Some students may have needed to act it out and use their metre benchmark as a non standard unit of measure.
  • Others may have looked at the distance and visualised a metre and estimated that way.
  • If there were carpet tiles on the ground another student 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.
  • Another student 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.
  1. Share any of the strategies not shared by saying “I saw another student do it like this”.
  2. Summarise the discussion by saying that we have on board benchmarks that include body parts but there will be other benchmarks that we can use for example visualising the length of a 30 cm ruler, or knowing 1 stride back from an opponent in netball is 1 metre.
  3. 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.
  4. Test out students' benchmarks by asking the various strategies and benchmarks they could use to work out how tall the chair is or how high the table is.

Session 4

Exploring and using standard units of measure.

  1. Provide groups of students with metre rulers, tape measures and 30 cm rulers. Talk about where you begin measuring from. Many students have misconceptions about where you start measuring from. Reinforce that they should start measuring from the zero, and not the edge of the ruler.
  2. Students then need to measure accurately a list of given items. For example they may be asked to measure the stapler, a window or the length of chalk.
  3. Compare the measurements students come up with to ensure all students are using the ruler or tape measure correctly.

Reflecting

Putting it all into practise.

  1. Quiz time – Organise students into groups of 3 or 4, ask students to select five to ten items that are visible around the room. The items must include things more than a metre, around and metre and less than a metre.
  2. The lists of items are exchanged so that each group gets a new list of 5-10 items.

Students’ task is to:

  • Firstly decide which benchmark they are going to use to help aid in their estimation.
  • Record their estimation and use the correct units (m, cm).
  • Then accurately measure using a standard measurement tool to see how close their estimation was to the actual length.
  1. At the end of the session groups can hand their answers to the group that developed the list of items to discuss the benchmark used, the estimate and actual measurement.
  2. Conclude by sharing the strategies that students feel that they can now use to work out the length of given items.
  3. What are the key benchmarks you have equipped yourself with and aim to use when asked to measure certain items?

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