Metric Conversion Lesson: Differentiated Instruction in Action

This lesson is applicable in particular anywhere where metric units are standard, though it wouldn't be such a bad thing to teach it in a place where they're not, since the lesson so beautifully reinforces the base-ten system and multiplying by tens. In Ontario, this is a grade five lesson because of all the conversions; lower grades aren't expected to be able to go quite that many. It could easily be adapted for grades four and six.

Metric Conversions Lesson: Differentiated for Special Needs
Expectations:
– select and justify the most appropriate standard unit (i.e., millimetre, centimetre, decimetre, metre, kilometre) to measure length, height, width, and distance
- solve problems requiring conversion from metres to centimetres and from kilometres to metres
– multiply decimal numbers by 10, 100, 1000, and 10 000, and divide decimal numbers by 10 and 100, using mental strategies

Materials: Base-ten blocks, graph paper, rulers and metre sticks, calculators

Prior knowledge: pattern rules, basic multiplication, use of calculators

Lesson:
Problem: Mr. Johnson (the gym teacher) is setting up an obstacle course in the form of a maze, using string. He's calculated the perimeter of the course to be 1.24 kilometres, but the balls of string he is using are measured in metres. Each ball contains 50 metres of string. How much string does he need? If one ball of string, from a different company, is listed as having 400 cm, how does that change your calculations?

Allow students to work in groups to solve the problem. When one group comes up with the conversion for metres to kilometres, get everyone's attention and point it out to the class. Discuss how we need a manipulative that can be divided into a thousand parts, so the whole will represent one kilometre and the parts will represent one metre. As students realize the metre sticks and base-ten blocks both fit that bill, the ones who get it will start to solve the problem quickly. Assess who is getting it easily, who needs more practice, and who is lost.

After that, divide students into centre groups to work on related activities. Kids who got it can write a math journal or create a video explaining how they got the answer, using manipulatives as examples. Kids who need more practice work on similar problems at centres to practise conversions, possibly using calculators to come up with a pattern rule for multiplying and dividing by multiples of ten. Kids who were lost come for a guided math lesson using metre sticks and string. They can set up a mini-obstacle course using fifty metres of string, and mark off the string in one-metre lengths as they unravel it. Explicitly teach the strategy of measuring a small amount, then multiplying to get a big amount; allow for calculators and multiplication charts for this. Practise with the string and metre sticks. Once they're comfortable with the smaller amounts of string and measuring for centimetres, then multiplying, go back to the original question and help them draw the connection between centimetres, metres, and kilometres. Kids with spatial sense deficits or visual deficits will have the most trouble with this activity, and will need the most opportunities to develop and apply pattern rules using manipulatives and calculators. There is a good chance this part of the lesson will take several guided math sessions, so centre work to extend the understanding of the kids who get it will be necessary while working with this group.

Extensions:
1) Research the metric system in detail. Why did our problem skip decimetres and decametres? Are these units used elsewhere in the world? Develop a pattern rule that covers conversions in the metric system (or extend your pattern rule to include these two units, if you've already made one.)
2) Use our measuring cups and beakers to extend your understanding of the metric system into litres. Do you need to make any changes to your pattern rule to make it work for measurements of volume?