Lesson objectives: For the topic of length, students should be able to: (1) visualise how long 1 km is (2) state that 1 m = 100 cm and 1 km = 1000 m (3) convert from cm to m and cm and vice versa (4) convert from m to km and m and vice versa
Lesson ideas: (1) Students measure their heights and their arm spans in m and cm and convert the measurements into cm. Interesting facts: – The height of a person is approximately equal to his arm span. – Using one arm’s length to estimate one metre is not accurate for children. A child’s arm’s length is usually shorter than one metre.
(2) Students measure the length of real life objects (e.g. height of door and length of whiteboard) and convert the measurements from cm to m and cm and vice versa.
(3) To get a sense of how long 1 km is, students can use Google Maps to find the distance between their school and their home. They can also find out the length of Singapore from east to west (50 km) and from north to south (27 km). Students are told that 1 km is 2.5 rounds around a stadium track or 20 laps of an Olympic-sized pool.
Common errors:
(1) Students may think 1 m = 1000 cm, since 1 km = 1000 m.
How to rectify: Tell students that “centi” means 100. For example, century means 100 years.
(2) Students may not understand the concept of 0 as a place holder. For example, when converting 4 km 90 m to m, students may write 490 m instead of 4090 m.
How to rectify: Tell students to write 1 km = 1000 m 4 km = 4000 m 4 km 90 m = 4000 m + 90 m = 4090 m
This post concerns model-drawing. The two problems discussed are from the Primary 3 level. I will show how the comparison model and the part-whole model are more suitable for the first and second word problems respectively.
Word Problem 1
In Word Problem 1, there are two separate quantities, Jug A and Jug B. The second sentence compares the amount of milk in Jug A and Jug B. Thus, a comparison model is appropriate.
Conditions for comparison model: (1) Separate quantities (2) Amounts of quantities are compared
Model and solution for Word Problem 1:
Word Problem 2
In Word Problem 2, the total number of people (the whole) is given. The number of adults (the part) and the number of boys (also the part) are given. The questions asks for the number of girls (the part). Hence, the part-whole model is appropriate.
Conditions for part-whole model: (1) the whole is given (2) one or more parts of the whole is / are given or (1) the parts are given (2) questions asks for the total (whole)
I have been teaching addition and subtraction of money in Primary 3 the last two weeks. In Primary 2, the students have learnt how to add dollars only or cents only. In Primary 3, they learn how to add amounts with dollars and cents (e.g. $4.25 + $3.20). At this point of time, the students have not learnt decimals. Thus, the decimal point is referred to as the dot that separates the dollars and the cents.
Learning objectives: Students should be able to: (1) Add money in the following ways: – Add the dollars first, then the cents (good when the sum of the cents is less than $1) – Algorithm – Make whole dollars
(2) Subtract money in the following ways: – Subtract the dollars first, then the cents (good when the cents in the minuend is greater than that in the subtrahend) – Algorithm
Lesson ideas
Part of the teaching was carried out during home-based learning (HBL). I made a video in which I was a bookshop owner and a customer came in to buy two books. I demonstrated how to find the total cost of the two books in the video.
I made another video in which Brainy Smurf bought presents to celebrate Smurfette’s birthday. He had to find how much the presents cost. The idea of this story came from a former student (Pamela Foong) in NIE. I attempted to make the video more engaging by including music and narration. The link to the video is: https://www.youtube.com/watch?v=P0gl7T1yYi4&t=84s
If not for safe distancing measures, I would have got students to set up stalls and pretend to be cashiers and buyers. They would practise using play money to buy and sell things.
Image from The Learning Store
Students were shown a real advertisement and asked to buy two things to celebrate a family occasion with a budget of $20. They were supposed to find the total cost of the two items as well as the change they would get if they paid with a $20 bill. Students were also asked to write down why they chose the two items. Most of the times, mathematics worksheets are focussed on mathematical concepts and skills. I wanted students to consider various reasons for making their purchases, so that they can relate their learning in mathematics to real life.
Image from FairPrice website
Some of their responses are shown below:
I have done research in critical thinking and the following are four critical thinking characteristics that are commonly found in definitions of critical thinking: -Gathering and assessing information, -Recognising assumptions, -Considering different perspectives and -Justifying decision(s) with reasons and evidence
I used the following task to elicit some of these characteristics from students.
Please obtain permission from the author at pandapea@hotmail.com if you are using this activity.
As this was the first time the students were exposed to critical thinking, I went through some considerations they might make when choosing which store to go to. Students were able to state that they would consider the cost, distance and the expiry date of the milk. I reminded students that they should not make a hasty decision and they should consider the advantages and disadvantages of each option. Finally, students were asked to make their decision and explain why they chose that store.
Some students demonstrated that they were able to consider a few factors in making their decision. I would share their responses in a later post.
Finally, the students solved word problems in money. As with word problems of other topics, they circled key information, made annotations, drew models, solved the problems and checked their answers for accuracy and reasonableness.
Common errors: – A few students forgot to align the digits properly when adding and subtracting using the algorithm.
How to rectify: I had to constantly remind students to align the dots when using the algorithm.
– Some students had difficulty with regrouping.
How to rectify: I had to remind students that adding and subtracting money is the same as adding and subtracting whole numbers, which they had learnt earlier. The only difference was that they had to remember to add the dot to separate the dollars and the cents.
Pea's Teaching Blog 