106 Appendix 1: The Teacher Guide
A. Activity 1: Measuring Activities
107 sub district are preparing to make some small souvenirs made of colorful ribbons for the visitors who will come to the celebration in the hall. They decided to make some big flowers, key chains, and some small flowers. To make one big flower, they need one meter of ribbons, and to make one key chain and one small flower, they need respectively a half meter and three quarters meters of ribbons. At the current time, the committee of the celebration only has 9 meters of ribbons. The committee decides to create some souvenirs from the 9 meters of ribbon, and creates the other souvenirs later after buying more supply of ribbons. Can you help the committee to estimate how many big flowers, key chains, and small flowers that can be made from all of the 9 meter of ribbon?
Ask students to read the problem carefully in the group, and give them opportunities to ask whether they miss some information from the problem. While students are working in groups, choose secretly some groups which have some different answers which are interesting to discuss in the whole classroom discussion.
Tell students that you already prepare the 9-meter ribbons and some length measurement scales and ask them if they need the real ribbon and length measurement to solve the given problem.
3. Discussions
In the discussion, let students share their different strategies to solve the problem. Make sure that some different strategies are shown and give time for each group to write down their strategies in the whiteboard, and then to explain how they solve the problem.
Conjectures of Students’ Work Teacher’s Responses Instructional activity:
To find the number of souvenirs for the Kartini’s Day There are some possibilities to
divide the 9 meters of the ribbon.
Some students may be able to divide all of the 9 meters of ribbon, or some of them may have some leftover ribbons.
The teacher should remind the students that the ribbon should be evenly divided, without any leftover.
108 Some students may change the
meter into centimeters to find the answer of the problem.
The teacher lets students to change the scale, like changing the 1 m into 100 cm, and a half meter into 50 cm, and then dividing the whole number. However, don’t forget to ask students to reconvert again their answers into meter.
Some students may ask how long is the length the ribbon used to make each of the souvenirs. They may also ask whether they can make only one kind of souvenirs, for example, to make only the big flowers.
The teacher should say that the students can make any number of the souvenirs from all of the 9 meters of ribbons. However, they are not allowed to make only one or two kinds of the souvenirs. For each of the souvenirs, at least they have made one.
Some students may be struggling to divide. They cannot make any models to solve it, or they cannot use the repeated addition or subtraction, or use the
multiplication operations among fractions.
The teacher can give the students the real 9 meter ribbon, so the students can measure it using the length measurement to determine how long is the ribbon used to make each souvenir.
Some students may use additions or subtractions, which are
combined by multiplication. For example, they’ll make the three quarter into a nicer number, like making two of three quarter, so there’ll be 2 small flowers from one and a half meter of ribbon.
One key chain which has length a half meter, so they already use 2 meters of ribbon. The rest 7 meters can be used to make 7 big flowers.
And other combinations.
The teacher can make the following table in the white board, and let the groups write down their findings.
Group Length Big Flower
(1 m)
Key Chain ( ½ m)
Small Flower
( ¼ m)
1 Total Each 2 Total Each
Then, the teacher asks one or two groups to explain and write down their strategies to solve the problem in the whiteboard.
Some students may make a
drawing of the ribbon by rescaling the length. Instead of drawing the 9 meter of ribbon, which is impossible, they’ll make 9 cm of the ribbon. Then they’ll measure the length for each of the
souvenirs with a ruler and predict how many souvenirs they can make to fit the 9 cm.
The teacher let the students to explain and to write down their strategy in the whiteboard.
This will become an example to do the next activity, relating to measuring and
partitioning with a measurement scale.
109 Give emphasize on the strategies of using repeated additions to solve the problem. If some students notice that they can solve the problem by using multiplication involving fractions, ask students how to express the problem a multiplication problem.
Talk about the expression (the equation that can be made relating to multiplication involving fractions).
4. Making Conclusions
In the end of the discussion, ask a simple division problem for students, like if there are 6 meters of ribbon, how many small flower (each length ¾ m) that can be made. Some students will probably say 8 small flowers. Ask the reason why. Try to guide students to come to the expression that the paper flower will be 8 because .
B. Activity 2: Making Relations between Multiplication and Division