Worm Wipe-out

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Purpose

This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

A PDF of the student activity is included.

Achievement Objectives
NA4-4: Apply simple linear proportions, including ordering fractions.
Student Activity

    

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Specific Learning Outcomes

use linear proportions to solve problems

Description of Mathematics

Number Framework Links
Use this activity to:
• help the students who are beginning to use advanced additive strategies (stage 6) to become confident at this stage in all three operational domains (addition and subtraction, multiplication and division, and proportions and ratios).
• encourage transition from advanced additive strategies (stage 6) to advanced multiplicative strategies (stage 7)

Required Resource Materials

FIO, Levels 2-3, Number Sense and Algebraic Thinking, Book One, Worm Wipe-out, pages 10-11

 

A classmate

Activity

In this activity, the students can use a variety of strategies for simple ratio and proportion problems, ranging from advanced counting approaches to early proportional thinking. They will also consolidate their understanding of simple mixed fractions.
This activity should be introduced through guided teaching rather than as an independent activity unless students are confident at stage 7 or above on the Number Framework.
Begin with some mental exercises to check that the students understand how to find quarters and halves in mixed fractions and equivalences between halves and quarters. For example: How many quarters are in 3/4? How many halves are in 1 1/2 ? So how many quarters are in 1 1/2? You should also check that the students understand that fractions can equally well be expressed as decimals. They may use both in this activity.
Introduce the context using the vet’s instructions. The students could act out this initial situation using large paper circles folded or marked in quarters to model the tablets. Have them mark each quarter of the cat’s tablet as 1 kilogram. This is a good opportunity to introduce the students to the concept of “rate” as a multiplicative relationship between two or more different measurement
units. Here it is tablets per kilogram, but another common example is kilometres per hour, as in 60 km/h.
Send the students to their small groups to work out how many kilograms they need to link to each quarter of the dog’s tablet. Have the students report back on their strategies. If they cannot solve this, give each group 10 rectangular labels of the same size labelled “1 kg of dog”. Have them share these out onto the quarters of one of the dogs’ tablets and insist that they assign all 10 equally to the quarter tablets.
Use the diagram below and ask: How do we share these 2 kilograms among 4 quarters?

diagram.
Send the students back to their groups to attempt question 1 and then report back on their strategies. Encourage a number of strategies, for example: “I counted the kilograms on each quarter” or “I divided the total cat kilograms by 4 because 4 kilograms makes 1 tablet, and I divided the dog kilograms by 10 and then looked at the remainder.” Rocky’s mass doesn’t fit neatly into the 1/4 tablet rate, so his dosage has to be rounded up.

Question 2 extends the problem by adding the relationship of cost. This involves using two different rates simultaneously, the rate of mass to dose and the rate of tablets to cost. Send the students into their groups with the question: What will you need to know to work out the cost of 1 dose? When they realise that it depends on the number of tablets, they should attempt questions 2a and 2b and report back on their strategies.
For question 3, ask the students: What will you need to know to work out the mass of Brock the dog? After the students have responded, sketch the complete set of relationships used in this problem (using multiples of 1/4 of a tablet):

diagram.

In question 4, you may need to show the students how to record their trials systematically so that they can use each result as a hint until they find the best result.

table.


Before the students attempt question 5, have them record the cost of each fraction of a tablet for a dog and a cat, for example:

table.

They can use this information to help them make a table (as in question 4) or set up a double number line. For example:

double number line.

Extension

The students may be able to see that the 35 in $3.50 is the lowest common multiple of 7 x 5. You could also ask them why the answers for questions 3 and 4 are approximate. The reason is that the cat mass doesn’t go up in 1 kilogram steps to match the tablets. A cat weighing 1.1 kilograms would also get tablet. This also introduces the concepts of limits of accuracy and rounding, which is also needed for question 1c.


Answers to Activity

1. a. 1 1/2 tablets
b. 2 1/2 tablets
c. 2 tablets. (Rocky needs 1 4/5 tablets, so 1 3/4 won’t be quite enough.)
2. a. $3.50. ($2 + 3/4 of $2)
b. $15.60. (2 x 1 + 2.80 x 2 + 2.80 x 2
= 3 + 7 + 5.60
= $15.60)
3. More than 5 kg and less than or equal to 7 1/2 kg. (It costs $1.40 per tablet for 5 kg, and 70c per tablet for 2.5 kg. $1.40 + 70c = $2.10)
4. a. Approximately 6 kg (cat) and 15 kg (dog)
b. One strategy is to draw up a table and use trial and improvement. For example:

answers.

5. a. The most likely answer is: cat 7 kg and dog 12.5 kg.
b. Strategies will vary. You might use a table, increasing the cost in both the cat and dog columns:
 

table.

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Level Four