B1.7 Convert between fractions, decimal numbers, and percents, in various contexts.
Activity 1: Who Has More ?(Fraction, Decimal and Percent Conversions)
Context
Three roommates, Karl, Samantha and Gab, share everything in the house. However, they don't always agree on who owns some of the belongings found in the house.
Your task will be to determine "who has more" of each item listed.
Materials
- Envelope with cards (about 10) with problems
- 1 whiteboard per student
- erasable felt-tip pen
Divide the class into teams of 3.
Distribute the envelopes.
A student picks an index card from the envelope and reads the card to the other members and places it on the desk.
Each student has a few minutes to write their answer and rationale on the whiteboard.
Afterwards, they discuss their reasoning.
Examples of cards
Problem 1
- Plates
Karl
35% of plates
Samantha
0.4 of plates
Gab
\(\frac{1}{4}\) of plates
Who has more? How do you know?
Problem 2
- Cans of food
Karl
0.47 of cans
Samantha
38% of cans
Gab
\(\frac{{150}}{{1\;000}}\) of cans
Who has more? How do you know?
Problem 3
- Candles
Karl
34% of candles
Samantha
0.31 of candles
Gab
\(\frac{{21}}{{40}}\) of candles
Who has more? How do you know?
Consolidation of Learning
What strategies did you use to determine who had more? What do all of the cards have in common? (The total represents 100% or 1)
Activity 2: Plant Growth (Using Familiar Fractions and Percents)
Individual, small group and whole class activity.
Project a statement on the board. The student thinks about it and writes down the answer.
Afterwards, the student shares their reflection with 3 classmates.
In turn, a spokesperson from each group expresses their reasoning/strategies to the class.
Examples of statements
- In one month, a tomato plant has grown 50% (or half) of its original length.
What does this statement mean?
*Using the conversion to a decimal or fraction will help the student in their explanation/justification.
Example of a response
The tomato plant has grown to half its original length.
- The branch of a tree has lengthened by 25%.
What does this statement mean?
- After cutting, the length of the maple trunk has decreased by 3 cm.
What does this statement mean?
- The duckweed stem increased by 100% of its length in 24 hours.
What does this statement mean?
- The length of the bamboo trunk is 150% longer.
What does this statement mean?
- The lightning bolt reduced the length of the oak branch by 20%.
What does this statement mean?
Consolidation of Learning
Use a ruler (1 m) and string to have students visualize the meaning of each statement assuming that the metre represents the part of the plant identified in the statement.
Activity 3: Analyzing the Results (Converting a Ratio Into a Percent)
The student is given a series of questions regarding a7th grader's scores in several subjects. The student must find, alone or with partners, an efficient way to compare the different scores (for example, convert the scores to decimal and then back to percents).
Present or distribute a results table like this one. The last column of the table will be used for the conversion made by the student.
| Subject | Assessments Results | |
|---|---|---|
| Language Arts | Summary: \(\frac{{7.5}}{{10}}\) | |
| Written Lesson 1: \(\frac{{31}}{{30}}\) | ||
| Test 1: \(\frac{{62}}{{70}}\) | ||
| Written Lesson 2: \(\frac{{13}}{{15}}\) | ||
| Test 2: \(\frac{{42}}{{60}}\) | ||
| Mathematics | Written Lesson 1: \(\frac{{12}}{{20}}\) | |
| Written Lesson 2: \(\frac{{27}}{{30}}\) | ||
| Project: \(\frac{9}{{12}}\) | ||
| Test 1: \(\frac{{49}}{{55}}\) | ||
| Science | Lab 1: \(\frac{{15}}{{18}}\) | |
| Project: \(\frac{{25}}{{30}}\) | ||
| Test 1: \(\frac{{34}}{{40}}\) |
Following the assignment, ask the following questions:
- In what subject did the student achieve the highest score on an assessment or assignment?
- In what subject did the student receive the lowest score on an assessment or assignment?
- In Language Arts, on which assessment or assignment did the student perform better?
- In Language Arts, on which assessment or assignment did the student perform the least well?
- In Mathematics, between which 2 values do the results lie?
- In Science, which assessment or assignment was the most challenging for the student?
To go further in the analysis :
- In which subject do you think the student is most successful? Explain/Justify.
Circulate and analyze students' approaches. Review their strategies.