B2. Operations
Demonstrate an understanding of numbers and make connections to the way numbers are used in everyday life.
Learning Situation: A New Pizza
Duration: 2 hours
Summary
In this learning situation, students explore the concept of decimal numbers by creating a Nutrition Facts table for a new pizza.
| Overall Expectation | Specific Expectations |
| B2. Operations Use knowledge of numbers and operations to solve mathematical problems encountered in everyday life. |
B2.1 Use the properties of operations, and the relationships between operations, to solve problems involving whole numbers and decimal numbers, including those requiring more than one operation, and check calculations. B2.3 Use mental math strategies to multiply whole numbers by 0.1 and 0.01 and estimate sums and differences of decimal numbers up to hundredths, and explain the strategies used. B2.4 Represent and solve problems involving the addition and subtraction of whole numbers that add up to no more than 100 000, and of decimal numbers up to hundredths, using appropriate tools, strategies, and algorithms. B2.6 Represent and solve problems involving the multiplication of two-digit whole numbers by two-digit whole numbers using the area model and using algorithms, and make connections between the two methods. |
Learning Goals
The purpose of this learning situation is to allow students to:
- deepen the sense of quantity represented by decimal numbers;
- increase their sense of operations;
- develop personal algorithms for addition and subtraction of decimal numbers.
| Learning Context | Prerequisites |
|---|---|
| In Grade 4 , students learned to estimate and calculate the sum and difference of decimal numbers using concrete and semi-concrete materials. In Grade 5 , they continue to learn about decimal number operations by participating in activities to consolidate addition and subtraction strategies with decimal numbers. | This learning situation allows students to develop mental math strategies and to estimate and verify the sum and/or difference of decimal numbers up to hundredths.
To be able to complete this learning situation, students must:
|
Mathematical Vocabulary
decimal, estimate, whole number, tenth, hundredth
Materials
- Appendix 5.1 Nutrition Facts Tables (1 copy per student)
- Appendix 5.2 New Pizza (1 copy per student)
- large sheets of paper
- markers
- concrete and semi-concrete material to represent decimal numbers
Before Learning (Warm-Up)
Duration: approximately 30 minutes
Present the following situation to students:
This learning situation is about making a new pizza. To complete the task, you will need to work with Nutrition Facts tables for various foods. Let's look at a set before we start.
Distribute a copy of Appendix 5.1 to each student and briefly explain the various components of the tables. Review with them the nutritional value of a food. Read some of the decimal numbers and ask them what they mean. For example, when reading the Nutrition Facts table for white pita bread, they see that it contains 1.2 grams of fat (read "1 and 2 tenths grams of fat"), which means that in one serving of white pita bread there is 1 gram plus 2 tenths of 1 gram of fat. Remind students that 1 tenth is one part of 1 gram separated into 10.
Continue with the presentation of the situation in these terms:
A pizza maker invites you to create new pizzas to add to his menu. To ensure that these pizzas meet the taste requirements of his customers, he has already selected the foods they should be made of. In addition, since his customers are increasingly concerned about the nutritional value of food, he wants each new pizza to be accompanied by a food information sheet.
Distribute 1 copy of Appendix 5.2 to each student, clarify the task, and review the foods that the new pizza should be made of.
Advise students that during the math conversation, they will need to present and justify their creation and the strategies used to perform the calculations. Emphasize that it is important to think about the meaning of numbers and to make estimations beforehand rather than applying algorithms randomly.
Make sure that the students have understood the task at hand by asking questions such as:
- Who would like to describe the task in their own words?
- What foods should the new pizza be made of?
- How many calories should it contain?
Active Learning (Exploration)
Duration: approximately 1 hour
Group the students in pairs.
Provide concrete and semi-concrete materials to perform the calculations (for example, plastic money, base ten materials, interlocking cubes, number lines, place value mats, decimal number templates).
Circulate among the teams and observe the work of each. Invite the students to consider the reasonableness of the results of the operations. Intervene as needed to help certain teams make progress, without explicitly telling them how to perform the calculations.
Students should begin by calculating the total caloric, fat and carbohydrate content of the toppings (see following table).
| Toppings | Calories | Fat | Carbohydrates |
|---|---|---|---|
| 2 cauliflower florets | 6 | 0.46 g | 2.66 g |
| 3 broccoli florets | 19.5 | 0 g | 5.19 g |
| 10 olives | 50 | 6 g | 0.4 g |
| 7 sliced mushrooms | 31.5 | 1.75 g | 5.81 g |
| 2 slices of pepperoni | 109.2 | 9.9 g | 0.8 g |
| 8 slices of zucchini | 88 | 0 g | 1.6 g |
| Total | 304.2 | 18.11 g | 16.46 g |
Note: The total caloric, fat and carbohydrate content that students record on the Food Information Sheet should also take into account the content of these components contained in the dough, sauce and cheese chosen.
| Possible Observations | Possible Interventions |
| Students forget to take into account the number of calories that the pizza must have or misinterpret this instruction. | Pose questions such as:
|
| Students arrive at inaccurate or unreasonable results. | Pose questions such as:
|
Once the task is completed, distribute markers and large sheets of paper to each team on which students will transcribe mathematical elements to be presented during the math conversation. Assign to each team elements to prepare, such as the reasoning behind their approach and the organization of their work, the approach to calculating the total number of calories, strategies for adding decimal numbers, strategies for following instructions, and strategies for checking the reasonableness of answers.
Allow sufficient time for students to prepare for the math conversation. Remind them that they must also present the Nutrition Facts table for the pizza they created.
Consolidation of Learning
Duration: approximately 30 minutes
Invite teams to take turns presenting their work. Ensure that all the mathematical elements to be highlighted are presented. Encourage students to add comments by leading the discussion with questions such as:
- How can we explain this team's approach?
- What other strategies are possible for performing the addition? Are they applicable to any addition?
- Which other teams have used the same or a similar strategy?
- At what point in the process did you begin your calculations?
- In what ways is this computational strategy similar to the other team's?
- What other way is there to check the reasonableness of this answer?
Ensure that students understand the importance of estimating the result of a calculation before performing it, in order to establish what is a reasonable answer to expect. Then, the reasonableness of the calculated result can be verified by comparing it with the estimation. Also highlight the variety of personal strategies used to perform the calculations.
Differentiated Instruction
The activity can be modified to meet the needs of the students.
| To Simplify the Task | To Enrich the Task |
|
|
Follow-Up at Home
At home, students can prepare a snack that includes a few foods (for example, fruit salad, granola bar, yogurt, cheese, cookies) and determine the number of calories and the number of grams of fat, carbohydrates and protein in it. Students can then discuss the nutritional value of their snack with a family member.
Source: adapted and translated from Guide d'enseignement efficace des mathématiques de la 4e à la 6e année, Numération et sens du nombre, Fascicule 3, Nombres décimaux et pourcentages, p. 149-156.