Big Idea(s): Fractions

Expectations:

Number Sense

• B1. demonstrate an understanding of numbers and make connections to the way numbers are used in everyday life

  • B1.6 use drawings to represent and solve fair-share problems that involve 2 and 4 sharers, respectively, and have remainders of 1 or 2

  • B1.7 recognize that one half and two fourths of the same whole are equal, in fair-sharing contexts

Social Emotional Learning Skills in Mathematics and the Mathematical Processes

• A1. Throughout this grade, in order to promote a positive identity as a math learner, to foster well-being and the ability to learn, build resilience, and thrive, students will apply, to the best of their ability, a variety of social-emotional learning skills to support their use of the mathematical processes and their learning in connection with the expectations in the other five strands of the mathematics curriculum

In this lesson, to the best of their ability, students will learn to think critically and creatively as they apply the mathematical processes of representing (select from and create a variety of representations of mathematical ideas (e.g., representations involving physical models, pictures, numbers, variables, graphs), and apply them to solve problems) and selecting tools and strategies (select and use a variety of concrete, visual, and electronic learning tools and appropriate strategies to investigate mathematical ideas and to solve problems) so they can make connections between math and everyday contexts to help them make informed judgements and decisions.

Watch the following video with the students. (It is not necessary to watch it in its entirety).

Ask students these questions:

• What do you see in this video?

• Have any of you ever been to the zoo?

• What kinds of animals have you seen?

Role-playing :

I (the teacher) would like to organize a class visit to the zoo. During our visit, I would like to feed some of the animals. My only challenge is that I have a limited budget that allows me to buy a limited amount of snacks.

Present Appendix A to the students. Here are the animals that we will be able to feed during our visit.

• There are 2 giraffes, 4 lions, 2 chimpanzees, 4 zebras and 2 elephants.

Present Appendix B to the students. Here are the snacks I bought:

• I bought 2 apples, 9 bananas, 5 bags of peanuts and 5 pieces of meat.

Important information to share with students:

• Giraffes and chimpanzees prefer bananas.

• Lions love meat.

• Zebras prefer apples.

• Elephants love peanuts.

Instructions to students:

• You must share food fairly among each type of animal. Be sure to respect their snack preferences.

Students work in pairs or small groups to solve the problem.

Attach enough chart paper to the wall for each group (classroom, hallway, etc.). Have the children work vertically. (Research suggests that working on vertical surfaces has a positive impact on learning by bringing the task closer to the children’s eyes.), as students must work vertically.

Students use the methods, strategies and manipulatives of their choice to resolve the problem.

Students record the mathematical reasoning they used to solve the problem. Students are instructed to write and print in marker. We want to see all evidence of their thinking, even errors and corrections made.

Opportunities for Differentiation

• Continually evaluate and adjust lesson content to meet the needs of students.

• Concurrent Tasks: Reduce the number of animals and snacks. Modify work settings for students with special needs.

• Allow students to work individually if they wish.

• Create quiet spaces where there are no distractions.

• Provide concrete handling materials (e.g., fruit) to students.

Opportunities for Assessment

Assessment for Learning

Conversations: Ask students questions to check their understanding of the problem. What strategies did they use?

Evaluation as learning

Observations: Observe the students and their ability to explain the reasoning behind the choices they make. Observe students and see how they express themselves and organize themselves.

Conversations:

Observe students and see how they express themselves and organize themselves in teamwork. Listen to conversations between students. Encourage class and small group conversations that allow students to clearly express their thoughts and

develop their thinking.

Bansho: (This strategy is recommended in the middle and intermediate grades. However, it is easily achievable in the primary grades).

The teacher encourages a whole class discussion in which students explain the mathematical reasoning used in their solutions, methods and strategies.

Post the student work of 3 or 4 groups chosen by the teacher on the board.

Students could upload their work to Jamboard or to a Google Slide deck. Notes and comments could be added as the presentation is being made.

Explain the Bansho to the students :

• The 3 or 4 selected groups present their work and the strategies used, one group at a time.

During the presentations, the other students listen to and analyze their peers' mathematical reasoning. Students are invited to ask mathematical questions to the other groups.

The teacher asks open-ended questions to further their thinking. (The Art of Effective Questioning)

• What questions did you ask yourself while working?

• How did you feel during work?

• Why did you make this decision or choose this strategy to solve the problem?

• What changes did you make to solve the problem?

• What was the most difficult part of the task?

• What strategy did you use? Did your strategy work?

• What steps did you take?

• How else can you solve the problem? How did you divide the 9 bananas amongst the 2 giraffes and 2 chimpanzees? Are there any remaining pieces? Possible answer: We gave 2 bananas to each animal. We had 1 banana left so we cut it into four pieces (fourths) and gave a piece (a fourth) to each animal. So each animal got 2 whole bananas and a fourth of another.

• How did you divide the 2 apples between the 4 zebras? Are there any remaining pieces? Possible answer: We cut the apples into halves, which gave us a total of 4 pieces, so each animal received one half of an apple.

• How did you divide the 5 bags of peanuts between the 2 elephants? Are there any remaining bags? Possible answer: They each got 2 bags and we divided the remaining bag into halves. Therefore, they each got 2 bags and half of another bag.

• How did you divide the 5 pieces of meat among the 4 lions? Possible answer: We first gave a piece to each lion. Then we had one left, and so we divided it into fourths. We then gave an additional fourth to each of the lions. Another possible answer might be : We cut each piece of meat into 4 equal pieces (fourths) and gave them to the lions. Each lion got 5 one fourths.

• What model or manipulative did you use to solve the problem?

• How did you divide the different fruits? Did your strategy work?

• What fractions of snacks are each group of animals receiving?

• Which animals get bigger portions? How do you know? What observations did you make?

After the presentations, invite the other groups to place their solutions below the posted one that most closely resembles their own. At this stage, students learn to discern similarities and differences in mathematical reasoning, methods and strategies. If the group has used a different strategy, they can place it separately on the board.

Assessment as, for, and of learning are embedded throughout the lesson.

SEL Self-Assessments (English) and Teacher Rubric