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

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 process 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.

Materials

• Playdough

• Paper

• Pencil

• Pencil Crayons

• Pattern blocks, double sided counters

• Basketballs, soccer balls

• This video “Exploring the Set Model of Fractions” is intended for educator use but could be shown without audio and the educator can pause the video to discuss the concepts.

• Virtual manipulatives

teacher background

Prior Learning:

• one to one correspondence

• decomposing whole numbers up to 12

• counting to 20

• skip counting

• simple addition

Day 1:

Each student will have a large piece of plain white paper (11x17 in size), 1 red crayon, 1 blue crayon, 1 green crayon, and 1 orange crayon. Students will fold their paper in half 2 times. First a hamburger fold (vertical), then a hotdog fold (horizontal).

When they open it up it should be sectioned into 4 equal parts. (Demonstrate if necessary). When they are done folding ask the following questions:

1. How many pieces of paper did I give you?

2. How many equal sections of the piece of paper do you see after folding it?

Instruct them to colour 1 of the sections red, 1 of the sections blue, 1 of the sections green and 1 of the sections orange. When they are done colouring have them use their fingers or a small object or toy to dance on the paper and tell them to get ready to dance! As the music is playing the teacher will call out commands (similar to the game “Twister”). For example “Dance on the green rectangle” “Now dance on the blue rectangle”.

Repeat the commands without the music. This time as they use their fingers on the colours, explain what fraction of the paper they are standing on. For example, after calling out the colour green, say, “You are now standing on ¼ (one fourth) of your paper. Call out several combinations until you feel that they are grasping the concept. Allow them to ask questions if they want to.

Day 2:

Tell students that today they are going to learn how to represent parts of a set, or a group of things, that we call fractions.

Tell them that a fraction represents a part of a set, and therefore it is not meaningful without knowing what the total of the set is.

Show a set of four balls consisting of three basketballs and one soccer ball.

Ask students what fraction of the balls are basketballs. (three-fourths)

Tell students that you have to know what the whole amount, or total number of items in a set, to know what the given part represents. Relate it back to your last example by bringing up that you have to know that there are four balls total to know that three fourths of them are basketballs.

Show a set of shapes containing 2 squares, 1 pentagon and 1 circle. Ask what fraction of this set of shapes are squares? Discuss how it could be one half or two one fourths. Ask what fraction of this set of shapes are circles? Ask what fraction of these shapes are triangles (none) and explain why.

If more examples are needed, you can collect shoes from students and determine what fraction require laces, or bring students to the front of the class and determine what fraction have siblings or no siblings.

At this point, review the notion that we have to know what the total amount of the set is before we can say what the fraction is.

Divide your students into groups of four. Give each group a set of twelve double sided counters.

Ask how would you share the counters into groups of four.

Give students other items such as pencils, markers, erasers etc to share equally among the group of four.

Ask students, “What have you learned about fractions from this activity?”. Students can draw to explain their learning and use key language from the lessons (whole, halves, fourths).

Use virtual manipulatives (e.g., Colour Tiles or counters, Sets) to generate and share out items.

Opportunities for Differentiation

• Continuously evaluate and adjust lesson content to meet student needs.

• Students complete only one or two activities.

• Allow students to work individually if they wish.

• Create quiet spaces where there are no distractions.

Opportunities for Assessment

Assessment for Learning

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

Assessment as Learning

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

Conversations: Listen to conversations between students. Encourage classroom and small group conversations that allow students to clearly express their thoughts and develop their thinking.

Have the students write and draw about fractions of a set in their math journals. Have them draw something easy to draw and colour, such as squares, flowers,fruits, lego. You will collect these for assessing once they are finished. This will help you know what the students have learned.

A prompt to help students in their Journal Writing might be:

• Tell two important things about fractions.

• How could friends share some toys fairly?

• Draw a design with equal fraction parts.

Use the Aquarium strategy to present their ideas about two important things that they have learned about fractions. Invite 2 groups (A and B) to settle in the aquarium (define an area in the classroom for this activity). These 2 groups of students will become the "fish.”

Invite all of the other students (the “cats”) to sit outside the aquarium area. These students will observe and listen to the “fish” presentations. The cats cannot speak at this time. They can only listen to the two presentations.

Group A presents their work and their thinking about fractions in the aquarium to group B. Group B can pose questions to group A about their thinking. Group B then presents their work and their thinking in the aquarium to group A.

When the two groups have finished presenting their ideas, the other students "cats" can now ask questions.

The teacher should also ask questions that will lead to mathematical conversations. Discuss together:

• How could 4 friends share three red toy sports cars and one green truck fairly?

• How could 2 friends share three baby toy dolls and one adult toy doll fairly?

• How could 4 friends share one toy fairly? (take turns!)

• How could 4 friends share one granola bar?

• Let’s look at some of the math journal designs with equal fraction parts. What fractions are represented in each design?

• What are some examples of fractions from real life? Where would you see them?

Before the “fish” and the “cats” leave the “aquarium,” teachers should have their students answer 2 oral “Exit Card” questions: (1.) Think of one whole item that can be divided into fourths and tell me what one fourth of it could look like. (2). Think of a set of four objects where three fourths of them look the same and tell me what objects could be in this set?

Assessment of Learning

The students’ work in their math journal provides a rich source of assessment to inform your future planning, particularly next steps. Their drawing and writing will show/tell you:

• what they remember from and consider to be the most important points about their fraction learning

• if they can apply their learning to an authentic problem

• whether they can divide objects into equal parts such as halves and fourths, and

• It may reveal misconceptions e.g., thinking that fourths are actually larger than halves because 4 is greater than 2!

Assessment as Learning

Observations: Observe students and their ability to explain the reasoning behind the ideas in their math journals.

Observe students and check how they express themselves and organize themselves during teamwork.

Do they use mathematical language e.g., whole, halves, fourths, equal, share, divide?

What social-emotional learning skills do they employ to support their use of the mathematical processes and their learning?

Assessment of Learning/Assessment for Further Learning

Exit Tickets or Exit Cards are short checks for understanding that are given to students at the end of a lesson before they move on to something else. They are used to check students' understanding by:

1. having them summarize key points from the lesson, and/or

2. solve a problem or answer a significant question based on the lesson.

They might be on paper, an oral question, a demonstration with math manipulatives or on a smart board, or using a pre-printed answer card.

SEL Self-Assessments (English) and Teacher Rubric

In small groups, give each student a ball of playdough. Provide a rolling pin for them to roll their balls flat into two snakes. If you don't have rolling pins, you can use pretty much anything - even a highlighter - or they can just smash it down with their hands.

Guide your students by having them cut one snake into two equal parts. Talk about how each of the 2 shares is a half and together they're called a whole. Then have them cut their other snake into half and then half again. Let them know these are called fourths because there are four equal parts. As they're looking at their halves and fourths side by side, ask them if they notice anything. Discuss how the more shares you cut it into, the smaller the shares get. You could also cut your snake in an unequal way and ask if it's cut into halves/fourths/etc. and help them see that the shares must be equal to be called halves/fourths/etc. There are so many great concepts you can teach with the playdough!