Students will continue exploring representing, comparing and ordering fractions through a curious task and a consolidation prompt that will act as purposeful practice.

The purpose of the Day 2 activities is to reinforce key concepts from Day 1. Students will engage in a string of related problems through a math talk and will have an opportunity to complete independent purposeful practice.

The math talk and purposeful practice serve to develop a deeper understanding of the following big ideas.

Number:

• Fractions can be represented in a variety of ways;
• How you partition the whole determines the fractional unit (i.e.: partitioning a whole into 6 parts will result in 6 sixth parts);
• As you partition a whole into more parts, the smaller the size of each part;
• As you partition a whole into more parts, the larger the unit fraction (called the denominator in later grades);
• In order to compare two or more fractional quantities, the whole must be the same;
• The count (called the numerator in later grades) indicates the number of parts relative to the number of parts in the whole indicated by the unit fraction (the denominator); and,
• Fractional amounts exist between whole numbers.

Ask students to cut a piece of paper into strips of equal length.

One-by-one, we’ll lead students through a string of related problems that will give them an opportunity to build their fluency and flexibility with partitioning a whole into fractional parts.

Partition each bar model into…

halves
thirds
fourths
fifths

Note that this activity may take longer than you anticipate, especially as students continue to grapple with folding paper into thirds and fifths. This is an important skill for students to build their spatial reasoning and their conceptual understanding related to partitioning – a key concept for fractions.

You might encourage students to have more strips ready and to abandon strips that have been folded incorrectly to avoid any unnecessary confusion or misconceptions.

Note that the fraction strips created through paper folding in this math talk will be useful for the Sense Making portion of the lesson.

Next, prompt students to:

Create a “truth” or a “lie” about two fractions and then ask a friend whether it is a truth or a lie.

For example:

“3 fourths is greater than 4 fifths.”

Is this a truth or is it a lie?

Use your fraction strips to help you convince your friend.

You can decide how many “truths” and “lies” you’d like students to create about fractions.

Show students this video:

While you’re welcome to do a notice and wonder routine with your students, you might also simply build the storyline of the Wooly Worm Race to another category involving hares.

After building the storyline about how four hares were competing in the longest jump competition, you can now share our prompt to get students estimating:

How far do you think the winning hare jumped?

We can now ask students to make an estimate (not a guess) as we want them to be as strategic as they can possibly be. This will force them to use spatial reasoning alone to try and come up with an initial estimate and to share it with their neighbours by trying to articulate why they believe their prediction is reasonable.

As we did in Day 1, we have intentionally left out the length of the jumping area in order to encourage students to use fractional thinking rather than measuring in standard units. It is clear that the winning hare jumped less than the total distance of one whole jumping area.

Consider asking students to think about a distance that would be “too low” and a distance that would be “too high” before asking for their best estimate in order to help them come up with a more reasonable estimate.

Let them chat with their neighbours and challenge them to an estimation duel or a math fight.

Monitor student thinking by circulating around the room and listening to the mathematical discourse.

Encourage students to use precise mathematical language and positional language (in front, behind, on top…) to articulate their defense.

If students’ estimates are unreasonable, encourage them to select a manipulative to represent the length of the jumping pit (perhaps linking cubes, a paper strip, etc.).

While we hope to engage in learning around fractions including partitioning a whole to represent fractional amounts for the purpose of comparing, we will welcome students who share their estimates in decimal form and will not impose the use of fractions on them. Because the calculator is introduced to students so early in their mathematical journey, many students default to expressing fractional amounts as decimals without necessarily having a deep conceptual understanding of how they work. Later in this lesson and in this unit, we hope to continue building the conceptual underpinnings necessary for becoming flexible with fractions and we encourage you to attempt making connections to decimals and percentages if students bring them up when estimating or sharing their thinking. If students do estimate using decimals, be sure to help students by using appropriate language utilizing place value and the fractional language associated.

Encourage students to share.

After students have had an opportunity to share their best guess, tell them that you will now be sharing the distances jumped by the top 4 finishers from the championship competition.

Share the distances jumped by the top 4 finishers from the championship competition:

Notice that the unit fraction is expressed in words rather than standard-notation. We will work towards standard-notation throughout this unit, but for the time being, we want to emphasize the fractional unit. You will also notice that we are only working with a limited number of denominators, and they have been strategically selected.

Prompt students to:

Represent the distance each hare jumped to help you compare and order from longest jump to shortest jump.

Login/Join to access the entire Teacher Guide, downloadable slide decks and printable handouts for this lesson and all problem based units.

Login/Join to access the entire Teacher Guide, downloadable slide decks and printable handouts for this lesson and all problem based units.

Login/Join to access the entire Teacher Guide, downloadable slide decks and printable handouts for this lesson and all problem based units.

Login/Join to access the entire Teacher Guide, downloadable slide decks and printable handouts for this lesson and all problem based units.

After consolidating learning by making connections using student generated solutions, you can share the following reveal video:

A still frame of all four jumpers is as follows:

Go back to student estimates from the Spark portion of the lesson to determine who had the closest estimate. Be sure to celebrate the student or students who were closest so that students realize that there was value in sharing with the group.

Did students use decimal notation and/or decimal language and/or percentages to share estimates at the beginning of the lesson?

Consider extending from here to give students an opportunity to explore and make connections with comparing and converting between benchmark fractions, decimals and percentages.

Provide students an opportunity to reflect on their learning by offering this consolidation prompt to be completed independently.

Consolidation Prompt:

Login/Join to access the entire Teacher Guide, downloadable slide decks and printable handouts for this lesson and all problem based units.

We suggest collecting this reflection as an additional opportunity to engage in the formative assessment process to inform next steps for individual students as well as how the whole class will proceed.

Download Editable/Printable Handout

Become a member to access purposeful practice to display via your projector/TV, download the PDF to upload to your LMS and/or print for students to have a physical copy

JOIN TO DOWNLOAD