A Mathematical Clothesline is a great visual tool to support students in reasoning proportionally with numbers. Students can work cooperatively to place a set of concept cards (various representations of number) on the line in a position that makes sense proportionally. As students place the cards on the line they need to consider the card they have, the cards left to position, and any benchmark numbers (numbers that assist in estimation and tend to be multiples of 5 or 10) that are already present. Mathematical Clotheslines differ from a formal number line in that cards are not placed in a measured and scaled sequence, but simply displayed in a specific order.

I have seen many clothes line activities online in recent months but only recently this activity for younger students. Janice Novakowski recently created this post which inspired me to explore her idea to use this tool with younger students. I expanded on her idea by adding in number words in English and French as indicated by our grade one curriculum outcome. I have also created a fraction version.

In both of the Mathematical Clotheslines below students have multiple representations of numbers to work with. Not all representations need to be introduced and used at the same time. As students expand on their understanding of different ways to represent numbers and fractions pictorially more and more representations can be added to the activity and become a topic of discussion in the classroom.

Three Act Math Video Design by Jennifer Brokofsky and Ryan Banow

Possible Curriculum Connections

Grade 3– N3.4 Demonstrate understanding of fractions concretely, pictorially, physically, and orally including:

• representing
• observing and describing situations
• comparing
• relating to quantity.

[C, CN, R]

Indicators:
a) Identify and observe situations relevant to self, family, or community in which fractional quantities would be measured or used and explain what the fraction quantifies.

d) Divide a whole, group, region, or length into equal parts (concretely, physically, or pictorially), demonstrate that the parts are equal in quantity, and name the quantity represented by each part.

i) Demonstrate how a fraction can represent a different amount if a different size of whole, group, region, or length is used.

k) Divide a whole, group, region, or length into equal parts (concretely, physically, or pictorially), demonstrate that the parts are equal in quantity, and name the quantity represented by each part.

Grade 4– N4.6 Demonstrate an understanding of fractions less than or equal to one by using concrete and pictorial representations to:

• name and record fractions for the parts of a whole or a set
• compare and order fractions
• model and explain that for different wholes, two identical fractions may not represent the same quantity
• provide examples of where fractions are used.

[C, CN, PS, R, V]

Indicators
a) Represent a fraction using concrete materials.

b) Represent a fraction based on a symbolically concrete representation (e.g., circles for cookies).

c) Name and record the fraction for the included and not included parts of a set.

e) Represent a fraction pictorially by indicating parts of a given set.

f) Represent a fraction pictorially by indicating parts of a whole.

g) Provide an example of a fraction that represents part of a set, a fraction that represents part of a whole, or a fraction that represents part of a length from everyday contexts.

Grade 5– N5.5 Demonstrate an understanding of fractions by using concrete and pictorial representations to:

• create sets of equivalent fractions
• compare fractions with like and unlike denominators.

[C, CN, PS, R, V]

Indicators:

a) Create concrete, pictorial, or physical models of equivalent fractions and explain why the fractions are equivalent.

b) Model and explain how equivalent fractions represent the same quantity

c) Verify whether or not two given fractions are equivalent using concrete materials, pictorial representations, or symbolic manipulation.

i) Determine equivalent fractions for a fraction found in a situation relevant to self, family, or community.

Act One- The Problem- Video

Two children are ready to eat but unsure how to cut the pizza so that they can enjoy equal amounts.

The key questions that the video will inspire are:

How can we cut the pizza?

How many pieces can we make?

What are the fractions equivalent to ½? (Grade 5)

Act Two- Classroom Connections

Key questions that the video will inspire are:

How can we cut the pizza?

How many pieces can we make?

What are the fractions equivalent to ½? (Grade 5)

Act Three- A Possible Solution

Here is one potential way the pizza can be divided to ensure that both children get the same amount and that the size of the pieces is reasonable.

Sequel-Extending the Learning

Three people- Video

The pizza already cut for two people and the third person shows up.- Video