Big Idea(s):

Numbers tell us how many and how much

Numbers are related in many ways

Quantities and numbers can be grouped by or partitioned into equal-sized units

Expectations:

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

• Fractions: 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

teacher background

Students may benefit from prior experience with:

• skip-counting by 2s, 5s, and 10s

• counting collections by grouping

• composing and decomposing numbers to 20

• comparing numbers to 20

Fair-sharing or equal-sharing means that quantities are shared equally. For a whole to be shared equally, it must be partitioned so that each sharer receives the same amount.

Note

• Words can have multiple meanings. It is important to be aware that in many situations, fair does not mean equal, and equal is not equitable. Educators should clarify how they are using the term "fair share" and ensure that students understand that in the math context fair means equal and the intent behind such math problems is to find equal amounts.

• Fair-share or equal-share problems provide a natural context for encountering fractions and division. Present these problems in the way that students will best connect to.

• Whole numbers and fractions are used to describe fair-share or equal-share amounts. For example, 5 containers of playdough shared between 2 people means that each person receives 2 containers and half of another container. Or each person could receive 5 halves, depending on the sharing strategy used.

• Fractions have specific names. In Grade 1, students should be introduced to the terminology of “half/halves” and “fourth/fourths”.

Show students 10 counters.

Ask: “How many groups of 5 can we make? Will there be leftovers?”

Have a volunteer make groups of 5 to check.

Ask, “How can we count the counters?”

Students may suggest skip-counting by 5s. Count the counters as a class.

Repeat the activity making groups of 4, 3, and 2.

Give each pair a recording sheet (Master 52) and 20 linking cubes. Have half of the class work with the number 20 and the other half work with 18.

• Take 18 or 20 linking cubes and join them to make a train.

• Break off 2 cubes at a time and stand them up to make towers. How many towers did you make? Do you have any cubes left over? Count the cubes. What do you notice? Record your findings.

• Put your cubes back together. This time, make towers that are 3 cubes tall.

• Repeat the activity to make towers that are 4, 5, and 10 cubes tall.

LOOK-FORS:

• Do students recognize that no matter how a given number of cubes are grouped, the number of cubes doesn’t change?

• Are students able to group the cubes in more than one way?

• Do students count the cubes by 1s each time, or do they skip-count when cubes are grouped in 2s, 5s, and 10s?

• Do students realize that when the towers contain more cubes, they will be able to make fewer towers?

Have students share their findings with the class. Discuss conservation of number: no matter how the cubes are grouped, the number of cubes does not change.

Ask what students noticed about the number of towers they were able to make with or without leftovers. Prompt students to see that as the height of the towers increases, they are able to make fewer towers.

Also discuss which groupings were easiest to count and why. Ask, “Is there a number where there would be no leftovers with towers of 2, 3, 4, 5, and 10 cubes?” (60)

Highlight for Students

• Numbers can be broken into equal groups, with and without leftovers.

• No matter how objects are grouped, the total number of objects doesn’t change.

Accommodations: Give students a number between 6 and 10 and have them make towers 2 and then 3 cubes tall.

Extension: Have students also make towers that are 6, 7, 8, and 9 cubes tall and look for patterns in their results.

Combined Grades Extension: Give students a number greater than 20. Have them make towers of 10 cubes. Students relate the number of towers and leftover cubes to the digits in the number.

All assessments, in the moment feedback/prompts, and independent tasks can be accessed by logging into your Mathology/Mathologie account.

SEL Self-Assessments (English) and Teacher Rubric

Log in to your Mathology.ca / Mathologie.ca account to access Intervention and Extension activities, Professional Learning Videos and Assessment tools.