Grade 3: "Exploring Division"
(From: Mathology)
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This Mathology lesson plan can be accessed in both English and French by logging into your Mathology.ca/Mathologie.ca account and searching for Activity Card 28: Multiplication and Division: "Exploring Division")
Content
Big Idea(s):
Exploring division using models
Subtracting numbers to 25 fluently
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, solve, and compare the results of fair‐share problems that involve sharing up to 20 items among 2, 3, 4, 5, 6, 8, and 10 sharers, including problems that result in whole numbers, mixed numbers, and fractional amounts
B2. Operations: use knowledge of numbers and operations to solve mathematical problems encountered in everyday life
• Math Facts: 2.2 recall and demonstrate multiplication facts of 2, 5, and 10, and related division facts
• Multiplication and Division: B2.6 represent multiplication of numbers up to 10 × 10 and division up to 100 ÷ 10, using a variety of tools and drawings, including arrays
C4. Mathematical Modelling: apply the process of mathematical modelling to:
• represent, analyse, make predictions, and provide insight into real‐life situations
Learning Goals
We want students to...
Explore division using models (repeated subtraction, number lines, arrays)
Explore equal sharing/grouping
Success Criteria
I can...
think of division as equal sharing and equal grouping.
use repeated subtraction, number lines, and arrays to help us divide.
Materials
Counters
Math Mats: (All Math Mats can be accessed by logging into your Mathology account)
Math Mat 5: Number Lines
Math Mat 6: Number Lines
Master 14: Pawty Planning
Math Mat 1: Thinking Space
Exit Ticket (Exit ticket can be accessed by logging into your Mathology account)
Vocabulary
Equal grouping
Equal sharing
Skip-count
Repeated subtraction
Division
Division sentence
Array
teacher background
Students may benefit from prior experience with:
skip-counting backward
multiplying using models
decomposing numbers and objects into equal groups, with and without leftovers using a number line
subtracting numbers to 25
representing multiplication as equal grouping and division as equal sharing
Pedagogy
Minds On
Equal Grouping game:
Play a herding game with 8 volunteers. For example: “Rabbits, herds of 4.“ Students pretend to be rabbits and hop to make groups of 4. Record the result: 8 divided into groups of 4 is 2 groups.
Model other strategies students could use to find the number of groups:
– arranging 8 counters into groups of 4
– skip-counting backward by 4s: 8, 4, 0
– using repeated subtraction: 8 – 4 – 4 = 0
– taking jumps of 4 backward on a number line:
Repeat for herds of 5, 3, and 2. Discuss any leftovers.
Repeat with different numbers of volunteers.
Equal Sharing activity:
Use 20 counters. Act out the equal sharing of the counters into 5 piles.
Count the number in each pile to see that each loot bag should have 4 biscuits.
Form an array with 5 rows of 4. Discuss how the array shows 5 loot bags with 4 biscuits in each.
Action!
Give each pair a copy of the master. Have counters and number lines available. Students work together to plan parties for dogs and cats.
Assign each pair a party game for dogs (equal grouping) and a treat for cats (equal sharing). Have students give each team a mascot and draw designs for the loot bags. Encourage students to record their work on the Thinking Space Mat.
Teacher Moves
Probing Questions:
How did you divide the dogs into equal teams?
What would you do if there were any dogs not on a team?
How did you share the treats among the bags?
What would you do if there were treats left over?
LOOK-FORS:
How do students group the dogs to find the number of teams (e.g., modelling with counters, skip-counting backward, using repeated subtraction, taking jumps backward on a number line)?
How do students share the treats (e.g., using counters, using an array)?
How do students deal with any leftovers (e.g., ignore them; don’t make teams of that size as dogs will be left out; don’t share the leftover treats so all cats get the same amount)?
Are students able to check their answers using a different strategy?
Consolidation Of Learning
Have students share the strategies they used to find the number of teams and number of treats in a bag. Make a poster of students’ findings to finalize the plans for the parties.
Introduce the division sign. For example, 20 treats shared among 4 loot bags = 5 treats can be written as 20 ÷ 4 = 5. 10 dogs arranged in groups of 2 = 5 groups can be written as 10 ÷ 2 = 5.
Explain that the array shown here represents a strip of stickers. Ask, “If the stickers are shared among 5 people, how many will each person get?” (4) “Among 4 people?” (5) Relate the answers to the array. Record the related division sentences.
Discuss how repeated subtraction and division are related. Have students share times when they have had to share or group items equally.
To allow students to show what they have learned in this lesson, go to the Exit Ticket and/or Practice page.
Highlight for Students
We can think of division as equal sharing and equal grouping.
We can use repeated subtraction, number lines, and arrays to help us divide.
Supports for student learning
How to Differentiate:
Accommodation: Focus on equal grouping and have students use counters to represent the dogs.
Extension: When a situation has leftovers, have students suggest what they could do so there aren’t any.
Assessment
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
Extension
Log in to your Mathology.ca / Mathologie.ca account to access Intervention and Extension activities, Professional Learning Videos and Assessment tools.
Technology
If you require support logging into your Mathology/Mathologie account, please contact Kerry Stack or Erica Doucet.
Use the Counters Tool to explore equal sharing. Drag 3 bear counters to the top of the workspace, then drag 20 counters to the bottom of the workspace. Have volunteers model sharing the counters among the bears. Discuss any leftovers. Or start with 20 counters and have volunteers make groups of 5, skip-counting backward from 20, or subtracting 5 with each group removed. Record a repeated subtraction sentence and connect repeated subtraction to equal sharing/grouping.
Pearson Interactive Tools (log into your account) / Mathies app / Math Learning Centre)