School Boards TDSB
School Lanor JMS
Grade(s) 2/3
Lesson Title
Date LESSON 1
Relationship Between Addition and Multiplication
Learning Goal (Curriculum Expectations)
Students will be able to recognize the relationship between addition and multiplication by making equal sized groups and
supporting it with an addition number sentence.
Lesson Components
Before
- Show students a picture of apples divided in 2
columns and 6 rows.
- ASK: How many ways can you make equal sized
groups with 12 apples?
- Write down all student answers on chart paper.
- STRATEGIES: skip counting, counting by 1s, 2s,
3s, 4s, and 6s (repeated addition patterns)
- ASK: What is the difference between
multiplication and addition
During
-
After (Practice)
-
Example:
1+1+1+1+1+1+1+1+1+1+1+1= 12
2+2+2+2+2+2= 12
3+3+3+3= 12
4+4+4+4= 12
6+6= 12
Hand out bags of counters with 18 counters in each (grade 2s work with a partner, grade 3s work independently)
QUESTION: Find all the different combinations of equal sized groups for the number 18.
Co-create with students a KWC chart before students begin working.
K: I have 18 counters, I have to make equal sized groups
W: I need to know how many equal sized groups I can create
C: Each group must have equal number of counters.
Students are expected to write all combinations on their sheet, and start thinking about what strategies they used.
After (Consolidation)
- Review the KWC chart, and as a whole class fill in
the H portion of the chart (strategies shared by
students)
- Highlight what the condition was in the question.
- ASK: Is there a more efficient way to think about
or write 1+1+1+1+ …?
- How do you know?
- Do you have all the combinations? How do you
know?
- What tool can you use to find all the
combinations?
After (Highlights and Summary)
-
Anticipated Student Responses
Handout multiplication practice worksheet for
homework.
Students are encouraged to prove their work with a
picture
KWCH:
- H: Organized Chart, T-Chart, Pattern
Students may think about the relationship between addition
and multiplication (ex: 6+6=12 is the same as 6x2=12)
School Boards TDSB
School Lanor JMS
Grade(s) 2/3
Lesson Title
Date LESSON 2
Relationship Between Addition and Multiplication
Learning Goal (Curriculum Expectations)
Students will be able to recognize the relationship between addition and multiplication by making equal sized groups and
supporting it with a picture (array) and a addition / multiplication number sentence.
Lesson Components
Anticipated Student Responses
Before
ASK:
- Counting by 1s, 2s, 3s, 4s, 6s
- What strategies did we think of yesterday?
- Skip counting
- What was the least efficient (slowest) way to
- Repeated addition
come up with all the combinations of equal sized
- Making equal sized groups
groups?
- multiplication
- What was the most efficient (fastest) way?
- multiplication?
- but if you don’t know how to multiply, what
could you use?
During
Grade 2s can work with a partner
Grade 3s work independently
-
Hand out bags of counters (12, 16, 18 in each) and a 11x17 sheet of paper
Students are to draw an array and write the addition and/or multiplication sentence for all combinations they can
think of for the selected bag.
- If students are finished, have them select another bag.
After (Consolidation)
- Look at the number 12 as a whole class
ASK:
-
How many groups did you find?
What did your pictures (array) look like?
How would we read it in a math sentence?
Is there a more efficient way to think about or
write 1+1+1+1+ …?
How do you know?
Do you have all the combinations? How do you
know?
What tool can you use to find all the
combinations?
If more time is needed carry on the next day and review:
- What does multiplication mean?
- How will you know you have all combinations of
equal sized groups for the items in your bag?
- Does it matter what number comes first?
After (Highlights and Summary)
After (Practice)
- Handout multiplication practice worksheet for
homework.
-
Counting by 1s, 2s, 3s, 4s, 6s
Skip counting
Repeated addition
Making equal sized groups multiplication
4 x 3= and
3 x 4=
Students should be able to
Identify the multiplication
number sentence is from
the given array:
4 groups of 3 is the same
as 3 groups of 4.
-
What matters is HOW it is distributed
The picture (array) still looks similar
Students are encouraged to prove their work with a picture
School Boards TDSB
School Lanor JMS
Grade(s) 2/3
Lesson Title
Date LESSON 3
Relationship Between Addition and Multiplication
Learning Goal (Curriculum Expectations)
Students will be able to create an organized list with all multiplication number sentences for each given factor.
Lesson Components
Before
Review Key Terms and add words to word wall:
Array, Product, Multiplication, Equal Sized Groups,
Combinations, Factor, Addition, Skip Counting, Repeated
Addition
Anticipated Student Responses
What are all the equal sized groups of the number 15?
1 x 15 = 15
15 x 1 = 15
3 x 5 = 15
5 x 3 = 15
Now, Let’s put these multiplication number sentences
into an ORGANIZED LIST. Which sentence should we
start with? 1 x 15?
Why is the number 2 a factor of 15?
Why is the number 4 a factor of 15?
The number 15 is not an EVEN number.
#5 rule: What do you notice about the one’s column in the 5
times table or when you skip count by 5s?
The one’s column for each product ends in a 0 or a 5
#2 rule: What do you notice about the one’s column in the 2
times table or when you skip count by 2s?
The one’s column for each product ends in a repeating
pattern 0, 2, 4, 6, 8. The tens column grows by 10s.
During
QUESTION:
Design a floor plan for the desks in the classroom. The only rule is you must keep all 24 desks in equal groups.
Encourage students to create a KWCH chart before beginning, and look at the success criteria for Problem Solving.
Answers should be represented in an ORGANIZED LIST.
There are a total of 8 combinations.
1 x 24 or 24 x1, 2 x 12 or 12 x 2, 3 x 8 or 8 x 3, 4 x 6 or 6 x 4
After (Consolidation)
-
What was our learning goal?
Students will share their answers in an organized
list
- How did you know?
- What are the best combinations for the classroom?
- Do you have all the combinations? How do you
know?
After (Highlights and Summary)
After (Practice)
- Handout multiplication practice worksheet for
homework.
School Boards TDSB
School Lanor JMS
Grade(s) 2/3
Lesson Title
Date LESSON 4
Relationship Between Addition and Multiplication
Learning Goal (Curriculum Expectations)
Students will be able to create an organized list with all multiplication number sentences for each given factor.
Lesson Components
Before
ASK:
- What are all the equal sized groups of the
number 13?
Anticipated Student Responses
1 x 13 = 13
13 x 1 = 13
(2 combinations)
-
Why do you think there are there only 2
combinations?
The number 13 is an odd number and it cannot be divided
equally by 2
-
What is the definition of multiplication?
A number that can be divided into equal sized groups
-
What number is close to 13 that can be divided
into equal groups?
The number closest to 13 is numbers 12 and 14.
-
What are the combinations of the number 12 and 1 x 12
14?
12 x 1
2x6
6x2
3x4
4x3
1 x 14
14 x 1
2x7
7x2
During
QUESTION:
Design a floor plan for the desks in the classroom. The only rule is you must keep all 17 desks in equal groups. We
will vote on the best design and actually create it.
Encourage students to create a KWCH chart before beginning, and look at the success criteria for Problem Solving.
Answers should be represented in an ORGANIZED LIST.
After (Consolidation)
-
Students will share floor plans (Gallery Walk)
Do you have all the combinations? How do you
know?
Which would be the most logical plan for our
classroom? Why?
As a class vote on one floor plan and create the
plan with 17 desks.
After (Highlights and Summary)
After (Practice)
Students may have looked at the combinations for the
number 16, and just add one desk to a group
School Boards TDSB
School Lanor JMS
Lesson Title
Date LESSON 5
Relationship Between Addition and Multiplication
Learning Goal (Curriculum Expectations)
Students will be able to recognize how an array for a factor is organized in a square or in a rectangle.
Square Numbers and Rectangle Numbers
Lesson Components
Before
ASK:
- What are the properties of a square?
- What are the properties of a rectangle?
Grade(s) 2/3
Anticipated Student Responses
-
A square has 4 equal sides
A rectangle has 2 sets of equal sides
Show a square and a rectangle. Using hatch marks, identify
the equal sides in each figure.
During
- Looking at the number 10 and number 9 (grade 2s)
- Looking at the number 15 and number 16 (low grade 3s)
- Looking at the number 24 and 25 (high grade 3s)
Hand out a plastic bag containing coloured tiles.
Students are to create an array with the tiles, and identifying the relationship between their number and the shape of the
array (square or rectangle)
While walking around, ASK:
- What 2D shape can you make from each bag? Use all tiles.
- What is the array for your combination? Prove with a mathematical number sentence.
- Why can you not make a square with one of the numbers? You must use all tiles (condition).
After (Consolidation)
- Students share their ideas for each grouping of
Any number that multiplies with itself is a square
numbers
- What did you notice when creating an array for each
number?
- Did you get all combinations?
After (Highlights and Summary)
After (Practice)
-
Handout multiplication practice worksheet for
homework.