Grade 2
Grade 3
- solve problems involving the addition and subtraction of one- and two-digit whole numbers, using a variety of strategies, and investigate multiplication and division solve problems involving the addition and subtraction of single- and multi-digit whole numbers, using a variety of strategies, and demonstrate an understanding of multiplication and division
Specific Expectations:
Grade 2
Grade 3
- solve problems involving the addition and subtraction of two-digit numbers, with and without regrouping, using concrete materials (e.g., base ten materials, counters), studentgenerated algorithms, and standard algorithms
- solve problems involving the addition and subtraction of two-digit numbers, using a variety of mental strategies (e.g., to add 37 + 26, add the tens, add the ones, then combine the tens and ones, like this: 30 + 20 = 50, 7 + 6 = 13, 50 + 13 = 63);
– add and subtract three-digit numbers, using concrete materials, student- generated algorithms, and standard algorithms
 I understand place value for ones, tens and hundreds
 I know that addition means to bring numbers together so they get larger
 I can use doubles or near doubles to help me add
 I can use strategies like counting on, splitting and mental math to help me add double digit numbers
 I can use tools like the number chart and base ten blocks to help me add
 I will highlight the important information in the word problem
 I can make a K/W/H chart to help me find out what the question is asking me to solve
 I will choose a strategy to help me solve the problem
 I will try my strategy (carry out the plan)
 I will check to see if my answer is reasonable
 I will use math language to justify my thinking/answer
Strategies: count on, add on, add, split the numbers, mental math, doubles, near doubles
Tools: Base Ten blocks, manipulatives, number line, number chart
 They have not yet mastered many addition facts and find it difficult to use the many facts often required to perform a single calculation with greater numbers.
 They may not have fully grasped procedures required to perform the task. For example, they might add in columns correctly when the numbers have the same number of digits but add incorrectly when the numbers have different numbers of digits.
 Some students have misunderstandings about place value that interfere with their understanding of addition. For example, they might have difficulty when 0 is used as a placeholder.
 Some students may struggle when the total number of ones or tens is greater than 10. For example, they might think that 43 + 59 = 912.
 Some students might not recognize situations that call for addition or might not be able to create situations to match particular addition expressions.
 Some students might be unfamiliar with greater numbers, so adding those numbers would not be meaningful.
(Based on Marian Small’s research in Leaps and Bounds)

Lesson
Diagnostic
Give the students the question
LG: Determine what the students know about subtraction
Sub Task #1
LG: doubles strategy can be used in addition as an efficient strategy to help students visualize and make the connection of doubling and possibly multiplication
Before
Activating Prior
Knowledge
We know that adding numbers means bringing them together and subtraction means to take away from the original amount. We have also been working on problem solving and breaking the question down so we can understand the question.
Today you will work on a question and solve the problem. Please try your hardest to answer the question. Answer as much as you can. I just want to know and understand what you already know about addition, subtraction and problem solving.
Show students various pictures to help them visualize doubles (6 eggs on one side of a carton, plus six on the other side makes 12).
Repeat this for all numbers up to 10
Hands On!
Task
Some Grade Two students are in a read-a-thon. Each person has to read 100 pages.
Name Mon Tues
24
35
Each person in Grade 3 has to read 500 pages. Who has the most pages left to read?
Grade 3
Name Mon Tues
320
289
125
37
45
110
147
125
Spinner activity:
Students spin a spinner numbered from 1 to 10. They use the number they land on to create the double then tell what strategy they used to find the answer. They can use visualization, counting, double facts.
Students in grade 3 can use a spinner increasing by increments of 10. (10,
20 , 30, 40, 50, 60, etc.)
Choose several students to showcase their thinking. Have them show how they solved the problem.
After
Congress
Congress: Choose several students to showcase their thinking. Have them show how they solved the problem.
Possible strategies:
Visualizing
Adding
Find a pattern
Multiply by 2
Assess if students need more practise with doubles. If more practise is needed do not move on.
Co- create Student Success
Criteria for Doubles with the students
Questions
How did you solve the problem?
What strategy did you use to solve the problem?
Is there more than one answer?
How do you know?
How did you solve the problem?
What strategy did you use to solve the problem?
Could you use another strategy to solve the problem?
How could using doubles help you solve a math problem?
Can you double any number?
What do you notice about these doubles?
When you double a number is it always an even number? Why?
After Practice: Solve a word problem using doubles

Sub Task #2
LG: Near Doubles plus or minus one can be used to solve addition and subtraction problems
Sub Task # 3
LG: gain a better understanding of place value and carrying over
Remind the students of the work they did with doubles.
Ask: How can we use doubles to help us answer,
7 + 8 = ?
Explain that it is about the process of how we answer a question rather than the answer itself. Have a student come up and explain how they can use what they already know about doubles to help them
7 + 7 = 14
7 + 8 = 15 (8 is one more than 7 so the answer is one more)
Show students the
Base Ten Blocks. Ask:
What is the name of one block? (unit)
What is the name of a group of 10 blocks
(rod). What is the name of 100 blocks joined together? (flat)
Ask various questions regarding the number of tens and ones in specific numbers and how they are represented. Ask:
What happens when we have more than ten ones?
Worksheet with questions on asking students to use doubles to solve various questions.
Word problem:
There are 8 people in the shallow end of the pool and 9 in the deep end of the pool. How many people are in the pool. Use near doubles to help you solve the problem.
Substitute 80 and 90 for grade 3. Have the students justify how they solved the problem using near doubles
Congress: Choose several students to showcase their thinking. Have them show how they solved the problem.
Assess if students need more practise with near doubles. If more practise is needed do not move on.
Co- create Student Success
Criteria for Near Doubles with the students.
Co-create or re-iterate with the students the Success
Criteria for problem solving if you have not already done so.
Introduce the students to the game
Race to 100. The game can be found in the Guide to
Effective Instruction.
Roll a die and place the correct number of units on the place value section of the game sheet. Once you have ten or more ones you must change the units for a rod. Play continues until you reach 100
Ones Tens
Congress: Choose several students to showcase their thinking. Have them explain what happened when they had more than ten ones. How did they trade or re-group the units?
Assess if the students understand how to trade units for rods. Assess how students are adding single and doubledigit numbers.
How did you solve the problem?
What strategy did you use to solve the problem?
Could you use another strategy to solve the problem?
How could using near doubles help you solve a math problem?
Can you double any number to help you with near doubles?
What do you notice about the near doubles?
When you double a number is it always an odd number? Why?
Can you use addition and subtraction when using near doubles?
After Practise;
On the playground 6 (60) students want to play soccer, 7 (70) students want to play Four Square.
How many students are on the playground? Use the near doubles strategy of plus one and minus one to help you solve the problem.
Who won the game?
What did you do when you got ten units?
What did you do when you got more than ten units?
What was the largest number of units you could have in the ones column?
What was the largest number of units you could have in the tens column?
Would that be the rule for any column on the Place Value chart?
Why or why not?
Why do we use trading or regrouping in math?
Can you think of any activities in which you use re-grouping?

Sub Task #4
LG: use Base Ten
Blocks to solve double-digit addition
Sub Task #5
LG: use Base Ten
Blocks to solve double-digit addition
Ask the students the names of the Base Ten
Blocks. Show the students how to add using the base ten blocks and ten frame template. Show:
34 + 25
34 is 3 groups of ten and 4 ones
25 is 2 groups of ten and 5 ones the groups of ten go on the tens side of the place value mat and the one go on the ones side in the ten frame. Add the units together if it is 10 or more then you regroup and add the new group to the tens column.
Tens Ones
Reiterate the lesson from the day before on using base ten blocks to add double digit numbers
Give students numerous opportunities to practice using the base ten blocks to place under the correct section of the place value mat and have them regroup the tens.
Have them answer questions using the worksheet provided and explain how they used the strategy to help them solve the problem.
Congress: Choose several students to showcase their thinking. Have them show how they solved the problem.
Assess if students need more practise with Base Ten. If more practise is needed do not move on.
Co- create Student Success
Criteria for Base Ten with the students.
What did you do when you got ten units?
What did you do when you got more than ten units?
What was the largest number of units you could have in the ones column?
What was the largest number of units you could have in the tens column?
Would that be the rule for any column on the Place Value chart?
Why or why not?
Why do we use trading or regrouping in math?
Can you think of any activities in which you use re-grouping?
After Practise;
Have students practise questions at home using chart to add doubledigit numbers.
Tens Ones
To go to the local zoo on a field trip the school must bring 100 students. There are
49 grade 2 students and 35 grade 3 students. How many grade 1 students need to go on the trip? Explain how you used the strategy to help you solve the problem.
Congress: Choose several students to showcase their thinking. Have them show how they solved the problem.
Assess if students need more practise with Base Ten. If more practise is needed do not move on.
Co- create Student Success
Criteria for Base Ten with the students.
What was the largest number of units you could have in the ones column?
What was the largest number of units you could have in the tens column?
Would that be the rule for any column on the Place Value chart?
Why or why not?
Why do we use trading or regrouping in math?
Can you think of any activities in which you use re-grouping?

Sub Task #6
Formative
Assessment
Give them a question and see what strategies they use
Are they able to add double digit numbers using a variety of strategies?
Can they extend their thinking into hundreds and thousands?
Sub Task #7
LG: use the splitting strategy to solve double-digit addition problems
Sub Task #8
LG: use a number chart to solve double digit problems
When we use the base ten blocks to add, what are we doing to the number
(breaking it into friendly or smaller numbers)
Splitting:
36 + 22 split into 10s, 1s
30 + 20 + 6 + 2
50 + 8 = 58
Model for the students how you break the number apart and then add the numbers
Use a hundreds chart to show students how you can add doubledigit numbers. Refer back to the work you have been doing with breaking numbers into groups of tens and ones and splitting.
Show an example of how you can use the chart to track the numbers as on a number line, the numbers going across on the chart count on by one. The numbers going down count on
There are 43 Canada
Geese on the soccer field and 44 geese on the baseball field.
How many geese are on the two fields?
Use 2 strategies to solve the problem and explain how you used the strategy to help you solve the problem.
Place out index cards that have been numbered 1 to
100. Students pull two cards and then add the cards using the splitting strategy.
Students will then write about how they broke the number into more manageable pieces
Students who finish early can play Race to 100
Congress: Choose several students to showcase their thinking. Have them show how they solved the problem.
Assess if students need more practise with splitting. If more practise is needed do not move on.
Co- create Student Success
Criteria for splitting with the students.
Have students work on a worksheet that has them create several paths for adding double digits on a 100s chart
(included). Then have the students use the index cards numbered 1 – 50, students pull 2 cards add the numbers using the hundreds chart to show how to add the numbers.
Check to see if the students can extend their thinking beyond
Congress: Choose several students to showcase their thinking. Have them show how they solved the problem.
Assess if students need more practise with a hundreds chart. If more practise is needed do not move on.
Co- create Student Success
Criteria for hundreds chart with the students.
How did you solve the problem?
What was the strategy you used to solve the problem?
How was using the strategy helpful?
Are there any other strategies that you could use?
What words helped you to know how to solve the problem?
How did using the splitting strategy help you to add the numbers?
How far did you break the numbers down?
When could you use this strategy?
Why would you use this strategy?
Is this strategy efficient? Why or why not?
After Practise:
Have students practise questions at home using the splitting strategy to add double-digit numbers.
What are some of the number patterns we can see on the hundreds chart?
How did you use the hundreds chart to help you solve the problem?
When could you use this strategy?
Why would you use this strategy?
Is this strategy efficient? Why or why not?

Sub Task #9
LG: use the K/W/H chart to help solve a multi-step problem by 10, for example, 7,
17, 27.
Then give the students numbers from 1 -100 all mixed up and have them put the numbers onto the Learning
Carpet. Have students demonstrate how to use the carpet to add double digit numbers.
Show students the problem on the board.
Have the students cocreate the K/W/H chart. Discuss what they know from the question, what they want to know and how will they solve the problem.
Know Want to
Know
How to solve
100.
Meeta makes a table to show the number of toys she collects for the Fall Fair in 3 days
Days
Mon.
Tues.
Wed.
Toys
39
?
24
Meeta collects a total of 99 toys. How many toys does she collect on Tuesday?
Numbers can be changed for gr. 3
Congress: Choose several students to showcase their thinking. Have them show how they solved the problem.
Assess if students need more practise with deconstructing a question. If more practise is needed do not move on.
Re-iterate Student Success
Criteria for problem solving with the students.
Sub Task #10
LG: use the K/W/H chart to help solve a multi-step problem
Show students the problem on the board.
Have the students cocreate the K/W/H chart. Discuss what they know from the question, what they want to know and how will they solve the problem.
Know Want to
Know
How to solve
To get a free slice of pizza at the basketball game the
Raptors must win the game, and score 100 points. In the first and second quarter of the game the
Raptors scored 46 points. In third quarter they scored
29 points. How many points do they need in the fourth quarter?
Congress: Choose several students to showcase their thinking. Have them show how they solved the problem.
Assess if students need more practise with deconstructing a question. If more practise is needed do not move on.
Re-iterate Student Success
Criteria for problem solving with the students.
How did you solve the problem?
What was the strategy you used to solve the problem?
How was using the strategy helpful?
Is there more than one strategy that you could use?
How do you know?
What words helped you to know how to solve the problem?
After practise:
Aland makes a table to show the number of seeds he collects in 3 days. Mon. 26, Tues.?, Wed. 38. He collects a total of 98 seeds.
How did you solve the problem?
What was the strategy you used to solve the problem?
How was using the strategy helpful?
Is there more than one strategy that you could use?
How do you know?
What words helped you to know how to solve the problem?
Final Assessment: See the diagnostic to re-administer as the final assessment.