Mastering Addition: Counting Up and Expanded Form
Grade 2 Math - Term 1, Week 8. Designed for Grade 2 learners to master addition strategies.
SESSION 1 • OBJECTIVE
SESSION 1: LEARNING OBJECTIVES
Today we will learn to illustrate and solve the addition of a 2-digit number and a 1-digit number by counting up on a marked number line.
SESSION 1 • REVIEW
REVIEW: BASIC ADDITION
Let us practice our basic addition facts up to 20. What is 8 + 5? What is 12 + 4? Use your fingers or mental math to find the sum quickly.
SESSION 1 • MOTIVATION
THE CANDY SURPRISE
Imagine you have 25 delicious candies in a jar. Your best friend comes over and gives you 4 more candies. How can we find out how many you have without counting every single one from one?
SESSION 1 • PRESENTATION
THE NUMBER LINE STRATEGY
We can use a tool called a number line. It is a straight line with numbers marked at equal intervals. When we add, we move to the right because the numbers get bigger.
SESSION 1 • DISCUSSION
STARTING OUR JOURNEY
Look at our number line from 20 to 40. To solve our candy problem, we find our starting number. Since we began with 25 candies, we put our finger right on the number 25.
SESSION 1 • DISCUSSION
TAKING THE FIRST HOP
We need to add 4. This means we will take 4 small hops to the right. Let's take the first hop together. Move from 25 to 26. We say 'Twenty-six' out loud.
SESSION 1 • DISCUSSION
THE SECOND HOP
Now we take our second hop. Move your finger from 26 to 27. Every hop represents adding one more candy. We are now at 27.
SESSION 1 • DISCUSSION
THE THIRD HOP
We are not done yet! We need 4 hops. Let's take the third hop. Move from 27 to 28. We are getting closer to our final answer.
SESSION 1 • DISCUSSION
THE FINAL LANDING
Take the fourth and final hop. Move from 28 to 29. Look at the number where we landed. It is 29! This means 25 + 4 equals 29.
SESSION 1 • ACTIVITY
INDIVIDUAL PRACTICE
Use your own number line strip. Solve 42 + 6. Circle 42 first. Then draw 6 small hops to the right. Where did you land?
SESSION 1 • ACTIVITY
FLOOR NUMBER LINE GAME
One student will stand on number 34 on the floor tape. Another student will roll a die. Jump forward that many steps and count the numbers as you land.
SESSION 1 • GENERALIZATION
WHAT HAVE WE LEARNED?
When we add numbers on a number line, we count up. This means we move to the right because addition makes our total amount larger.
SESSION 1 • ASSESSMENT
QUESTION 1
What is the sum of 34 + 5 using a number line?
A. 38
B. 39
C. 40
D. 41
SESSION 1 • ASSESSMENT
QUESTION 2
If you start at 56 on a number line and count up 3, where do you land?
A. 58
B. 59
C. 60
D. 61
SESSION 1 • ASSESSMENT
QUESTION 3
Which direction do you move on a number line when adding?
A. Left
B. Down
C. Right
D. Up and Left
SESSION 1 • ASSESSMENT
QUESTION 4
What is 72 + 6?
A. 77
B. 78
C. 79
D. 80
SESSION 1 • ASSESSMENT
QUESTION 5
If a number line shows a jump from 15 to 20, how many units were added?
A. 4
B. 5
C. 6
D. 10
SESSION 2 • OBJECTIVE
SESSION 2: LEARNING OBJECTIVES
Today we will demonstrate the 'counting up' strategy on an open number line to solve addition problems that cross over the next ten.
SESSION 2 • REVIEW
REVIEW: YESTERDAY'S HOPS
Who can show 15 + 3 on our board? Remember to start at 15 and take 3 hops. Where did we land? Yes, 18!
SESSION 2 • MOTIVATION
THE BIG JUMP CHALLENGE
What happens when we add 28 + 5? If we count one by one, it might take a long time. Is there a way to 'jump' to the next big number first to make it easier?
SESSION 2 • PRESENTATION
THE OPEN NUMBER LINE
An open number line is a line with no numbers pre-marked. We only write the numbers we need. This helps us solve bigger problems much faster.
SESSION 2 • DISCUSSION
BRIDGING TO TEN
Let's solve 28 + 5. First, we look for the nearest 'ten' after 28. The next ten is 30. How many do we need to get from 28 to 30? We need 2!
SESSION 2 • DISCUSSION
CALCULATING THE REMAINDER
We needed to add 5 in total. We already added 2 to reach 30. How many more do we have left to add? 5 minus 2 is 3. We still need to add 3.
SESSION 2 • DISCUSSION
THE FINAL JUMP
From 30, we take one more jump of +3. 30 plus 3 is 33. So, 28 + 5 = 33. Using 30 as a 'landmark' made it very easy to calculate!
SESSION 2 • DISCUSSION
ANOTHER EXAMPLE: 57 + 6
Let's try 57 + 6. Start at 57. What is the next ten? It is 60. How many to get to 60? We need 3. So we jump +3 to reach 60.
SESSION 2 • DISCUSSION
FINISHING 57 + 6
We wanted to add 6. We already added 3. We have 3 left. From 60, jump another +3. We land on 63. The sum of 57 + 6 is 63.
SESSION 2 • ACTIVITY
WHITEBOARD PARTNERS
With a partner, use your whiteboards to solve 39 + 7. Try to jump to 40 first. Then solve 66 + 8 by jumping to 70 first.
SESSION 2 • ACTIVITY
LANDMARK NUMBERS
On your worksheet, draw the hops for five addition problems. Always circle the 'landmark' number (the ten) that you jump to.
SESSION 2 • GENERALIZATION
THE POWER OF TENS
Jumping to the nearest ten makes addition easier. We call this 'bridging to ten.' It helps us break a big addition into two smaller, easier steps.
SESSION 2 • ASSESSMENT
QUESTION 1
To solve 28 + 4 by bridging to ten, which number do you jump to first?
A. 20
B. 25
C. 30
D. 35
SESSION 2 • ASSESSMENT
QUESTION 2
Solve 47 + 5 using an open number line.
A. 51
B. 52
C. 53
D. 54
SESSION 2 • ASSESSMENT
QUESTION 3
What is the sum of 69 + 3?
A. 71
B. 72
C. 73
D. 74
SESSION 2 • ASSESSMENT
QUESTION 4
On an open number line, a jump from 38 to 40 is +2. If you need to add 7 total, what is the next jump?
A. +3
B. +4
C. +5
D. +7
SESSION 2 • ASSESSMENT
QUESTION 5
85 + 7 equals:
A. 90
B. 91
C. 92
D. 93
SESSION 3 • OBJECTIVE
SESSION 3: LEARNING OBJECTIVES
Today we will learn to express three-digit numbers in expanded form and perform addition with sums up to 1000 without regrouping.
SESSION 3 • REVIEW
REVIEW: PLACE VALUE
Let's look at the number 243. How many hundreds are there? (2). How many tens? (4). How many ones? (3). This is the key to expanded form!
SESSION 3 • MOTIVATION
DECOMPOSING NUMBERS
What if we have a very big number like 456? We can break it apart into its values: 400, 50, and 6. It is like taking a toy apart to see how it works!
SESSION 3 • PRESENTATION
EXPANDED FORM ADDITION
When we add big numbers, we can write them in expanded form vertically. This helps us align the hundreds with hundreds, tens with tens, and ones with ones.
SESSION 3 • DISCUSSION
SETTING UP THE PROBLEM
Let's add 243 and 125. First, expand 243 into 200 + 40 + 3. Then, expand 125 into 100 + 20 + 5. Line them up carefully on your paper.
SESSION 3 • DISCUSSION
ADDING THE ONES
Start with the ones place. 3 plus 5 equals 8. We write 8 right under the ones column. It is simple because we don't have to carry anything yet.
SESSION 3 • DISCUSSION
ADDING THE TENS
Now move to the tens. 40 plus 20 equals 60. Write 60 under the tens column. Remember, this 4 and 2 really represent 40 and 20!
SESSION 3 • DISCUSSION
ADDING THE HUNDREDS
Finally, add the hundreds. 200 plus 100 equals 300. Write 300 under the hundreds column. We now have three parts of our answer.
SESSION 3 • DISCUSSION
THE FINAL SUM
Now, combine the parts: 300 + 60 + 8. When we put them back together, we get 368. This is the sum of 243 and 125!
SESSION 3 • ACTIVITY
BASE-TEN BLOCK BUILDING
Represent 132 and 214 using blocks. Physically group the hundreds together, the tens together, and the ones together. Write the expanded form of your total.
SESSION 3 • ACTIVITY
EXPANDED FORM RACE
I will show a 3-digit addition problem. On your whiteboard, expand both numbers and find the sum as fast as you can. Show your work clearly!
SESSION 3 • GENERALIZATION
WHY EXPANDED FORM?
Expanded form helps us see the 'value' of each digit. It prevents us from getting confused by large numbers because we only add similar values together.
SESSION 3 • ASSESSMENT
QUESTION 1
What is the expanded form of 342?
A. 300 + 4 + 2
B. 30 + 40 + 2
C. 300 + 40 + 2
D. 3 + 4 + 2
SESSION 3 • ASSESSMENT
QUESTION 2
Add (100 + 20 + 3) and (200 + 50 + 4). What is the total?
A. 377
B. 357
C. 373
D. 327
SESSION 3 • ASSESSMENT
QUESTION 3
In the number 567, what is the value of the digit 6?
A. 6
B. 60
C. 600
D. 67
SESSION 3 • ASSESSMENT
QUESTION 4
Solve 412 + 135 using expanded form.
A. 547
B. 545
C. 537
D. 647
SESSION 3 • ASSESSMENT
QUESTION 5
Which shows the correct expanded form addition of 250 + 120?
A. (20 + 5) + (10 + 2)
B. (200 + 50) + (100 + 20)
C. (200 + 5) + (100 + 2)
D. (2 + 5 + 0) + (1 + 2 + 0)
SESSION 4 • OBJECTIVE
SESSION 4: LEARNING OBJECTIVES
Today we will solve addition problems with sums up to 1000 using the expanded form method involving regrouping in the ones and tens places.
SESSION 4 • REVIEW
REVIEW: MENTAL MATH
Let's practice adding 10s and 100s. What is 400 + 200? What is 50 + 30? What is 80 + 40? That last one is tricky!
SESSION 4 • MOTIVATION
THE OVERFLOWING ONES
What happens if we have 6 ones and we add 7 more? We get 13. But we can only fit one digit in the ones place! Where does the extra 'ten' go?
SESSION 4 • PRESENTATION
INTRODUCTION TO REGROUPING
Regrouping is like trading. If you have 10 ones, you can trade them for 1 ten rod. If you have 10 tens, you can trade them for 1 hundred flat.
SESSION 4 • DISCUSSION
ADDING 456 + 237
Let's write these in expanded form. 456 is 400 + 50 + 6. 237 is 200 + 30 + 7. We start by adding the ones: 6 + 7 = 13.
SESSION 4 • DISCUSSION
TRADING ONES FOR TENS
Since 13 is 10 + 3, we keep the 3 in the ones place. We take the 10 and move it over to the tens column. Now we have an extra ten to add!
SESSION 4 • DISCUSSION
ADDING THE TENS COLUMN
Now add the tens: 50 + 30 + the 10 we moved. 50 + 30 is 80, and 80 + 10 is 90. So we write 90 in the tens column.
SESSION 4 • DISCUSSION
ADDING THE HUNDREDS
Finally, add the hundreds: 400 + 200 = 600. Our parts are 600, 90, and 3. When we combine them, our total sum is 693.
SESSION 4 • DISCUSSION
REGROUPING TENS TO HUNDREDS
What about 382 + 154? The tens are 80 + 50, which equals 130. 130 is 100 + 30. We keep the 30 and move the 100 to the hundreds column!
SESSION 4 • ACTIVITY
REGROUPING MATS
Use your 'Regrouping Mats.' Solve three problems. When your ones sum is more than 9, physically move a ten-rod to the next column.
SESSION 4 • ACTIVITY
PLACE VALUE T-CHARTS
Work in pairs. One student expands the first number, the second student expands the second number. Together, decide when you need to regroup.
SESSION 4 • GENERALIZATION
TRADING UP
Regrouping is just another way to say 'trading.' We trade 10 of a smaller value for 1 of the next larger value. It keeps our numbers organized.
SESSION 4 • ASSESSMENT
QUESTION 1
When adding (40 + 8) and (30 + 5), what is the sum of the ones (8+5)?
A. 10
B. 12
C. 13
D. 15
SESSION 4 • ASSESSMENT
QUESTION 2
If the ones sum is 14, how much do you 'regroup' to the tens place?
A. 4
B. 1
C. 10
D. 14
SESSION 4 • ASSESSMENT
QUESTION 3
Solve 245 + 138.
A. 373
B. 383
C. 393
D. 385
SESSION 4 • ASSESSMENT
QUESTION 4
What is 560 + 270?
A. 730
B. 830
C. 800
D. 770
SESSION 4 • ASSESSMENT
QUESTION 5
Add in expanded form: (300 + 90 + 2) + (100 + 20 + 5). The tens sum is 110. What is the final total?
A. 417
B. 517
C. 512
D. 412
SESSION 5 • OBJECTIVE
SESSION 5: LEARNING OBJECTIVES
Today we will compare and apply the number line and expanded form strategies to solve real-life addition word problems.
SESSION 5 • REVIEW
REVIEW: PARTS OF ADDITION
What do we call the numbers we are adding? They are Addends. What do we call the final answer? It is the Sum. We have two tools to find it!
SESSION 5 • MOTIVATION
MARIA'S STICKER COLLECTION
Maria loves stickers. She has 45 stickers in her album. Her brother gives her 7 more. Later, her grandmother gives her 120 more! How many does she have now?
SESSION 5 • PRESENTATION
PICKING THE RIGHT TOOL
When we have different sized numbers, we can pick different tools. For small numbers, a number line is fast. For very large numbers, expanded form is best.
SESSION 5 • DISCUSSION
SOLVING MARIA'S PROBLEM - PART 1
First, Maria had 45 and got 7 more. Since 7 is a small 1-digit number, let's use the number line. Start at 45 and count up 7 hops. We reach 52.
SESSION 5 • DISCUSSION
SOLVING MARIA'S PROBLEM - PART 2
Now Maria has 52 and gets 120 more. These are bigger numbers. Let's use expanded form! (50 + 2) + (100 + 20 + 0). 100 + 70 + 2 equals 172.
SESSION 5 • DISCUSSION
THE CLASS CHALLENGE
Look at these two problems. 88 + 9 and 455 + 322. Which one would you use a number line for? Most people find 88 + 9 easier on a number line!
SESSION 5 • DISCUSSION
COMPARING RESULTS
Did you know you can use both methods for any problem? But choosing the 'easier' one helps us avoid mistakes. Math is about having a 'toolbox' of ideas.
SESSION 5 • DISCUSSION
REAL LIFE: TOY STORE
Imagine a toy car costs P250 and a ball costs P145. To find the total, we expand: (200+50+0) + (100+40+5). The total is P395. Easy!
SESSION 5 • ACTIVITY
THE PRICE IS RIGHT GAME
I will show two toy pictures. You must choose to use either a number line or expanded form to find the total price. Show your choice on your whiteboard.
SESSION 5 • ACTIVITY
STRATEGY POSTER
In small groups, create a poster showing when to use a number line and when to use expanded form. Use drawings to explain your reasons.
SESSION 5 • GENERALIZATION
MY MATH TOOLBOX
We now have two great ways to add. We can count up on a number line for small additions, and use expanded form for large additions with regrouping.
SESSION 5 • ASSESSMENT
QUESTION 1
Ana has 56 beads and buys 8 more. Which method is best to show 'counting up'?
A. Multiplication
B. Number Line
C. Subtraction
D. Division
SESSION 5 • ASSESSMENT
QUESTION 2
A bag has 230 blue marbles and 150 red marbles. What is the total in expanded form?
A. 300 + 80
B. 200 + 30 + 100 + 50
C. 380
D. Both A and B
SESSION 5 • ASSESSMENT
QUESTION 3
Solve: 67 + 9 using the number line method.
A. 75
B. 76
C. 77
D. 78
SESSION 5 • ASSESSMENT
QUESTION 4
What is the sum of 444 and 555?
A. 999
B. 888
C. 900
D. 1000
SESSION 5 • ASSESSMENT
QUESTION 5
If you add 321 + 123 in expanded form, which of these is part of the sum?
A. 400
B. 40
C. 4
D. All of the above
SESSION 5 • GENERALIZATION
COURSE REFLECTION
Think about what you learned this week. You can now add small and large numbers with confidence! Keep practicing your hops and your expansions.
SESSION 5 • ASSESSMENT
SUMMATIVE TEST Q1
What is the result of 25 + 9 on a number line?
A. 33
B. 34
C. 35
D. 36
SESSION 5 • ASSESSMENT
SUMMATIVE TEST Q2
In expanded form, what is 400 + 50 + 6 + 100 + 20 + 3?
A. 579
B. 589
C. 576
D. 479
SESSION 5 • ASSESSMENT
SUMMATIVE TEST Q3
When you regroup 15 ones, you get:
A. 1 ten and 5 ones
B. 5 tens and 1 one
C. 15 tens
D. 1 hundred
SESSION 5 • ASSESSMENT
SUMMATIVE TEST Q4
What is 88 + 5 using the bridging to ten strategy?
A. 90
B. 92
C. 93
D. 95
SESSION 5 • ASSESSMENT
SUMMATIVE TEST Q5
What is the sum of 675 and 218?
A. 883
B. 893
C. 890
D. 993
SESSION 5 • ASSESSMENT
SUMMATIVE TEST Q6
Which strategy is best for 5 + 4?
A. Expanded form with regrouping
B. Number line counting up
C. Long division
D. 3-digit place value chart
SESSION 5 • ASSESSMENT
SUMMATIVE TEST Q7
What is the value of the 7 in 742?
A. 7
B. 70
C. 700
D. 7000
SESSION 5 • ASSESSMENT
SUMMATIVE TEST Q8
If you add 120 + 30, what is the sum of the tens?
A. 20
B. 30
C. 50
D. 150
SESSION 5 • ASSESSMENT
SUMMATIVE TEST Q9
Solve 39 + 6 on an open number line.
A. 44
B. 45
C. 46
D. 47
SESSION 5 • ASSESSMENT
SUMMATIVE TEST Q10
What is the expanded form of 999?
A. 9 + 9 + 9
B. 90 + 90 + 9
C. 900 + 90 + 9
D. 900 + 9