Minds On
Exploring new strategies
Student Success
Think
Roby the robot collected 175 stamps for their collection. Then, their uncle Andy the android gave him 138 more stamps.
How many stamps does Roby have in total? Use base ten blocks and a place value chart to model the solution. How many different ways can you model the solution? Share your thinking in your notebook.
Baker #1 made 138 scones to sell at the fair. Baker #2 made 74 scones to sell at the fair.
How many more scones did Baker #1 make than Baker #2? Use base ten blocks and a place value chart to model the solution.
How many different ways can you model the solution? Share your thinking in your notebook.
Note to teachers: See your teacher guide for collaboration tools, ideas and suggestions.
In this learning activity, we are going to learn how to add and subtract whole numbers using an algorithm based on place value.
An algorithm is a set of rules of steps to be followed in a calculation problem.
Action
Place value
Place value refers to the value of each digit in a number.
Adding using place value
When we add two numbers it is important to keep the place value of each digit in the answer in order. To do this we use a strategy called regrouping.
Each digit in a number has a specific value within its place. For example, in the number 34 the 3 represents 3 tens and the 4 represents 4 ones. We have to think about place value when we add.
In this example, we start by adding the ones. We know 4 + 9 = 13, but there is not enough space in the ones column to write 13 ones.
So, we have to regroup 10 ones for 1 ten. Then, we can carry over the 1 ten into the tens column and add.
| Tens | Ones |
|---|---|
| (Carry 1) 3 | 4 |
| + | 9 |
| 4 | 3 |
To add two- and three-digit numbers:
- find the total of ones
- find the total of tens
- find the total of hundreds
- regroup when needed
You may ask, “When do I regroup?” Here is your answer.
Let’s follow Teacher Charmain as she explains three-digit addition.
Practice
If possible, work with a partner or with someone at home to solve the following addition sentence. Show your work using base ten blocks and a place value chart to add the numbers.
Susan needs 600 stickers to win a prize. They have 429. Susan’s sister gives them 275 more stickers. Does Susan have enough stickers now? Use a variety of representations to show your thinking.
Share your work in your notebook.
If possible, work with a partner or with someone at home to solve the following addition sentence. Share in your notebook. Use math language to communicate your thinking.
What number makes the addition sentence true?
How did you solve this question? What strategies did you use?
Check your answer by completing the addition sentence. Did you get that same result?
Subtracting using place value
It is important to know the place value of digits when we subtract. We cannot subtract a larger number from a smaller number so there are times when we have to exchange hundreds, tens and ones. In subtraction, we call this borrowing. Access the video “Subtraction” to learn how this is done.
Each digit in a number has a specific value within its' place. For example, in the number 34 the 3 represents 3 tens and the 4 represents 4 ones. We have to think about place value when we add.
In this example, we start by subtracting the ones. However, we cannot take 9 ones from 4 ones, so we have to borrow from the tens column.
So, we have to exchange 1 ten for 10 ones. We borrow 1 ten from the tens column leaving 2 tens. We turn 1 ten into 10 ones and place them in ones column making 14 ones. Now we can subtract 14 − 9.
To subtract two- and three-digit numbers:
- subtract the ones
- subtract the tens
- subtract the hundreds
- borrow when needed
You may ask, “How do I know when I need to borrow?”
Let’s follow Teacher Shahana as they describes two-digit subtraction. Access the video “Subtracting with a place value chart” to learn about this way of subtraction.
Practice
If possible, work with a partner or with a family member to solve the following subtraction word problem.
Athlete #1's team has 73 points. Athlete #2’s team has 38 points. How many more points does Athlete #1's team have compared to Athlete #2’s team? Represent your thinking in a variety of ways.
Did you have to borrow to solve? How did you know you had to borrow?
Share your answers in your notebook. Use math language to communicate your thinking.
If possible, work with a partner or with someone at home to complete the problem. Read the question and review Jacey’s solution. Is she correct?
850 streamers were created to decorate the gym. 372 streamers were used to decorate tables and chairs. The students need 500 streamers to decorate the walls. Are there enough?
Jacey completed the question
There are 522 streamers for the students. So, yes, there are enough to decorate the walls.
Consolidation
It's your turn
Complete the following word problem. Record your answer on paper and communicate your thinking in an audio-visual way, such as explaining it in your own video clip.
Question:
Jumper #1 completed 145 jumping jacks in a row. Jumper #2 completed 89 jumping jacks in a row.
How many more times did Jumper #1 jump than Jumper #2?
Use addition to solve the problem.
Use subtraction to solve the problem.
Reflection
How do you feel about what you have learned in this activity? Which of the next four sentences best matches how you are feeling about your learning? Press the button that is beside this sentence.
I feel…
Now, record your ideas about your feelings using a voice recorder, speech-to-text, or writing tool.