Adding Numbers with Sums up to 10 000
In this section, I will be able to add 3 and 4 digit numbers together by:
- Estimating sums and differences. This is an informed guess!
- Using many different personal strategies to solve problems (that work for you).
- Solving real-world problems related to this topic.
What are some ways that I can add?
Break-apart / Expanded Form Method
This strategy involves taking the numbers you are adding and breaking them apart. This method is also called Front End Addition. Let's look at a quick example:
386 + 292
Adding my hundreds: 300 + 200 = 500
Adding my tens: 80 + 90 = 170
Adding my ones: 6 + 2 = 8
Adding all my sums together: 500 + 170 + 8 = 678
Using a Friendly Number
This strategy involves taking one or both of the numbers and making them into a friendly number. A friendly number is any number that is easier to add and usually ends in 0. Let's look at a quick example:
697 + 256
- I can add 3 to 697 to make it a friendly number:
697 + 3 = 700
Because I added 3 to 697, I need to do the same with 256.
256 + 3 = 259
Adding them together I get:
700 + 259 = 959
This strategy involves taking one or both of the numbers and making them into a friendly number. A friendly number is any number that is easier to add and usually ends in 0. Let's look at a quick example:
697 + 256
- I can add 3 to 697 to make it a friendly number:
697 + 3 = 700
Because I added 3 to 697, I need to do the same with 256.
256 + 3 = 259
Adding them together I get:
700 + 259 = 959
Using the Count On Method
This strategy involves taking one of the numbers and breaking apart the second number and adding it on to your first. Let's look at a quick example:
387 + 256
387 + 200 = 587 Adding the hundreds
587 + 50 = 637 Adding the tens
637 + 6 = 643 Adding the ones
In this method, you could choose to break apart your hundreds, tens or ones further. For example, instead of adding 50, I could add 20 and 30 if it is easier.
For more information on this strategy as well as the lining up method for addtion, view the video on the right.
This strategy involves taking one of the numbers and breaking apart the second number and adding it on to your first. Let's look at a quick example:
387 + 256
387 + 200 = 587 Adding the hundreds
587 + 50 = 637 Adding the tens
637 + 6 = 643 Adding the ones
In this method, you could choose to break apart your hundreds, tens or ones further. For example, instead of adding 50, I could add 20 and 30 if it is easier.
For more information on this strategy as well as the lining up method for addtion, view the video on the right.
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Practice Activities
Choose one of the following addition problems to complete:
Choose one of the following addition problems to complete:
- Find the sum of 3 185 and 628 using a personal strategy. Show how you know that your strategy works.
- Create a story problem involving the following equation: 185 + _____ = 2 330. Explain how you know the equation works.
- You drink 250 mL of milk on the first day, 375 mL of milk the second day, and 450 mL of milk on the third day. Write down an estimate for how many mL of milk you drank altogether THEN find the exact sum using one personal strategy.
Consider the following problem...
Part 1:
Joey and his family took a road trip all the way to Toronto, Ontario that took 2 days. They stayed the night in Montreal, Quebec. How many kilometers did they travel each day? How many kilometers did they travel altogether?
Write down a guess for both questions. How did you estimate?
Hint:
Look at the distance across Canada in the first picture
THEN
Compare it to the distance between Halifax, NS to Montreal, Quebec. The star on the second map shows you where Halifax is.
AND
The distance between Montreal, Quebec to Toronto, Ontario.
Part 2:
Record the following:
1) What information do you need in order to figure out how far they traveled on the first and second days?
2) What information do you need in order to figure out how far they traveled altogether?
Record the following:
1) What information do you need in order to figure out how far they traveled on the first and second days?
2) What information do you need in order to figure out how far they traveled altogether?
Part 3:
Find out how far Joey and his family traveled to get to Toronto, Ontario using the information on the maps provided below. Let's assume Joey's family took the route in blue with the distances underneath the green time indicators. Choose at least 2 strategies for adding and make sure to show what you know.