Addition and Subtraction

The focus of this unit is solving problems using addition and subtraction. We focus on adding up to 3-digit numbers. You will notice in the list of topics below that the phrase "personal strategy" is used. That's because students are expected to explore a variety of strategies for calculating, and choose the one that they best understand and that works for them. There is no one right way to add or subtract. Students who are good at thinking flexibly about numbers may be comfortable with several strategies, while others may stick to one tried and true method. It's all good! 

Topics covered include:

(Topics for grade 2 and grade 3 are very similar. Expectations for grade 2 include adding and subtracting 1 and 2-digit numbers within 100,  while grade 3s should add and subtract 1, 2 and 3-digit numbers within 1000.)

• using mental mathematics strategies and personal strategies to determine a sum or a difference of two 2-digit numbers (grade 3)

• understanding story structures for addition and subtraction (join, part-part-whole, and comparison) by acting out, modeling and solving story problems using concrete materials, pictures, words, and symbols.  

• using and describing a strategy for determining an estimate and estimate the solution for a given story problem. 

• creating and solving addition and subtraction story problems involving the sum or difference of two given numbers that are meaningful to them. 

• using and describing personal strategies for determining sums and difference of two numbers using concrete materials, pictures, and mental mathematics strategies.  

• modeling addition and subtraction using concrete materials and visual representations and record the process symbolically. 

• determining the sum or difference of two given numbers using a personal strategy.  

Why Problem Solving?

Addition and subtraction is best learned in a problem solving context. Students need to recognize that these are not just operations that we do on paper at school, they have real-world applications. Knowing when to use addition or subtraction to solve a problem is an important skill, and is best learned in a real-world context. When there is a need to solve an addition or subtraction problem around the house, have your child help out. Encourage them to:

• • • • • visualize or draw a picture of what is happening - this will help them figure out whether addition or subtraction can be used to solve the problem

        • act out the problem or use objects to model it

        • write down the problem using numbers and symbols

        • use addition and subtraction strategies they know to solve the problem

"I don't get new math!"

I'll bet that you understand "new" math better than you think you do. The math isn't new, but the thinking about the math is. Many of us grew up learning that adding and subtracting was a set of rules to be followed and that there was only one way to get the answer. The "new" approach is to teach children how they can think about numbers in different ways and combine them and take them apart in different ways to solve problems. This flexibility in thinking about numbers makes kids better and more efficient problem solvers, because they can manipulate the numbers in the way they find easiest. Many of the "new" ways of doing adding and subtracting aren't new at all, they simply take the old fashioned way and help it make more sense. Students who understand the hows and whys of addition and subtraction are going to be better at solving problems.

Let's say that I'm buying something from you that costs $6.35. Let's also say that you don't have a cash register or a calculator. I need change from my $10.00 bill. You could pull out paper and a pencil and do all of that borrowing and subtracting, but you probably wouldn't. You might think to yourself: I'll start at $6.35 and count how much money I need to get to $10.00 - that would be the change. Five cents makes $6.40, 10 more cents to $6.50, 50 cents gets us to $7.00, then $3 to finish it off - total change $3.65.  We just used adding to solve that subtraction problem, and we just did "new" math!

If I present you with the equation 47 + 26, your first instinct may be to pull out the paper and pencil and do the adding and carrying. We can do this one easily in our heads if we know how numbers can be manipulated. I know that multiples of 10 are easier to add, so I take 3 from the 26 and put it with the 47. Now I have 50 + 23. That's easy... 73. I could also think of it this way: 40 and 20 is 60.  That leaves 7 + 6 which is 13, so I add those together to get 73.  It may seem more complicated, but it's actually exactly what you would do when you write it down and do the carrying, and it can more easily be done in your head. 

"New" math actually makes a lot of sense, and when you have a chance to practice it and think about it, you'll find that it changes the way you think about numbers and solve problems (I know it did for me!). If you need a crash course in any of the strategies that we're using in class (in other words: "my child was doing this math and I had no idea what they were doing so I couldn't help") let me know and we can arrange a time to meet. 

Estimating

Estimating the solution to a problem is an important skill. Contrary to what some students think, estimating is not about trying to guess as close as possible to the correct answer. Estimating is about using numbers that are easy to calculate mentally to get a rough idea of the correct answer. This is important so that we can tell if our answer is reasonable or not. If you estimated the answer to be 500 and your calculated answer is 943, it seems that the answer is not reasonable and maybe something went wrong. 

In the past, estimating strategies were based very closely on rounding numbers to the nearest ten or hundred. I'm not so worried about that (again, not a competition to get close to the real answer), I want the students to choose close numbers that they can work with easily while getting an estimate that is fairly close to the actual answer.

For example: if the problem is 367 + 549, some acceptable estimates would be:

• 300 + 500 = 800

• 400 + 500 = 900

• 400 + 600 = 1000

• 400 + 549 = 949

• and many more

Of course there is a range in the estimates, but they are all in the same ballpark, and will give us an idea of whether or not our answer is reasonable.

I talk a bit about estimating in the videos below.

Addition and Subtraction Strategies We Use in Class

There are several different types of problems for which addition or subtraction can be used to find the solution. Often, both operations could be used in different ways, and this is where the students' flexibility of thinking comes into play. As you might recall from above, students are encouraged to use a personal strategy. A problem that you might read as a subtraction problem, might be more easily solved using addition by some students (think about the money problem above). 

Each type of problem has a set of strategies that work for that problem. I encourage students to start by visualizing the problem in some way or by drawing a bar chart (see the video below if you don't know what that is!!) so that they can see what type of problem they are trying to solve. That way they can choose the strategy that works best for them and that type of problem.

The more common strategies that we use are best shown to you than described to you, so take a look at the videos below for a quick tutorial of how we might do addition and subtraction in grade 2/3 (these videos were made with grade 3 in mind, but the same strategies can be used for adding 2-digit numbers like we do in grade 2). 

Addition Strategies Videos

Subtraction Strategy Videos

Ways to Help at Home

• Find problems to solve at home and have your child give it a try. Remember to get them to estimate first.

• Use a deck of cards (remove the faces, 10s are 0 and Ace is 1). Deal 6 cards to each player. Have them use the cards to make two 3-digit numbers then find the sum or difference. The one with the greatest (or least) answer wins. If you're not ready for numberrs in the hundreds, use 4 cards to make 2-digit numbers.

• Have your child help with paying the bills. Give them the bill amounts (without the decimals) and have them find the total for you. 

• If your child is saving up to buy something, have them keep a record of money they save and a running total. From time to time, figure out how much is left to save.

• Give your child riddles that need to be solved using addition or subtraction (maybe the answer is the combination to a lock) or if you're really creative set up an escape room!

• Have your child be the teacher and create a problem for you to solve. They will need to make sure they know the answer in order to correct your work. Of course you won't always get it right on the first try (wink, wink).