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Lesson 43: Relating Addition and Subtraction – Discussion
Posted by Jon on December 6, 2019 at 5:37 amCreate a context involving one of the addition or subtraction structures shared in this lesson (missing addend or missing subtrahend) and identify which structure it is.
Share your reflection below along with any wonders you still have.
Luke Albrecht replied 9 months ago 19 Members · 22 Replies 
22 Replies

When teaching elementary math, I’d never really thought of using a balance scale to represent equations. Makes total sense. I have used that analogy when teaching middle years but , thinking back, definitely not enough. I was always in a rush to get to the algorithm.
Briggs” Grandpa gave him some money to buy ice cream. He bought an ice cream cone for $3.50. He got $1.50 in change. How much money did his Grandpa give him?
Subtraction:
X – 3.50 = 1.50
 This reply was modified 2 years, 2 months ago by marianne aamodt.

Me too Marianne. The closest I came to using a balance scale in my career has been when I talk to students how the Right Hand Side (RHS) is always equal to the Left Hand Side (LHS). This usually comes up when I write and equation with the “answer” on the left instead of the right. Our students are so conditioned that equations can only be written with the answer on the right side. This always leads to a great conversation about why it doesn’t matter.
Anyway, here is a digital app that was shared with me to use for balance scales: https://www.didax.com/apps/mathbalance/
I wish there was one that has items you can put on instead of just the numbers but, this this would be a good way to help students check if their thinking is correct (and balanced)!

This is a very timely comment. Just yesterday, I came across a URL that was shared on the Build Math Minds FB page that I will try with my 7/8 class as a prealgebra experience. It looks like it may be helpful for my weaker students.


Marianne,
I’d suggest adding the algebraic expression below. If you are a smartboard ( Smartnotebook 11) user they have a dynamic Scale within the Smart Exchange.
X – $3.50 = $1.50
Scale:
X – 3.50 + 3.50 = $1.50 + 3.50

I love linking addition and subtraction together– especially since many students feel stronger in addition than they do subtraction.
With any contextual problem, I think my students rush to an algorithm that may or may not be correct, because they have a tendency to not read the problems very carefully. Pairing it with a model– number line, balance or tape diagram, makes it so much easier for students to identify what they are looking for and answer the question accurately.

Love that you are mixingup addition and subtraction which is called “interleaving” under the 6 cognitive learning strategies. This is particularly effective in mathematics and has shown effective results in longterm memory. So thanks. Now to a problem situation:
A teacher bought 20 pencils for her class. One week later she only had 14 pencils left. How many pencils did she give to her students?
Result known and start known change unknown.
for some reason image will not post.
 This reply was modified 1 year, 11 months ago by Jeanette Cox.
 This reply was modified 1 year, 11 months ago by Jeanette Cox.
 This reply was modified 1 year, 11 months ago by Jeanette Cox.
 This reply was modified 1 year, 11 months ago by Jeanette Cox. Reason: trying to upload image of illustration of problem
 This reply was modified 1 year, 11 months ago by Jon Orr.

Mork the cat had 10 kibbles in his dish. Wilbur the cat ate some kibbles are there are 3 kibbles left. How many kibbles did Wilbur eat?
The subtrachend is missing in this problem.
I really like the idea of introducing the balancing scale in early elementary.

Sarah has some chocolates. She gave 6 chocolates to Maya. Now she has 8 chocolates left. How many chocolates did Sarah have to start with?
Active Separation; Start Unknown
Students can access this problem by way of:
an algebraic equation using addition
a number line; counting forward
a mathematical model using “?” to represent the sum of the two sets and two smaller sets below to represent the amount Maya has (6) and the amount Sarah has now (8)

I have always talked about solving problems is like having a scale however I never usually bring out the visual aspect of it. Basically, I use my hands to as the scale, I can’t believe I never thought to create a visual for solving equations using a scale. From learning class one can see that after using the scale visual to solve such problems, then one can bring in the number line to show how it works.
Problem that I would use when comparing two people’s earnings. I would be essentially introducing students to systems of equations. Tim makes $15 an hour and Kate earns $12 but got $100 bonus. How long until they earn the same amount?
As you stated numerous time – if bring it math models it really helps you with your thinking.

<div>I dug into my Smart Board app and discovered a great dynamic multimedia scale.</div>
I am going to try it out with my class.
Here is a screen shot.
 This reply was modified 1 year, 10 months ago by Chris Laurie.

Mary had some money, she gave $10 to her friend and now she has $200 left. How much money did she have to start with?
x 10 =200
I have used a visual of scale to represent the problem to show that equation is like a balance.

On Monday morning you had 11 of your favorite red jellybeans. By lunch time you had 7 red jellybeans. How many red jellybeans did you eat?
This is “change unknown” or missing subtrahend. It is a subtraction problem. Students might use a part/part/whole diagram, or counting on with a number line (or counting backwards) or the balance model.
I would like to see the balance model used more than it is! (I have encouraged teachers I support to use these concrete tools and they always are surprised that it works!!!!)
When we were in brick and mortar (and not remote) I had a balance out on my bookshelf for coworkers to see and play with any time they wanted to. Now that we are remote I have encouraged teachers to use a virtual manipulative balance. (Didax.com has a decent one that is free to use.) It is such a great algebraic thinking tool that is underappreciated.

Bob has 10 cookies
Bill comes over and eats some of his cookies.
How many cookies did Bill eat if Bob now has only 2 cookies left?
10 – x = 2
The student could draw a number line and go to 10 and then count the jumps back to 2 and would know the answer is 8. Or the student could consider a scale. If you put 10 apples on one side and 2 on the other, how many would you have to remove from the left side to balance the scale?

I have caught 2 llamas but I need 6 for my pack trip. How many more llamas do I need to catch? Missing addend. Can be solved with pictures, number line, part part whole model or scale.

We have 3 players. We need a total of 12 players. How many more players do we need?
Missing addend.
I think a big take away for me is to keep reminding students that they can use either addition or subtraction to actually find a solution. There is more than one path to the correct answer.

Such a huge take away! So important for students to know this AND to understand that just because you used one operator for your strategy, doesn’t necessarily mean that it was that “type” of problem.


This is a big part of the concept of equality and equations in Grade 5. I read in the comments that someone said their students have a lot more trouble understanding the equation when the “answer” is on the left instead of the right side of the equal sign! It is important for us to “normalize” this representation so students become more flexible in their thinking.
As we seem to be doing a lot of carrot problems in my class these days, here is one for this forum:
I had 7752 grams of carrots in my fridge in September when I harvested them. My family has begun eating them. I now have 6439 grams left. How many has our family already eaten?
7752g = t + 6439g OR 7752g – t = 6439g
I find that the student have a bit of trouble solving this type of question. They much prefer knowing the number consumed rather than the number left. Putting the variable into the equation makes solving it tricky in Grade 5! Actually these numbers are really too large to start doing equations with because they need to understand the idea of comparing with visuals before applying the concept to large numbers, so I would likely use kg with them.

The idea of normalizing is so important. When students are uncomfortable with different notation or structures, it is because it is foreign to them. The more we introduce math in different ways, the more flexible students will become.


Coby’s grandma gave him $10 to go to the Merc (our convenience store).
Coby brought her $4 as change.
How much did he spend?
Students can either subtract from 10 or add up from 4.
What I love is the different structures students can use to solve this equation:
the part/part/whole model, the number line or the balance scale. When we start solving equations, I do have my students begin with a website where they use a balance scale, but I love the idea of anchoring that first to these other models. I also am happy to know that I have a model on my Smartboard!

This is a good place for money questions. They’re usually about a deficit or saving up for some bigger amount.
I think the balance scales and showing kids that they are actually doing algebra and subtraction is very important too – gets them used to being comfortable with those concepts and seeing them in everyday contexts.

I have $20 and I buy a book at the bookstore. I have $3.95 left. $16.05 is the missing subtrahend. This is a subtraction structure.