Math Problem Solving Part 1: Join (aka Some and Some More)

by C. Elkins, OK Math and Reading Lady

I have 1 penny in one pocket. I have 6 more pennies in another pocket. This is a Join or “some and some more” story structure.

Many teachers I work with have asked for advice on problem solving in math. Students often don’t know how to approach them or know what operation to use. Should teachers help students focus on key words or not? What about the strategies such as CUBES, draw pictures, make a list, guess and check, work backwards, find a pattern?

While all of those strategies definitely have their purpose, I find  we often give kids so many steps to follow (underline this, circle this, highlight that, etc.) that they lose sight of what the problem is basically about.

In this post, I will focus on two basic questions (who and what) and a simple graphic organizer that will help students think about (and visualize) the actions in a one-step Join story problem. KG and first grade students can act out these actions using story mats or ten frames. Late first through 5th grade can use a part-part-whole box. There are two FREE items offered.  

These are the types of problems I will focus on in the next few posts.

  1. Join (also referred to as SSM – Some and Some More)
  2. Separate (also referred to as SSWA – Some, Some Went Away)
  3. Part-Part-Whole
  4. Comparing
  5. Equal groups

JOIN problems have 3 versions: 

  • a + b = ___     (The result is unknown.)
  • a + ____ = c   (How the story changed is unknown / missing addend.)
  •  ____ + b = c  (The start is unknown / missing addend.)

They can also be referred to as “Some and Some More” stories (SSM). This means, you have some and you get some more for a total amount. These present themselves as additive stories, but it doesn’t necessarily mean you have to add to solve them. The second and third version above are often referred to as missing addend problems.

In these stories, students should identify these 2 things: who and what. They should also notice the action in the story. Focus on the verbs used such as: find, buy, receive, get, collect, come, join, etc. Click here for a FREE copy of my Addition Story Actions chart  (See picture below). Start a list in your class and add to it whenever you find more examples. 

Here’s an example of result unknown:  a + b = ____.  There were 4 birds in the tree. Then 3 more joined them. How many birds in the tree now?

  • Who is this story about?  birds
  • What is this story about? some birds join some other birds in a tree
  • How many birds were at the start of this story?  4
  • Do we know how this story changed? Yes, some more birds (3) joined them.
  • Join means to add them together.  4 and 3 = 7.
  • How many birds in the tree now? 7
  • This makes sense because if we have some, and some more join them, then we will have more than we started with.

Other questions could be:

  • Is 4 all of the birds or part of the birds? part
  • Is 3 all of the birds or part of the birds? part
  • When we know both of the parts, we can add them together to find the total / whole amount.

Using a picture workmat, 10 frame, or graphic organizer, students of different levels can solve this problem. For primary students, start off with manipulatives first before going to a pictorial representation. Keep in mind the CPA progression of developing understanding in math (Concrete, Pictorial, Abstract). Increase the numbers for higher levels, but the process is the same. See examples below.  Here’s the FREE Part-Part-Whole Boxes template.

Repeating these same questions over and over again will allow you to scaffold the students’ learning so they are gradually thinking of those same questions in their mind. With all good intentions, many primary teachers focus on the key words in all and tell children to add when they see those words. BUT, those same key words can appear in a story which requires multiplication (There are 5 pizzas. Each pizza has 10 slices. How many in all?)  How many students do you think will add 5 + 10? Probably a lot because they had been drilled with key words.

So my advice is to focus on who and what — and put more emphasis on the verbs / action in the story than the key words.

Here’s an example of a change unknown / missing addend type:   a + ___ = c  There is a plate of 8 cookies in the kitchen. Mom added some more to the plate. Now there are 10. How many cookies did Mom add to the plate?

  • Who is this story about?  Mom
  • What is this story about? cookies on a plate
  • How many cookies were at the start of this story?  8
  • Do we know how this story changed?  Yes, mom added some more
  • Do we know how many total cookies are on the plate? Yes, 10
  • When we know one part and the total (whole) amount, we can add up or subtract to solve.  8 plus how many more give us 10?  or 10-8 = 2
  • Let’s check to see if it makes sense: If there are 8 cookies on the plate and mom puts on 2 more, would there be 10 cookies on the plate now?

Other questions could be:

  • Is 8 all of the cookies or part of the cookies? part
  • Is 10 all of the cookies or part of the cookies? all
  • When we know one part and the total (whole) amount, we can add up or subtract to solve.

Here’s an example of a start unknown / missing addend type:    ___ + b = c.  Some crayons were in my box. I found 5 more and put them in my box. Now I have 8  crayons all together. How many crayons were in the box to start with?

  • Who is this story about?  Me
  • What is this story about? crayons
  • Do we know how many crayons were at the start of this story?  No
  • Do we know how this story changed? Yes, I found some (5)
  • Do we know how many total crayons are in the box? Yes, 8 are in the box.
  • When we know one part and the total (whole) amount, we can add up or subtract to solve.  What goes with 5 to make 8?  or 8 – 5 = 3
  • Let’s see if this makes sense:  If I had 3 crayons in my box to start with and I found 5 more, would I have 8 crayons all together?

Other questions could be:

  • Is 5 all of the crayons or part of the crayons? part
  • Is 8 all of the crayons or part of the crayons? all
  • When we know one part and the total (whole) amount, we can add up or subtract to solve. 

This is also a good time to reinforce the meaning of the equal sign.  It means “the same as.”  The amount on one side of the equal sign must be “the same as” the other side of the equal sign. All too often, students think the equal sign means “the answer goes here.” This is why they typically add  a and c together in the second example and put 18 in the blank. Or in the 3rd example, they add 5 + 8 together and put 13 in the blank.  This is why it is good to vary the location of the blank, so they don’t get too complacent and think they should follow the sign with the 2 numbers available.  Think of the equal sign as a balance scale.

Happy problem solving! Next week will be another type (Separate aka “Some, Some Went Away”).

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