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

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. Continue reading

# Making Sense of Division (3rd-5th)

Is division a dreaded topic on your list of objectives to teach? Like many math topics, students have a harder time understanding it most likely because it’s not something they use regularly in their lives. Students should understand why division is useful before they have to start solving division problems. In this post, I will focus on helping students see the relationship between subtraction, multiplication, and division both with concrete objects, pictures, and the partial quotients model. Freebies available below!!

Then let’s talk about what division really is — it is repeated subtraction; much the way multiplication is repeated addition. The issue is that repeated subtraction is not always very efficient. Here’s what I mean.

Let’s say I have the basic problem 25 ÷ 5.  I could start with 25 and then subtract 5, subtract another 5, another 5, another 5, and another 5 until I run out and reach zero.  I would have to do this 5 times. If I had 25 cookies that I wanted to share equally among 5 friends, I could do the “one for you, one for you, one for you, one for you, and one for you” process and still end up with 5 cookies for each. Or I could try “two for you, two for you,” etc. to make the action of passing out the cookies faster. When I get down to 5 cookies, I return to the “one for you . . .” to make it work.

With a larger problem such as 72 ÷ 6, I can again try subtracting 6 at a time until I reach zero. This would take 12 repetitions — not efficient, but still accurate. Could I subtract 12 at a time instead (2 groups of 6) to be more efficient? Or 18 at a time, or 24 at at time? This is the idea behind the partial quotients model I will refer to a little later. Continue reading

# Using Color Tiles to Measure Area of Irregular Shapes

by C. Elkins

I have heard from a few 4th grade teachers that a new standard is difficult for their students to grasp. It is 4.GM.2.2: Find the area of polygons that can be decomposed into rectangles.

I have a couple of suggestions which help students with a concrete-pictorial-abstract progression approach to this problem (which is more developmentally appropriate).

1. I have attached an activity which involves the use of 1” color tiles to partition off irregular shapes and then determine the area of each smaller rectangle. It’s free and in 2 parts:
2. I located an excellent reference which shows pictorially how to do this step-by-step. It also includes good information about perimeter. It is:  Area and Perimeter