Month: October 2018

Math Problem Solving Part 4: Equal Groups Story Problems

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by C. Elkins, OK Math and Reading Lady

Are you ready for a way to help students solve multiplication and division word problems? I have developed a template that will help students record the given facts and think through the process involving equal groups. There are 3 basic types of equal groups problems:

  • # of groups and # in each group are known
  • # of groups and total are known
  • # in each group and total are known

Pictured here is an illustration of the strategy which can be used for multiplication and division problems. Get my FREE packet right here: Equal groups strategy with template.

One of the most important steps I recommend when working with equal groups problems is for students to brainstorm things that typically come in equal groups. There is a great book titled “What Comes in 2’s, 3’s, and 4’s” which can set the stage. It’s a picture book, but helpful to get kids’ brains warmed up.  Here are some visuals I made to illustrate the point. Click here for your FREE copy. They are included in this set of Equal groups pictures and list template

Kids may need your help to think of things to add to the list. See some hints below. This template and a full list is included in the above FREE download. Continue reading →

Math Problem Solving Part 3: Comparing problems

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by C. Elkins, OK Math and Reading Lady

Solving comparison problems involves a different thinking process than addition or subtraction problems. In my previous posts Math Problem Solving Parts 1 and 2, I focused on addition and subtraction problems in which I advised students to think of the verbs used (found, bought, earned, spent, lost, gave away, etc.) to help visualize what is going on in the story.  In comparison problems, there are no additive or subtractive processes present – just analyzing which has more, which has less, and how much more or less one amount is compared to another.

I love using a double bar method for comparison problems. It can be represented with manipulatives for a concrete experience (ex: connecting cubes, tiles) or with a drawing of two rectangular bars for a pictorial representation. These two visual models provide students with the concept of comparison — they can see right away which has more, which has less. Then the information can be used to compare the two amounts. Look for the FREE resource at the end of this post.

With manipulatives:

I recommend the use of manipulatives when dealing with students’ first experience with comparison problems. Dealing with quantities less than 20 make using manipulatives manageable. I will show this in a horizontal format, but it can certainly be done vertically. You can also apply this quite well to graphing problems.

Problem:  I have 12 crayons. My friend has 8 crayons. How many more crayons do I have than my friend?

  1. Determine that this problem is not an addition / subtraction process (because no one is adding to what they have and no one is giving away what they have), but in fact a comparison problem.
  2. Be cautious about focusing on the question”how many more” and telling students that when they see this they need to subtract. When we tell kids to focus on the specific words in a question with a “rule” for adding or subtracting, they start to lose sight of the actual story.
    • Consider that this question can also be used with a SSM (some and some more) story which is not a comparison problem:  What if it read: “I have 8 nickels. I want to buy a candy bar that costs 80 cents. How much more money do I need?” This story means: I have some (40 cents) and I need some more (?) so that I have a total of 80 cents. This is a missing addend or change unknown story: 40 + ___ = 80.  Even though it could be solved in a similar manner as a comparison story, we want students to be able to tell the difference in the types of stories they are solving.
  3. Determine who has more (represented by yellow tiles), who has less (green tiles).
  4. The crayon problem can be solved by lining up 2 rows of manipulatives (pictured):
    • Notice the extras from the longer bar. Count them (4)., or
    • Count up from 8 to 12 to find the difference.
    • Even if the question was “How many fewer crayons does my friend have?” it would be solved the same way.

With pictorial double bars:

Problem Type 1 (Both totals known):  Team A scored 85 points. Team B scored 68 points. How many more points did Team A score than Team B?

  1. Determine this problem is not an addition / subtraction process (because the teams are not gaining or losing points).
  2. Ask “Who?” and “What?” this story is about:  Team A and B and their scores.
  3. Draw double bars (one longer, one shorter) which line up together on the left side.
  4. Label each bar (Team A, Team B).
  5. For the team with the larger amount (Team A), place the total outside the bar (85).
  6. For the team with the smaller amount (Team B), place the total inside the bar (68).
  7. Make a dotted line which extends from the end of the shorter bar upward into the longer bar.
  8. Put a ? inside the extended part of the longer bar. This is what you are trying to find.
  9. To solve, there are 2 choices:
    • 68 + ____ = 85     This choice might be preferred for those with experience using mental math or open number lines to count up.
    • 85 – 68 = _____

Continue reading →

Student Engagement

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by C. Elkins, OK Math and Reading Lady

Student engagement is a huge concern among most (if not all) educators. This means students are actively involved in the learning process. Research definitely supports the notion that higher incidents of engagement result in increased achievement (Marzano, etc.).  Attached is my guide to student engagement strategies for reading / ELA lessons.  Many of these strategies also will apply to math, social studies, or science lessons.

Click here to get my guide:  Student Engagement – Whole Class Reading

Math Problem Solving Part 2: Separate (aka Some, Some Went Away)

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by C. Elkins, OK Math and Reading Lady

In the previous post, I addressed problems dealing with an additive process (join; aka SSM).  In this post, I will show you some models to use for these types of problems:  Separate; aka Some, Some Went Away — SSWA.  I will share some models which are great for KG stories as well as templates that are helpful for intermediate students to use, especially when dealing with missing addend types.

As I previously mentioned, it is my belief that students should focus more on the verb / action in the story and not so much with the key words we often tell kids to pay attention to. Brainstorm actions that signify a subtractive process.  Post it in the class.  Keep adding to it as more actions are discovered. With this subtractive action, kids should quickly realize that there should be less than we started with when we take something away. Here is a FREE poster showing some of the most common subtraction action verbs. Click HERE to get your copy.

Some of the work mats pictures below come from the following source. These are great for KG-2nd subtraction storytelling.   Subtraction Pack: A Pinch of Kinder by Yukari Naka

Like with all story problems, I model how I reread the problem several times.

  • First read — Just read it
  • Second read –Identify who and what the story is about (the action).
  • Third read — Decide what to do with the numbers. Is a given number the whole / total amount or part of the amount? Do I know how the story started? How it changed? The result?

Here are 3 types of subtraction story structures: Continue reading →