From real objects in the physical world, to quantitative pictures, to story mats and acting out problems, each step in the developmental journey takes our littles closer to confidence in the word problem solving process. Each step is important so that we help them arrive in the proper way instead of trying to force application of word problem skills too soon.
As we take this next step in the developmental journey, concrete, pictorial and abstract means still anchor the child’s mathematical understanding as they work with a blank math work mat to act out problems using items from the Math Salad Bar. The more practice a student has with understanding word problems as they’re being applied in the pictorial and abstract means, the better off they are.
To help students take the next step of their word problem solving, we’ve created the My Math Word Problem Journal, which is developmentally appropriate for Kindergarten students at the end of the first semester or the beginning of the second semester.
This journal contains 75 days worth of journal experiences that reinforce concrete, pictorial, and abstract means and helps students slow down through the various types of word problems. We begin with part-whole addition problems, move into subtraction, and finally missing addend problems. It helps students turn the corner in their early childhood experience to prepare them for what word problems will start to look like as they get older.
Setting the Stage
In the corner of each journal page is an image that will relate to the story problem. This helps students hold a concrete image in their head as they work with all the other abstract things (writing and number sentences) on the journal page that might not be as familiar to them. Additionally, we are still building oral language, so if students aren’t as familiar with one of the objects, they can use the story they’re reading to help them picture what might be happening.
Read the Problem
Begin by reading the problem out loud – all of it, without stopping. After this, most students will want to jump right in and fill in the number bond, or start acting it out with concrete objects. They’ll grab the two numbers in the problem and, because we’re adding this week, they’ll add them. Or subtract them, or whatever we’re working on. However, we don’t want kids to look at story problems as things to be dissected – “circle the numbers” and “underline the important words,” etc. because that really in the end isn’t always going to work for students at this age.
We really want them to slow down and engage with the problem using something called chunking. Chunking has students put a line or highlight or underline a section in the story problem that is bringing in some new information. Even though kindergarten students might not be able to read the word problem themselves, we do want them to get into the habit of “reading” the problem, interacting with the words in the story, and repeating back different parts of the problem. It slows them down enough to really comprehend and visualize what the problem is asking, just like we do in reading. The same process we use for reading a book and trying to understand the author’s message holds true for reading story problems.
Let’s take this problem:
We could chunk our example by saying, “John made a paperclip chain.” And then the students repeat that back. Now you say chunk because there’s a new piece of information within that story problem that we just read. The next part says he put on five paper clips. chunk The kids repeat that section back. He added on three more paper clips chunk. How long is John’s paper clip chain now? chunk
The hard part about doing story problems in a slow, methodical, repetitive way, even though we know it helps build kids’ skills, is that students really want a quick and easy way to solve the problem. Spending a lot of time really looking at that story problem and getting that frame of reference using our template will be really helpful to our littles in kindergarten.
The second step in our step-by-step visual model process is to create a sentence form. In the kindergarten journal, we provide the sentence form since we felt that putting the question and a complete answer might be a little bit too difficult for some
For our example, our sentence would be, “John has ___ paper clips on his chain.” When we read the sentence form out loud and get to the blank, we usually say “hmm” and maybe shrug our shoulders because that’s the part we know we’re going to be solving for.
In Kindergarten, it’s really important to make a note of this sentence form because, as students get into 1st grade, they’re going to start to do more closed sentences with more blanks that require students to supply names and other information. By the time a child gets to 2nd grade, they should be able to read a story problem and be able to repeat back in a complete sentence exactly the way the problem is asking.
Some people ask why we would bother putting the sentence form in a Kindergarten journal. It all goes back to wanting to really slow the students down and keep them from jumping right into numbers and operations. Having students work with the sentence form encourages good decoding and reading skills as well, and guides students in their understanding of what the problem is asking. Also, I’ve seen many students solve story problems, but then forget to write in the sentence form, so a sentence form is a really great way to help train students’ brains so that when we get that final answer, it is going into the blank, which will complete the thought.
Math Mat & Quick Draw
Whether you use our horizontal or vertical math work mat, maybe a dry erase board or a purple piece of construction paper, this step is all about concrete tools. The student can go to the Math Salad Bar and choose manipulatives they can use to act out our story problem. They might get five of something, then show three and then count them all together to show how many paper clips John had.
Eventually, students will work more in the Quick Draw Box. We’ve made this section a little bit smaller in this journal because we want students to truly make it a “quick” draw using Xs or dots or something else small to represent the quantities in the problem. In our case, the students might do five large Xs, three small Xs, and then count them all together. ’
It’s very important for students’ mathematical understanding to keep things organized when we’re counting. We don’t want to always be one-to-one counting, so we use a 10-frame to guide us here. Students can use pencil, crayon, marker, or anything else to fill this in. I might choose five red circles for the large paper clips. Then I can represent the three remaining paper clips with blue circles. The idea is, when you look at that 10 frame, not only can you find the answer, but you also see it in an organized way based on what the problem is asking. Over time, we want the quick draw to be more organized as well
This next representation is what students are really learning a lot about in Kindergarten – part/part/whole. The number bond helps students visualize the relationship between those two numbers. In this case, the student fills in the two parts, the two bottom spokes, with 5 and 3, and then shows the total of 8 in the middle. The number bond would read 8 on the top, 5 on the bottom and 3 on the other side to complete the thought.
Number bonds lead into the algorithm where students can show their computations. This is the part they usually want to do first, but we’re only just now getting to it as we follow this developmental process.
We’ve given lots of thought to each part of the journal page so far, and this algorithm should be no exception. It would be easy to just grab the numbers out of the problem and plug them into the slots and call it good. But let’s start with that first box. In our word problem, we started with the 5 large paper clips and now we need to change that number in some way, whether we add or subtract. In our example, I’m going to be counting up the chain, so I know we need to put a plus sign in the circle. I write the 3 in the other square, because I’m changing the original number by that many. The equal sign is in another box to the right, and finally there is a place to write the total.
Every journal page takes students through this entire process, so by the end of 75 days, it should be ingrained in their brains! This will help our Kindergarten littles as they head into 1st grade, where they’ll continue to build on higher levels of understanding.
Types of Problems
We have three different videos to help you to see the different types of problems that can be solved. We also use a coding system on all of our journals to help teachers understand the different types of problems that we’re using. For this journal, we have PWA (Part-Whole Addition), PWS (Part-Whole Subtraction), and PWMA (Part-Whole Missing Addend).
My Math Word Problem Journal - Part-Whole AdditionThe Math Word Problem Journal is an introduction to word problems for Kindergarten students that brings words and numbers to life with concrete, pictorial and abstract means. This video shows how to use the journal and walks through all the steps to solving a part-whole addition problem.
Get the free download and read the blog post:
My Math Word Problem Journal - Part-Whole SubtractionThe Math Word Problem Journal is an introduction to word problems for Kindergarten students that brings words and numbers to life with concrete, pictorial and abstract means. This video shows how to use the journal and walks through all the steps to solving a part-whole subtraction problem.
Get the free download and read the blog post:
My Math Word Problem Journal - Part-Whole Missing AddendThe Math Word Problem Journal is an introduction to word problems for Kindergarten students that brings words and numbers to life with concrete, pictorial and abstract means. This video shows how to use the journal and walks through all the steps to solving a part-whole missing addend problem.
Get the free download and read the blog post:
Why do we code problems for students this young? To a parent or teacher, or even a student, It might feel like there are endless types of story problems. But in fact, we actually have families of story problems, like we have genres of books. Coding the story problems compartmentalizes these different types of story problems. If we are very clear on the type of story problems, we can help students understand the characteristics of the types of problems they will encounter so that problem solving isn’t so scary.
Part-whole problems are the first genre of story problems, and K-1 graders spend a large majority of time working in this group. However, there are lots of different types of part-whole problems – part-whole addition, part-whole subtraction, part-whole missing addend, etc. The next family of problems are the additive-comparison problems, which students will get to later in 1st grade.
In the bottom right-hand corner of each page, there is a number, up through 75. You can download the PDF, print it (or have it printed), and staple it together to make a journal for an individual student. They write their name on the front and it becomes something they work on every day, four or five days a week. Of course, we still do our number talks in the classroom, but this way we make sure we’re bringing our numbers into words and words into numbers on a daily basis as well.
Mix It UpIf you didn’t feel like going through the journal template on a particular day, you could mix it up a little and give a child an algorithm of 5 + 3, let’s say, and have them create their own story that might go with it! Obviously they aren’t going to be able to write the whole story, but they could certainly share out with the group a story that they came up with.
It’s a really important skill for a child to be able to construct a story problem based on an algorithm or even a missing addend. Let’s take: 4 + ? = 7 If I gave a student that problem, could they think of a story that goes with that? Maybe there were 7 sheep on the farm, but only 4 of them were in the barn. How many were outside? This type of thinking really works on Math Practice 2, which is to which is reason abstractly and quantitatively, to help bring numbers and words together.
Join us next week to find out what problem solving should be looking at with a child after the Kindergarten year. We’ll be working on taking our quick draw into a proportional visual model, and then into a non-proportional visual model.