February Focus: Word Problems
In these warm-ups, we’ll use a step-by-step visual model process, which will vary slightly depending on the grade level and what type of problem that we’re working on. Professor Barble helps students slow down, think about what the word problem is asking, and organize the information it conatins before they jump right into solving it. Yes, we even do this in Kindergarten! See sections below for more specific information about how word problems and model drawings are used in each grade.
“I Can” statement: I can solve word problems with both addends unknown. / I can solve word problems more than one way.
Extension Activity: Solving Word Problems
In episode 309 for Kindergarten, we warm up again with Professor Barble, looking at a word problem using our Kindergarten Journal. We want to see if students can do a quick draw, fill in the 10-frame, complete a number bond, and finish the number sentence. We take students through the step-by-step process on a very appropriate Kindergarten level to prepare them for what first grade is going to look like.
In the main part of the show, we start by looking at four different images created with linking cubes and two-sided counters and asking which one doesn’t belong? Javier and Miguel have a variety of different reasons for why they think each image might not belong. Some images are just in one color, some have two colors. In some, the total is five, but one is six. Asking inquiry-based questions really helps students go deeper with images like this.
Then, we look at different ways of breaking apart six, using different math tools to show the combinations. We have three and three, one and five, two and three, five and one and then two and four.
Next, it’s time for a treat! Paletas are a popular frozen treat in Mexico which are usually made with fruit. They look a lot like a fruit bar that you might see in the frozen section at the grocery store. When we do story problems like this, we really want kids to dive in and experience that real world connection. In our story, Jaida and her brother make six paletas. They made two different flavors – lime and coconut. How many of each flavor did they make? Well, the hard part here is that there are a lot of different possibilities! They could have made five lime and one coconut. Or maybe they made one lime and five coconut, and so on. We want kids to do a quick draw for this problem that shows a partition line. So if we think Jaida and her brother made five lime paletas, we would draw five circles, draw a partition line, and then one more circle for the last coconut paleta. We even can label those sets of circles to be a little bit more specific.
We practice the same idea with another problem. We bought seven pomegranates. We put some on the shelf and the rest in the basket. How many are in the basket? As we draw circles to represent the fruit in the two locations, we can also add “sh” for shelf and “b” for basket. This problem will help students understand the importance of labeling their drawings.
When it’s their turn for an independent activity, students are going to solve problems like we did in the show where they’re given a scenario and they have to figure out all the ways to come up with the total. They’ll have to break apart the number to come up with all the different combinations.
As we move into episode 310, we do another Professor Barble problem. This time, we are doing a subtraction problem using the same process and journal page. Students will act it out in their math work mat, do a quick draw, use the 10-frame model, complete the number bond and finally, finish that computation.
Our first scenario is pretty juicy! We have freshly squeezed grapefruit juice and freshly squeezed orange juice, and we have some pictures that students have drawn of word problems. What we have to decide is which picture matches our problem. In one picture, we see three orange juice and six grapefruit. Another student shows seven orange juices and two grapefruit. The idea here is to help the kids see that we’re working with the number nine as a total, and that BOTH of the drawings might match the story because we just said that there was a total of nine different fruit juices.
Once we have a total, we can look at all the different possible solutions: three orange juices and six grapefruits, which would be 3+6=9. We also could do seven orange juices with two grapefruits, which is 7+2=9. Showing the different combinations here really helps the students to decompose and understand the number.
Then, it’s snack time and dates are on the menu! Dates come from palm trees and sometimes, people like to stuff them with different things. Andre and his older brother had eight dates to make into snacks. They stuffed some of them with cheese and some with almonds. For this problem, we make a chart that will end up showing a pattern. If we had seven dates stuffed with cheese, then one date would have an almond. And then six and two, and five and three, and four and four – ultimately helping kids see how those combinations can go from one side to the other, creating the pattern.
The extension activity is very similar, just with pets that live in cages vs houses. This will help students be able to decompose numbers in lots of different ways so they can understand the different combinations really fluidly.
“I Can” statement: I can add two-digit numbers within 100. / I can add two-digit numbers by adding 10s and 10s and ones and ones.
Extension Activity: Addition with Value Pak
In episode 309 for first grade, we’re doing a Professor Barble problem using a non-proportional bar. Some frogs were in the pond, three jumped out, and now there are five frogs in the pond. How many frogs were in the pond at first? These story problems can be really confusing if you just start to solve it, but by following Professor Barble’s step-by-step process, students will be able to figure out what it is actually asking. We have a sentence form and a non-proportional unit bar on the journal page, and we are now starting to leave more spaces for students to fill in information from the problem on their own.
The “I Can” statement is: I can add two-digit numbers within 100. We start with the problem 17 + 36. We want students to show their thinking using drawings, numbers and words, and in the show, we wonder together if there’s more than one way to solve this problem. One of the students decides that they can solve this with Value Pak, decomposing by place value, but another student points out that they could also use D.C. and decomposing to make another decade. We go through different ways to solve two-digit plus two-digit numbers using the strategy of D.C., looking at it with place value.
We then play a game called Grab and Add, where each partner grabs a handful of base-10 blocks. They have to determine how many cubes they have, how many cubes their partner has, and how many they have all together. This really highlights the idea of Value Pak and being able to add 10s and 10s, and then ones and ones.
It’s the students’ turn at the end to play a game where they are trying to find the missing number. They’re going to add different pieces to the numbers to determine what the complete sentence is and add the two-digit numbers together correctly.
In episode 310, we continue with Professor Barble. This time, we’re really trying to let go of some of the scaffolds and we’re doing a two-step problem. Ten snowflakes fell on Sam’s mitten, and 6 fell on his coat. Nine of the snowflakes on Sam’s mitten melted. How many snowflakes are left? Multi step problems are often difficult for first graders, so Mrs. Markavich uses two non-proportional unit bars to help us walk through Professor Barble’s step-by-step model drawing process to solve the problem.
The “I Can” statement is: I can add two-digit numbers by adding 10s and 10s and ones and ones. Jose shows his work for 37 + 26. He’s showing it in base-10 blocks and he shows how he grouped the 10s and the 10s together, and then grouped the ones together. We certainly have Value Pak talk about why this is a great way to solve.
We go in depth with the idea of Value Pak by showing how we can decompose numbers, such as 28 + 56, which can be decomposed into 20 + 8 and 50 + 6. Then we can add the 10s and then the ones. We love using Value Pak with this concept, and it’s really important to use place value strips with students so they can understand it visually.
Of course, in the extension activity, we’re going to have students use Value Pak to solve addition problems by adding 10s and 10s and ones and ones.
“I Can” statement: I can identify and describe solid shapes. / I can compose and decompose shapes.
Extension Activity: 3D Match-Up / Describe the Shape
In second grade, episode 309, Professor Barble has a problem for us using a comparison bar. Additive comparison bars are often difficult for second graders. The key is to draw in a line for each character first, and then start to figure out who has more or less. Using Professor Barble’s step-by-step process is a really integral way to help second graders master this concept with harder word problems.
This episode has a classic Math Mights beginning! We show four different images and ask students our famous questions: What do you notice? What do you wonder?
Some of the shapes in the images are flat and some of the shapes are three dimensional. Students notice things like a cube that is made up of a bunch of different squares, a T-shape that is made up of six squares. They also wonder things like how many little cubes make up a big cube? The cube looks a lot like a Rubik’s cube, so they wonder how many cubes or squares might be in there? Then, they talk about the differences between the different shapes and we look at how they are alike, and how they are different.
In the main part of this show, we study attributes of different shapes such as cubes, cones, spheres, cylinders, rectangular prisms, and pyramids. How many faces does it have? How many corners? Does it have equal sides? Does it roll? What does it remind you of? A cone looks a lot like a party hat, a cube looks like a box, a sphere looks like a baseball, and so on.
Then, we talk about what shape is missing. By listing the attributes of a shape and giving different descriptors, we see if students can figure out what parts are missing and what the shape is.
Guess my 3D Shape is up next, where we have a flat shape that folds into a 3D shape, and students have to visualize what it will create. For their extension activity, students will continue matching up 3D shapes.
In show 310, we continue warming up with Professor Barble, again working on comparison bars. This a really difficult concept, but remembering to put in the bars as a starting point and taking time to chunk and check will really help students focus in on what’s being asked.
This is a fun show where we’re looking at decomposing and composing shapes! We present a picture to the students that is made of pattern blocks and ask them: What do you notice? and What do you wonder? Students might notice the different quadrilaterals and hexagons in the different pictures that they’re seeing.
They end up looking at a butterfly made of hexagon pattern blocks, and are asked if they can recreate it without using a hexagon? This helps students be creative and see different ways that they can make a hexagon, such as with a trapezoid, a rhombus, and a triangle. After doing that, we talk about how many different ways you can compose a hexagon with the same pieces or multiple pieces.
Then we look at things that are the same and different using just triangles and squares, and we work on composing three different shapes using two, three or four of the same shape. So with the hexagon, we were using different shapes to create it, but now, can we put three rhombuses together to make a hat? Or can you do four small squares to compose a large square?
We also talk a lot about being able to describe our shapes using a sentence stem: The ___ is made up of _____ _____. For example, The party hat is made up of three trapezoids.
For the extension activity, students will describe the shapes that are created using the same shape.
“I Can” statement: I can understand non unit fractions. / I can build fractions from unit fractions.
Extension Activity: Fraction Match-Up / Secret Fractions
In episode 309 for third grade, we’ll warm up with Professor Barble and one of his word problems. This particular problem will involve more than one step. There are 12 tables in the cafeteria. Five students sit at each of the first 11 tables, three sit at the last table. How many students are sitting at the 12 tables in the cafeteria? Using Professor Barble’s step-by-step process will help students really think through what is being asked. To solve this problem, students could create multiple bars and do it in multiple steps, or they could create one bar where they show all the lunch tables that have five students, and the extra one with three. There are several ways to solve it – multiple steps, such as multiplication and addition or some kids could do a really long addition.
The “I Can” statement is: I can understand non unit fractions. In the previous show, we talked about what unit fractions are, but in this show, we’re talking about non unit fractions, which represent all those fractions that don’t have one as the numerator. We see a square that’s cut into four pieces. In the first image, one piece is shaded, in the next picture, two are shaded, and then three are shaded, and then we have four shaded. What do you notice and what do you wonder? Students are wondering what is happening each time something’s being shaded, and why is one of them shaded 3/4. This begins our examination of non unit fractions as we observe how many pieces are shaded and which one is labeled ¾.
We then look at lots of different things with different shaded pieces. We want students to understand that the number of shaded parts gives us information about the fraction, as does the size of each part. Together, those two pieces of information create the number that’s represented. For example, we have a rectangle that is divided into thirds, but two parts are shaded. So the number of shaded parts is two, the size of each part (going back to that idea of the unit fraction) is thirds. And then the number that represents would be ⅔.
We do this with several different activities, and then we play a fun game called Fraction Match-up, where students have to look at the non unit fraction, and try to match it to the corresponding image. For their extension activity, students also get to play Fraction Match-up with a friend.
In episode 310, Professor Barble has a pizza problem for us! Natalie ordered five pizzas for dinner. Each pizza had eight slices. She and her friends ate 35 slices. How many slices are left? As we know, students that are in third grade really struggle with multi-step problems because you can no longer appeal and say, “Do I add or do I subtract?” because you’ll actually need to both multiply and subtract. Using Professor Barble’s step-by-step process, which is really a reading comprehension strategy, will help students to really uncover what the word problem is asking.
The “I Can” statement is: I can build fractions from unit fractions. Now, we start talking about unit fractions moved into non unit fractions, and we want to see if students can build fractions from a unit fraction.
The beginning part of the show presents two things to start our inquiry. We ask: what is the size of the shaded part of the rectangle? Students see one whole and then another rectangle that is shaded but unmarked or unpartitioned. Here we want students to make estimations and talk about what’s too low, what’s just right, or what’s too high. How would they know that half would be too low? Because the bar is shaded further than half, and obviously the whole entire bar isn’t shaded, so one whole would be too high. Maybe we could break it up into eighths and it might be 7/8.
We play a game called Secret Fractions, where we have a stack of unit fractions, such as 1/2, 1/4, 1/3, 1/6, and 1/8. Then we have a stack of secret fraction cards, which are going to be non unit fractions such as ⅔ or 3/6, and the idea is to build your secret fraction by drawing unit fraction cards. The first person to be able to compose or put together their three secret fractions, wins!
Of course, for the extension activity, the kids get to play Secret Fractions!
This ends the first set of shows that we have created! We have done a solid 16 shows for each grade level so far! After we take a small break, we’re going to continue creating 48 more shows – 12 for each grade level – starting up again on April 5! I sure hope you’ll join us!
M³ Members, want your very own animated Professor Barble to use in your warm-ups? Don’t forget, to download the PowerPoints and save them! He pushes his button, the bar pops out, and your students will be ready to go! Plus, all the work of drawing the visual models is already done for you!
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