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 find all the ways to break apart numbers. /I can show what happens in a story problem and solve.
Extension Activity: Make or Break Numbers / Label Story Problems
In episode 307, students will use their journal template that we’ve featured in past episodes, however, in this episode, we’re going to be really focusing on subtraction. We want to show kids that they can do subtraction with concrete tools, show it in a quick draw, use a 10 frame to show subtraction, and then see how you go about creating a number bond with subtraction and the computation that goes with it. Students should have a good understanding of this, as we’ve done it in past shows, so, at this point, we are fluidly using all of those processes with subtraction.
The “I Can” statement is: I can find all the ways to break apart numbers. We’re going to use D.C. here and see if kids can notice if one of the combinations is missing from a set. Obviously you could look at this in an expression and see if I came up with all the combinations for nine. Another way that I like to do it is for students to see the combinations within a number bond. They can look at the collection of number bonds and see if one is missing. In the show, we analyze a student that thinks they’ve come up with all the combinations to nine, but we use the process of elimination to discover that they’re actually missing one.
This also looks at that idea of the flip flop fact, if you will, where kids can see that 9 = 1 + 8, but also, 9 = 8 + 1. We want kids to include all of those facts, so we use D.C. and the Counting Buddy Sr. to show this. A great way to use the Counting Buddy Sr. is to push 10 beads towards his head and 10 beads towards his feet. This way, when you draw the beads into the middle, the colors will match the combinations. If I want to show nine, I could pull four beads to the middle and then five beads of another color. When kids look at it, they will see four and five equals nine.
We continue with combinations by playing a game called Make or Break Numbers, where students draw a card, and then have to put their counter on two number scatters that would total that number. If they drew the number seven, they have to be able to look at different configurations – five frames, dice pattern, or a domino format – and figure out which two numbers would end up making the seven. They might put a counter on a two that looks a lot like a dice, and maybe the five that’s also arranged like the dice.
We want students to really understand and see the patterns, which will help them create combinations more easily. If I have 0 + 7, 1 + 6, 2 + 5, 3 + 4, etc. you can see on one side, the numbers are counting up. On the other side, they’re counting down. We use a really great visual on the show to help kids understand this pattern, and then they get an opportunity to play Make or Break Numbers in the extension activity.
In Kindergarten 308, we continue with Professor Barble and another subtraction problem. Pro Tip: Have your students watch the first show (307) early in the week, then, they can try working through the problem in 308 a little bit more independently.
The I can statement is: I can show what happens in a story problem and solve. We give a scenario of a market, and Elena is shopping at the market with her grandfather. She chooses to buy some mangoes, and her grandfather chooses to buy some pineapples. How many pieces of fruit did they buy? A lot of times kids just appeal and ask for your help to get the idea of how to do word problems before they even think about it. We want them to slow down and pay attention to details! What do you notice and what do you wonder about that story problem?? We didn’t give any quantities! How are we going to solve it without quantities?? This gets students’ inquiry-based thinking going and then we give them an actual story to go with that scenario. Elena chooses four mangoes, her grandfather chooses two pineapples. NOW, How many pieces of fruit did they buy?
We also focus on drawings in this episode to see what else can we add to a drawing to give more detail. So, for our initial scenario, if I were to show four counters, draw a partition line, and have two more counters, does that depict the story enough? What if I drew four circles, a partition line and then two more, but above the four I wrote an M to represent the mangoes, and a P above the two to represent the pineapples? We want kids to be able to add more details to their organized drawings. We do a couple different examples with a bear eating blueberries and raspberries. We add more details to the drawing by labeling the B above the blueberries, adding that partition line, and then putting an R above the raspberries.
Giving kids the opportunity to really look at how to label that organized drawing is really important! In our extension activity, we have a few problems that someone can read to the students and they can pick out which drawing with the label matches that word problem. This really helps kindergarteners to attend to detail and slow down a little bit as they’re starting to look at different word problems.
“I Can” statement: I can add one-digit, and two-digit numbers to make an equation. / I can add one digit, and two digit numbers, and an equation.
Extension Activity: Closest to 95 / Closest to 95 (lower starting number)
In episode 307, we are continuing with a Professor Barble warm-up, but we’re using a non-proportional manipulative. You’ll also notice that we’re starting to scaffold away by not always including that sentence form. We’ll have more blanks in the sentence forms, and we’re also using a little bit higher numbers to continue to challenge our first graders.
In this subtraction problem, we don’t want kids to just guess and check. You’ll see that we use a number word instead of the actual numbers so that kids have to really pay attention to the details. They couldn’t just grab the two numbers and add or subtract.
The “I Can” statement is: I can add one-digit, and two-digit numbers to make an equation. 45 + ? = 50. At the beginning, we use 10 frames to get kids to understand this. We build 45 on 10 frames, which gives us four full 10 frames with five in another. How many more would it be to get to 50? The idea here is to give kids a visualization of 45. Instead of counting up by ones to get to 50, could I visualize five 10 frames with only 45 in it? It makes it a lot easier to figure out how to make that equation true by adding in the five. We do another example with 38 + ? = 40. Again, we build 38. We use 10 frames in the show, but you could also use an abacus to help kids see that it only takes two more for them to get to 40.
We also talk about the idea of decomposing using the 10 frames again. We have 34+ 9 and D.C. comes into play again to help us decompose and add by making the friendly decade number. This is something that students just will need a lot of practice with!
We play a game called Closest to 95, where students start at 55, they take turns drawing cards and adding that amount on, and try to see who can get to 95 first. In the extension activity, kids get to play this game with a partner. This really helps because, as you’re adding on numbers, can you decompose and make that next decade, and then add on a bit more to make it easier? Kids start to be able to do some of these strategies a little bit more independently as they start to have more practice with it.
In show 308, Professor Barble helps us look at the idea of missing addends. If we have a total and a part, can we figure out the other part? We have a visual model written out, but we have more pieces missing from the sentence form, so kids have to really pay attention and put in those details and label correctly.
The “I Can” statement is: I can add one digit, and two digit numbers, and an equation. We give them four equations to look at, 7 + 9, 22 + 5, 32 + 8, and 44 + 8, and we ask which one doesn’t belong? We want kids to do an analysis of each of those four problems, and maybe figure out a reason why one of them, or all of them, might not belong. Maybe only one problem is adding a single digit plus a single digit, so 7 + 9 might not belong. Another student might say, when you’re adding these together, everything has to make a new 10 except for 22 plus five. This kind of inquiry is a really great way to get kids to attend to precision and come up with their own formulations of why a certain problem might not belong.
The focus in this show is seeing, when we’re adding a single digit plus a double digit, does it make a new 10 or not? Not necessarily do we regroup? as you think of with T-Pops. For example, if I’m going to add 9 + 63, am I going to make a new 10? Well yes, nine is one away from 10. And if I’m adding it to 63, it’s going to make a new 10. But what about if I added 26 + 3? Is that going to make a new 10? Well no, because I’m not going to cross over into that decade of 30. This helps kids start to think about when they’re making a 10. I think sometimes kids use D.C.’s strategy and they just decompose numbers for the sake of breaking it apart. However, we don’t want to forget the other part of D.C. – he likes friendly numbers! We want students to remember to see if they’re going to make a new 10 or not.
The other thing that happens in the show is we have an algorithm where water has been spilled on one part of the problem! This game of Splat! really requires kids to use their number sense. I have 32 + SPLAT! There’s a splat over the second number so we can’t see what it was! But I can tell you it was a one-digit number and it made a new 10. There are multiple possibilities here – it could be an eight or nine in order for it to make a new 10. It can’t be a one because 32 + 1 doesn’t make a new 10. It couldn’t be a 2, because 32 + 2 doesn’t make a new 10. I love this activity to get kids to extend their thinking and apply their number sense.
In the extension activity, we played Closest to 95 again, But in this case, the kids start at a lower number of 25, and they get to decide when they pull that card, do they want to add 10s, or do they want to add ones when they do it? That’s a really great way for kids to apply that concept of place value as well.
“I Can” statement: I can sort and name shapes based on their sides and corners. / I can find and draw shapes with specific sides and lengths
Extension Activity: What Shape Am I? / Draw Shapes with Attributes
In episode 307, we do a word problem with Professor Barble where students look at pennies. We do an additive comparison problem, solving with a little bit higher numbers, as we have 37 pennies, and Blake has 55 more pennies.
After the warm-up, however, we completely switch gears in this set of shows away from place value and into shapes. The “I Can” statement is: I can sort and name shapes based on their sides and corners. We get the kids engaged by looking at two sets of shapes, one that has three corners and three sides, where the other set of shapes has multiple attributes. We want kids to notice those attributes by studying a non-triangle versus a triangle.
We do a really fun sort in this episode. Based on what they learned in first grade, I think a lot of second graders think a triangle always looks the same, a pentagon always looks the same, a hexagon always looks the same. In this sort, we focus on the attributes of shapes to help kids realize that, while a triangle has three sides and three corners, it doesn’t always look like a perfect triangle. A quadrilateral has four sides and four corners, but it can be a square, a rectangle or any other shape with four sides and four corners. The same goes for pentagons and hexagons. We play a game called Penta-What? to help kids understand this idea. In the game, we have a secret shape they have to guess and they can ask yes or no questions to narrow it down.
We also talk about shapes that are not shapes, and the idea of a “closed” shape. Or when we have things that don’t necessarily create either a triangle, a quadrilateral, pentagon or a hexagon. For the extension activity, kids are given more irregular-looking shapes and have to decide if it is one of the four shapes that we’ve been working on.
As we move into show 308, we’re going to do a Professor Barble problem again, where students are going to see if they can figure out a part-part-total problem that is worded a little bit differently. Mr. Arnold has a box of pencils. He passes out 27, and has 45 left. How many pencils did he start with? Some kids might think that they’re starting with 45 and subtracting, but they really have to listen to the details and look at the way that this visual model is described to be able to solve it correctly.
We continue with shapes and the “I Can” statement: I can find and draw shapes with specific sides and lengths. Getting kids to draw shapes, as you know, is quite difficult, and it’s a bit hard to show that in our show because we don’t have actual students, but we’ll give you the elements to work on!
We begin with a “Which One Doesn’t Belong?” exercise to get kids into the mindset of shapes. We want them to estimate, based on a description, what shape someone drew. Diego drew a shape that has fewer than five sides, two sides are three centimeters long, which shape could Diego have used? There’s a picture of a rectangle, a triangle, a hexagon, and a square. Students can think through the elimination process – If it only has five sides I can eliminate the hexagon and then bring back in some of the parts of measurement.
If we had been doing these shows throughout the entire school year, kids would have already done centimeters and meters, so we bring in some rulers here to get kids to look at the attributes of different shapes. How many sides? How many corners? How many inches are the side lengths? We also talk about the idea of square corners, not necessarily about making a 90 degree angle yet, but the idea that some corners are perfectly square and some aren’t.
We have fun drawing different shapes in an activity where they have a table with a certain number of sides to pick from: three sides, four sides, five sides, six sides. We can create corners of three, four, five and six. We can describe the length – do you want one side to be two inches, two sides to be two inches? And then how many square corners – zero square corners, one square corner, two square corners, or all square corners?
The fun discovery here is that, when you don’t have an even number or the same number of sides and corners, you might make a shape that isn’t a shape! We kind of talk about that concept a bit, and then for the extension activity, kids have to figure out What Shape Am I? They’re given the attributes of a shape, and they have to figure out what shape is being described.
“I Can” statement: I can name parts of a whole. / I can use fractions to describe parts.
Extension Activity: Name the Parts of Fractions / Describe the Parts of Fractions
In episode 307, students here are working with Professor Barble again with a problem where we’re using division. In these division problems, if you pay close attention, we’re going to be using kind of this “…” or “groups unknown”. Students are looking at someone having 36 balloons and they want to give each person four balloons. Well I don’t know how many people will be, so there’s a “…”, meaning that they’re going to take that bar, which is a total of 36 and chop it so that each person gets four. This kind of problem is a little bit harder for third graders sometimes, because we don’t give the number of groups. I didn’t say we want to take 36 balloons and divide them among a certain number of people. Instead, you have to figure out that result unknown.
In third grade, we’re now moving into fractions! We spend quite a few shows on fractions, which I’m really excited about. The “I Can” statement is: I can name parts of a whole. To get kids thinking, we give four options and they have to figure out which one doesn’t belong. Again with this kind of activity, there’s a descriptor for each of the four images as to why they might not belong, depending on the reasoning the child uses. Some of them are not partitioned equally, and so we talk about this new word partitioning which really means to split into parts. Yes, things can be partitioned, but are they always partitioned into equal parts? Kids are given a variety of images to sort based on how they are partitioned, some are non-equal parts, and some are equal parts, and this also helps give kids that language to use. And then, of the shapes that are partitioned, even if they aren’t equally partitioned, we sort them into the number of parts, two parts, three parts, and four parts.
Then we give kids the opportunity to partition rectangles. We wanted this to be hands on, so kids could do this at home with a post-it or a 3×5 card and see if they can partition a rectangle four different ways.
The main focus in third grade is to be able to understand that three equal parts equals thirds, four equal parts equals fourths, six equal parts equals sixths, and then eight equal parts equals eighths. Kids really practice with this idea in the extension by reading and writing fractions based on how many equal parts they have in order to apply this concept.
In episode 308, we continue with Professor Barble doing our visual model warm-up. In this one, we have 24 people lined up to go in canoes. Each canoe will have three people in it. How many canoes will they need? Again this is the “groups unknown.” The total bar is going to equal those 24 people, we’re going to break that bar into groups of three, but we don’t know how many groups of three are in 24. so we kind of put that “…” there. There are some really great examples in these visual models to help third graders with this idea!
The “I Can” statement is: I can use fractions to describe parts. We have another Which One Doesn’t Belong activity looking at parts that are divided equally vs not, and we have students look at horizontal partitions versus vertical partitions. We want students to see things in different ways to see how fractional parts are made up.
In this particular episode, we make fractions strips, which are a really great tool that anyone can use. It’s just pieces of paper that we encourage kids to keep in an envelope to pull out during this unit.
Remember that the fraction strips are labeled with the actual unit on them, and so in some ways kids might guess and check with this. We take a whole and split it in half. If you fold the halves in half, it’s going to make fourths. If you fold the fourths in half, it’s going to make eighths. Same thing if you took a piece of paper and a strip and fold it into thirds, and then folded it in half again, it’s going to make sixths.
As the extension activity here, students are going to make those fractions strips on their own to keep. This tool will be GREAT for students to have available to help them during this fractions unit!
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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