term iii math initial plan with comments

7/30/2019 Term III Math Initial Plan with Comments

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Duncan BusserMath Term III Lesson Plan

Writing Multiplication Story Problems

Duncan Busser

Term III - MathMultiplication word-problem lesson planTo be taught: 12/5/12

Pedagogical Focus

I want to see how my third graders do when writing word problems. Of the focuses wehave been working with this term, I mostly want to concentrate on how the third gradersin my classroom make multiplication (or, more likely, repeated addition) relative to theirown understanding. I want to see how they select and use representations of numbers intheir own created word problems and in the classroom with respect to manipulatives andother tools. I want to give them a multiplication problem, and I want to see how theyconvert that into multiplicative problem situation expressed in a representative andrelative in a word problem.

I feel that by describing grouping in units that they select for themselves, they canmake those representations more personal and more relatable and overcome challengesthey may perceive in multiplication as a daunting mathematical concept. They are nolonger doing 9 X 5 = 45, but they are buying nine pieces of candy that cost five centseach. They will be able to tell their peers, for example, that if they want a small handful(nine pieces) of Swedish Fish, they would need to have $0.45 in their hands.

What – I want my students to understand that math is practical, and I want to see themmake math personal through familiar representation. I want to see the students expressmultiplication in other, more relative terms. I want them to see everyday activities,particularly grouping, as practical applications of multiplication. When I teach thislesson, we will be midway through an Everyday Math unit on multiplication, and theywill have started thinking more multiplicatively. My content and process goals are tobuild upon this multiplicative thinking and have the students create their ownrepresentations of math. Given the opportunity to use representations in math, studentswill more completely understand the concepts of multiplication and overcome some of the challenges that they may perceive. In order to reach this goal, I will give the studentsan opportunity to translate number sentences into word problems. I will only work withequal grouping problems because multiplication is still very new to them.

How: In a small group setting, I will model examples of simple word problems that wewill solve together as a whole group. After that, I will give the students a couple of example number sentences that all of us will work together to turn into word problems.Depending on how quickly the group grasps the concept, I will offer the students severalexample math problems that they must first solve, then translate into word problems. Iwill let them know that they may choose to use their math problem any way they choose,and I will prompt them to use the Part-Part-Whole concept creatively and possibly to

have their word problem be such that it is one of the parts that they students are trying tofigure out (How many dozens of eggs do you have to buy to have 60 eggs?).In order to get the students thinking more representationally, I will encourage them to usemanipulatives in every aspect of the lesson. With physical or visual representations infront of them, I feel that they will more quickly and easily adapt to unseen representations

Comment [CE1]: Your pedagogical fobe one of the three listed on the assignmeguidelines. You seem to be getting into thhere..

Comment [CE2]: What are these concneed to focus more on the mathematics hedo students need to understand in order tomultiplicatively? Draw on Chapin and Johclass notes to help you flesh this out so thlesson is grounded in clear mathematical

Comment [CE3]: ?

Comment [CE4]: So this is now a div problem…

Comment [CE5]: This isn’t really a tethink you are trying to say that you want sthink concretely about grouping





of, say, groups of cats rather than groups of blocks. In order to promote individual

thinking, I will give the students a wide variety of manipulatives to work with so thatthey work with whatever tools they are most familiar or comfortable with.By this point in the curriculum, the students will have a basic understanding of partitivegrouping story problems. They have worked with story problems throughout the year as apart of the Everyday Math curriculum, so the tasks are not unfamiliar. I will start off withmodeling, then pass the responsibility of the learning slowly over to the students throughlead group work then independent work. I am a firm believer in inquiry-based learning,so I will not give any written instructions. Instead, I will ask, ―How can we make 3x4 into

something we can look at, even if it is only something we can see in our minds?‖ The

manipulatives from the classroom will be out and available, and I will have charts,scratch paper, graph paper, and a variety of writing and drawing implements. Thestudents are familiar with these tools, and they know that they are allowed to use any toolto solve a problem.

Why: When I was working on my Term II project, my student was what Smith and Smith(2006) referred to as a ―traditional student;‖ when given the task of creating a word

problem for 3x4, she first made up a story that was representative of 8+4. She knew shehad to get to 12, because she knew the math fact 3x4=12, but she wasn’t sure how to get

there. I want to learn how other students fare at the same project.I feel that personal and practical application of learning is by far the most

effective way to teach. When the students can see what they’re learning, they are more

likely to understand it. This is true across the board, and I want to incorporate that into allof my teaching. When teaching about similes in my Literacy lesson, I will have thestudents write similes into their own personal narratives that they are currently writing inLanguage Arts. They will play with magnets in my Science lesson because they are fun,and they will learn what magnets stick to and what they don’t. They might have been told

that magnets don’t stick to all metals, but when they physically try to stick a magnet to a

variety of coins, they can really understand that.I have seen my students struggle with understanding multiplication, particularly

while trying to understand perimeters and areas of rectangles. When they drew out theirown rectangles on graph paper, many of my students understood the concept a lot betterthan when they were measuring printed images or reading sentences describing thedimensions of the rectangle. I want to expand upon their visual thinking, andmultiplication is the easiest way for me to teach that, because I personally came tounderstand multiplication once I put it into visual terms. Understanding the concept of multiplication for me was a real turning point in my understanding of mathematics, and Iwant to see if it does the same thing with my students. Further, with the free use of familiar manipulatives, the students will understand that they can use whatever strategythey want to represent the problem they have to write.

Comment [CE6]: Are they using the b

represent the cats?

Comment [CE7]: Partitive refers to diThere are two ways to pose a division proreview this from notes and the book

Comment [CE8]: What does this reallme it means that students should be raisinand working to solve problems that are re(for which its not immediately obvious hothem). I’m not sure how that relates to wr

instructions.





Lesson Plan

Writing Multiplication Story ProblemsThird Grade, Friends Select SchoolSmall group instruction

Goals / Objectives:

Students will be able to identify and write the a number sentence to represent amultiplication situation in a story problem.Students will be able to translate abstract math problems into personal and relatable storyproblems. (Primary objective)

Standards / Assessment Anchors:

CC.2.2.3.A.1 Represent and solve problems involving multiplication and division.

Materials and Preparation:

Prepare several examples of multiplication story problems on individual index cardsManipulatives: Base-ten blocks, counting blocks, plastic coinsCharts: Multiplication tables, number chartsWriting materials: Markers, pencils, graph paper, blank paper, lined index cards

Classroom Arrangement and Management:

For this lesson, we will be working outside the regular classroom, so all manipulatives,charts, and materials will need to be brought with us to our workspace. We will work ineither the lunchroom or the library, depending on the day’s timing. I am working withfour students who will be working in pairs, so the pairs will need to be able to beseparated to work quietly together, either at adjacent tables or opposite ends of a longtable.

Manipulatives and supplies will be offered in a central location, and there will be plentyof each kind for each group (i.e.: two boxes of money, two sets of base-ten blocks, etc.).

I will be working under established classroom norms, which includes changing the colorof a student’s card on the classroom behavior chart (changing the student’s ―light‖) after

repeated inappropriate behavior. Classroom norms will be reiterated at the beginning of this lesson, reinforcing that the same rules apply even when I am the teacher and whenwe are outside the regular classroom.

Plan:

Introduction: (5 minutes)

Run through norms and discourse. All regular classroom norms apply, even outside thetraditional classroom. Consequences and rewards are the same, regardless of who isteaching and where we are.

Comment [CE9]: This needs some revSWBAT write a story problem to represegrouping in context?





Hook: I’m working on a pr oject where I am assembling some new word problems for an

assessment. I need your help writing the problems. When you are working with a mathproblem, you know that you have a lot of tools available to you. When we are working onthis project, just like in the classroom, you have the chance to use any of the tools around.You can use blocks to make groups, a multiplication table to solve problems, use anumber chart to count up, or the coins if you want to work with money. There is plenty of scratch paper and graph paper if you want to draw out your problems while you work onthem. Remember: The choice is yours. I’m really interested in learning about how youcome up with your word problems.

We will be working first as a group, then later as two pairs as you come up with yourmath problems. What are we working on right now in Math? [Multiplication]

Formative Assessment: (5 minutes)

OK, so what do we know about multiplication? What does it mean?What can you tell me about groups? What if you are counting several groups of the samesize? Does that count as multiplication? You have been working on your multiplicationmath facts for several days now. Do you feel confident in your knowledge of math factsto put them to the test?Do you like looking at number problems, like [written out on scratch paper] 3x4, or isthere a different way you like to think of multiplication?Have you ever worked with word problems or story problems? Tell me about what youthink about story problems.Let’s do an exercise about making multiplication fun. Let’s make it about you guys. Do

you think you can write your own story problems about multiplication?

Lesson: (10 minutes)

Let’s work together to go through a few word problems: First example word problem, written out on an index card:

If I had six pairs of shoes, how many individual shoes would I have altogether? How did you come up with that answer? Is doubling a kind of multiplication?

Second example: How many legs altogether are there on seven cats?

What’s the number sentence here? What are the numbers we’re looking for? What

information do we have? How many legs does a cat have?

Third example:George and Martha had four children. Each of those four children had three

children of their own. How many grandchildren do George and Martha have?

How do we figure out how many grandchildren George and Martha have? Can we do it

with addition, subtraction, multiplication, or division? What is the number sentence here?How can we show it as addition? How can we show it as a multiplication problem?

Fourth example: [If the students are amenable to more involved problems and partitivegrouping]

Comment [CE10]: OK, so this is a goset a purpose for the lesson. Just try to maclear and concrete as possible.

Comment [CE11]: This seems pretty might ask them to brainstorm some thingin equal groups (socks, packs of juice, quadollar). There is a book called "Each oranslices" that would also be a great introducequal groups.

Comment [CE12]: I think you are gettrack too much here. Try to keep it really Just gathering a few ideas about what theyabout multiplication, and highlighting theequal groups is sufficient here.

Comment [CE13]: Is this an index carIt seems like it would be too small for stusee. Do you want to write it on chart papeboard?

Comment [CE14]: What strategies doto see. Think this through ahead of time. connections could you draw between strat

Comment [CE15]: Are they working problems or are you? Do you expect themto do them mentally, or do they have acceand paper or manipulatives here? You migthis by asking ―How can we represent thiswith a picture or with blocks?‖

Comment [CE16]: It seems like you ato more abstract ways do this rather than lfigure it out.





Joe and Mary collect postcards. They have 99 postcards in their scrapbook. 9

postcards fit on each page of the scrapbook. How many pages are there in thescrapbook?

Can this a multiplication problem? Have we seen problems like this before? How do wewrite this number sentence? [9 x ___ = 99] What goes in the blank space? How do weknow that?

Transition example: How can we show 4x12 as a story problem?

I will write notes from the conversation on a black piece of paper. What is the answer tothe math problem? What do we want our story to be about? Do we want to make groups?How big are the groups? How many are there? Remember how we talk about ―units‖ in

out math problems, like the number of chickens or the number of fingers? What are the―units‖ in this story problem?

On a prepared index card, writethe example math problem at the top[4x12], the solution to the mathproblem [48], the names units in thestory [eggs] and the size of the groups[12]. Then write out the story problemcreated by the group. Repeat asnecessary with different problems untilthe kids ―get it.‖ Reinforce to thestudents that they may use any toolsthey want to figure out the solution.

Paired Work: (10 minutes)

Instructions: You will be given an index card with a math problem written on top of it, just like the one we had in the example we worked on together. Also on the card, there isa place to write the solution to the math problem, your units, the size of your groups, andfinally, your own story problem for which the number problem on the card is the same asthe number sentence used in the story problem.

One of you will be writing out the information on the index card. You have to decidetogether who is going to do it.

You can use any of the tools to solve the problem that we have in the classroom. It maybe helpful to see the groups when thinking about the multiplication.

The units in your story problem can be anything you want. You can make it aboutwhatever is important to you. It can be candy or horses or cars or giraffes, just so long asit is something you can relate to.

Send to tables to work in pairs.

Number problemmultiplication equation? :4x12=

Solution (total): 48

Tools used: Math fact

Units: Eggs

Groups: Dozens (12)

Word problem: Janet needs 48 eggsto color for an Egg Hunt. Eggs

are sold by the dozen. How

Comment [CE17]: Now I’m going tomultiplication problem. Can you think of problem that would go with 4 x 12?

Comment [CE18]: Are these follow uMake sure you give them a chance to resp

before posing all these questions. It mightto ask "How many groups should we havemany should be in each group?"

Comment [C19]: In Everyday Math tha number model. You could also call it amultiplication equation.

Comment [CE20]: I’m not sure why ythem to write out ―tools used‖ I would su

making this a bit simpler. You want themword problem, solve the problem and shosolved it, and perhaps show a drawing? Ugroups also seems confusing…how aboutgroups and number in each group ?

Comment [CE21]: One example is su

Comment [CE22]: Do you want themyou how they solved the problem? If theymanipulatives, they can draw out what ththe paper.





Check in with each pair. What are you writing about? Is that your ―unit‖? How big arethe groups? Where are you getting your numbers? What is the solution to the mathproblem on the card? Are you using any tools?

Closure: (5 minutes)

When both pairs have completed their problems, come back together as a group. Eachpair reads aloud their word problem.

Ask of the other pair about each problem: What are the units in their problem? How bigare the groups? Is the solution correct? How do you know? Does the word problem makesense? Why?

Ask of each pair: How did you come up with your solution? Do you prefer to draw things

out, make groups of actual objects, or do things some other way? Do you like wordproblems or number problems more? Why?

I think these are some really great word problems for the project. I’m going to take them

to my professors at Penn and show them what great mathematicians we have here in thirdgrade!

Anticipated Responses:

Content:I believe that the students will initially find the instructions confusing, even after workingon examples together in the exact same format. Given the freedom to decide their units,some students may get hung up on deciding little facts rather than focusing on theassignment as a whole.

Management Issues:Because the group has been hand picked, I do not expect any serious management issues.Students will get excited when working in pairs, and I expect the conversation to get alittle boisterous at times, but I also expect them to quiet down quickly as I will bebouncing back and forth between groups. Because the pairs are working on problems thatthey will later present to the group, they may very well be secretive about their work andtalk in a whisper to each other.

Assessment of Goals:

Throughout the inquiry-based lesson, I will be constantly assessing the progress of thestudents. I will write the math problem on each pair’s card after assessing what I think they can handle and what they can’t. Does one of the pair know math facts or how to use

manipulatives to do 7x13? Is one of the students doing more work than the other? Most

importantly, is the word problem valid, well-written problem that accurately depicts themath problem at hand?

Comment [CE23]: I’m not sure aboutquestion... do you mean how many are in group?I think you may be trying to draw on smi

here in relation to the components of undemultiplication. But these are components look for when assessing students understanot necessarily appropriate to ask studentreflect on them.

Comment [CE24]: How about gettingmore important math here. Can you try tosolutions to help make some connections Think about the transition from counting taddition to multiplicative thinking. Ask qhelp them consider different ways to solvemultiplication problems, e.g., I see you fohow many are in two groups... how can wto help finish solving the problem? or if scounts by ones "Is there a faster way to conumber of xxx? is there another number ycount by? "

Comment [25]: In relation to what? Tyou need to be clearer about the mathemaof you lesson in relation to the developmemultiplicative thinking.

Comment [26]:





Accommodations:

Throughout the entire lesson, I will be constantly assessing the progress of the students.Because the index cards to not have the math problem written on them, the assignmentfor each pair will be on the level I assess them to be able to manage. The assignment willbe to create just one word problem. By setting the assignment at the most basic level,work will be added or adjusted to meet the needs of the pair of students. Each of the pairswill be such that one of the students is a stronger math learner than the other. The firstpair to complete the task will be handed another card with another math problem on it.Through constant assessment and time monitoring, I will continue to hand out problemsto each pair until about 5 minutes before the end of the allotted time, when we willreconvene for the closing of the lesson and the sharing of the students’ work.

Duncan,This is overall a solid plan in terms of feasibility and developmental appropriateness.

The main thing you need to work on is getting clear about the mathematical goals. Drawon what we know about the development of mathematical thinking (course readings andnotes) to revise your what section, clarify your lesson plan goals, and create a checklistfor what you will be looking for in terms of components of multiplicative thinking (look at the one I posted on Canvas as an example to work off of). I addition, make sure youare giving students time to work out and make sense of the problems for themselvesbefore jumping in with all those questions. I'm hoping those are meant for follow upprobes to be used as appropriate. Think carefully about how students might respond--what strategies do you expect to see? What strategies do you want them to be exposed to?How might your lesson help them move towards more sophisticated strategies? Modelingone problem is sufficient then let them work and leave time for discussion of strategies.Again in this section you want to think about how to pull out the important mathematics.

term iii math initial plan with comments

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