kristenkaufmann.weebly.comkristenkaufmann.weebly.com/uploads/5/3/1/2/53122747/… · web viewmath...

Math Unit

Kristen Kaufmann

Section 1: Critical view of curriculum goals and your big ideas

Learning and teaching goals

The teaching and learning goals (what do I want my students to learn?) emphasize multiplication by 1-digit numbers. The goal or critical area as GO Math calls it for the entire unit wants its students to develop understanding and fluency with multi-digit multiplication, and develop understanding of dividing to find quotients involving multi-digit dividends. This goal does not consider my students needs, because it does not show how multiplication can be relevant in my students worlds. It also has no consideration for student exploration when introducing each lesson found within this unit. The curriculum is very straightforward with a lot of teacher talking at students vs. students finding and exploring patterns on their own.

When it comes to prior knowledge the majority of the lessons in this curriculum have word problems with contexts that students cannot access with background knowledge or relate to. They are worldly scenarios that students cannot hone into within their own personal experiences. When it comes to future knowledge, the curriculum does a better job at building up skills students will need at subsequent grade levels. The lessons are broken down into chunks that build on one another and ultimately lead into a fundamental skill.

I will make this goal more realistic for my students by, making world problems more fit to their own personal experiences, making lessons more interactive and more applicable for student exploration, and continuing to make sure skills continue to build on one another and flow in a cohesive way for student understanding.

Big Idea

Connecting multiplication to addition

When does multiplication become addition?

Using and looking at patterns and groups

Section 2: A Narrative of How of How You Were Taught and How You Will Teach this Topic

I was taught this unit using Everyday Mathematics as the curriculum. I cant remember how I exactly learned this unit, but The Go Math curriculum really focuses on students finding patterns to multiplying by one digit numbers. It also provides tables that I never used to help visually see how to solve the problems. I want the way I am going to be teaching this unit to be memorable. Its important for students to learn these patterns in multiplication in order to advance to more complicated multiplication problems. I want to make my tasks interactive and more student led. I want my students to solve the patterns not have me to tell them what the patterns are. I want to teach it this, to ensure higher-level thinking and for my students to fully understand the unit and its patterns not just listen to me talk to them and forget it later.

Section 3: How Project 1 and Ideas From Our Reading Inform Your Unit

In order to change the way my students have learned to see themselves in mathematics I will:

Provide students with the confidence they need to think more highly of themselves and their abilities to perform in mathematics

o This can be done through engagement techniques, positive feedback, and team building

Make word problem more applicable to their personal experiences, so that they can see themselves in the math.

Complex instruction can assist me in these transformations, because it will provide me with the necessary framework to make math more breathable and open and less constraining to the curriculum. This can happen through the windows and mirrors concepts presented in the article by, Higinio Dominguez titled, Mirrors, Windows, Into Student Noticing. The Window concept provides students and teachers the opportunities to see what makes sense in each word problem and then be able to solve the problem. The Mirror concept provides students and teachers the opportunity to see what students pick up on in the word problem that is applicable for solving that word problem (Dominguez 2016). These two concepts together can help my students visualize themselves in the problem and ultimately give my students a better-rounded lesson on multiplying by 1-digit numbers.

Section 4

Pre Assessment

Students will take the pre assessment below along with a show what you know pre assessment provided by Go Math!

Name ___________________________________________________

Arrays

1) How would you arrange the squares below that would make it easier to count them? (Possibly equal groups?)

Make a multiplication equation for the array you created

___________________________

Is there another way you could arrange the squares? Show below.

Distributive Property

2) How would you solve this problem? Show your work.

3 x (5+3)

3) Use the distributive property to model the product on the grid.

Record the product.

4 x 16= ___________

Estimation

If I gave you the number 49 and asked you to double it, what would your answer be closest to? Why?

Post assessment

This will be the same as the pre assessment, the students will also take the Chapter 2 test as well provided by Go Math!

Section 5

Lesson #2.1

Description/Overview of the lesson.

Multiplication comparisons

Go Math Objective: relate multiplication equations and comparison statements

Go Math Focus: Mathematically proficient students use models to solve real-world problems. In this lesson, students represent multiplication comparisons using a bar model. By drawing models, and translating between equations and verbal statements, students are able to interpret relationships and solve problems.

Main Task(s)

I will be having the students observe and model multiplicative comparison problems using cube manipulatives. I will give each table group 15 cubes and ask them to work together in their groups to model how to group the 15 cubes into even groups. The goal of this task is to see the two different ways the groups could possibly arrange these cubes. It could be 3 groups of 5 cubes or possibly 5 groups of 3 cubes. I want my students to explore the commutative property of multiplication and see the patterns of it of it on their own without me just telling them. After the students have had time to group the cubes evenly in their groups, I will ask a few table groups to share out how they grouped the 15 cubes. I will call on a table group that arranged them 3 groups of 5 cubes and one table group that arranged them 5 groups of 3 cubes, and ask them if one table group is more correct than the other, is one wrong? Or are they both correct ways of grouping the 15 cubes? Once student share this discussion I will ask them why they think both of these ways work. This will get them thinking of the commutative property. I will then continue the rest of the lesson the way it is presented in the GO Math! curriculum.

_________________________________________________________________________

Lesson #2.2


Comparison problems

Go Math Objective: Solve problems involving multiplicative comparison and additive comparison

Go Math Focus: In this lesson, students encounter two types of of comparison problems: multiplicative comparison and additive comparison. Students learn how to draw bar models and write algebraic equations to solve both types of comparison problems.

Main Task(s)

I will do this task before the actual lesson presented in Go Math! This lesson is all about comparing numbers in multiplication word problems. In order to set a better understanding of what they will be doing in the lesson I will demonstrate comparing numbers with a few objects. I will bring in two sticks. One small stick and one larger stick. I will tell the students that the larger stick is 3 times as much as the smaller stick, and ask them what I could do with the larger stick to show that three of the smaller sticks could fit into it. The students should reach the answer of breaking the stick into 3 equal parts or sizes of the smaller stick. If not, I will prompt them: if I broke this larger stick into three pieces that are the same size as the smaller stick, would that show me that it is 3 times as much as the smaller stick? I will demonstrate by actually breaking the stick into three parts. I will next ask the students, So how many sticks do I have all together? I have the larger stick thats broken down into three pieces to show that it is three times bigger and the actual small stick. The students should see 4 sticks in total. I will then do a similar problem as the one presented in Go Math! Again the larger stick is three times as much as the smaller stick. The two sticks length combined equals 12 inches. How many inches is the larger stick? As a whole group we will solve the problem. 4 x N =12 inches. The smaller stick will be 3 inches. 3 x 3 = 9 inches. The larger stick is 9 inches.

After completing this task, I will teach the rest of the lesson the way it is presented in the GO Math! curriculum.

_________________________________________________________________________

Lesson #2.3


Multiply tens, hundreds, and thousands

Go Math Objective: Multiply tens, hundreds, and thousands by whole numbers through 10

Go Math Focus: In this lesson, students are shown different ways to multiply tens, hundreds, and thousands by a whole number through 10. The first strategy involves students understanding of place value. In one way, students draw a picture of the problem using square for one hundred and a square with a T on the inside for thousand. Students regroup as needed to find the answer. In Another way, students rewrite the problem using place value. In the second strategy, students use patterns to find products. Students visualize patterns using number lines and patterns in multiplication problems. As the number of zeros in a factor increases, the number of zeros in the product increases.

Main Task(s)

In the GO Math curriculum for this lesson, it is showing students three ways to show multiplication by tens, hundreds, and thousands. The first way is through a model, the second way is through using place value, and the third way is through the use the of a number line. What I want to change about this lesson and add is a rotation of these three different ways. I dont want to talk at my students and show them these three strategies. I want them to explore them on their own. I will do this by setting up stations at each table group. The first two table groups will have way one (draw model), the second two table groups will have way two (place value), and the third two table groups will have way three (numberline) I will give the students a problem, in which they have to solve using that strategy or way that is presented. Each table groups will rotate as a group to the next station and work together to solve the problem in the different ways. The students will start off at their own table doing the way that is presented then after 5 minutes they will rotate to the next center/station to do the next way/strategy presented to them. This will continue until each group has done all three ways. It will look something like this:

The point of this task is to give students multiple options in strategies they can choose from thats more comfortable for them to comprehend multiplying tens, hundreds, and thousands. We will go over each of the problems and ways to solve those problems after they get the chance to explore them.

Stations:

Way one: Drawing a model

Each car on a train has 200 seats. How many seats are on a train with 8 cars?

Find 8 x 200

Way two: using place value

8 x 200 = _______ hundreds

= ________hundreds

=________

So, there are _________ seats on a train with 8 cars.

Way three: using a number line

Bobs sled shop rents 4,000 sleds each month. How many sleds does the store rent in 6 months?

6 x 4,000

Students should try and produce a number line similar to the one below.

Ex.

_________________________________________________________________________

Lesson #2.4


Estimate Products

Go Math Objective: Estimate products by rounding and determine if exact answers to multiplication problems are reasonable

Go Math Focus: In this lesson, students use different estimation strategies to decide if an answer is reasonable. Some students will check their work by reworking the computation, but most students wont check their work at all. Teaching them to use estimation will help them find their mistakes.

Main Task(s)

I will go over the Go Math lesson the way it is presented in the book, for teaching how to estimate products rounding up and down, and seeing if their answers are reasonable compared to the actual product. After teaching this lesson, I will introduce an activity/game they can do with a partner to review concepts learned in the lesson. For this activity pairs will roll a die to get a 1 digit number to multiply. They will then roll two dice to get a 2 digit number to multiply with the one digit number. The pairs will multiply the two numbers and get their answer/product. After getting their answer/product they will create a number line with the product they got in the middle, and the estimation of rounding it up and rounding down. In doing so, students will be able to describe the reasonableness in their estimations of the rounded numbers. For example, if students rolled the one die and got 2 and then rolled the 2 dice and got 34, their answer/product would be 68. The pairs would then create a number line for this product with 68 in the middle. They would estimate up and round it to 70 and they would estimate down and get 60. They would then determine if these estimations are reasonable for the product 68. After 5 minutes of working with 1 digit numbers and multiplying them by 2 digit numbers (tens) I will then add a third die so that students can estimate 3 digit numbers or (hundreds). The same process used to solve for the product/answer and estimating, will be used, so the pairs will roll 1 die to get a one-digit number and then the three dice to get the 3 digit number (hundreds). ____________________________________________________________________________

Lesson #2.5


Multiply using the distributive property

Go Math Objective: Use the distributive property to multiply a 2-digit number by a 1-digit number.

Go Math Focus: Students learn how to draw a model for multiplying a 2-digit number by a 1-digit number. They label the model with the partial products. They can see how multiplication is distributive over addition.

Main Task(s)

This task will take place before teaching the lesson presented in Go Math! I will reintroduce a problem that I gave them in their pre assessment, and have a math based discussion about it.

3 x (5+3)

I will ask them how I would go about solving this problem? As a whole group we will go through and try and figure out how to solve this problem. I can begin by asking, what would I do first to solve this problem? some students might say to add 5+3. Since they haven't learned that parentheses can be used to multiply. After getting 8 for 5+3 I can ask them: now what do I do? 3 x (8). Maybe at this point students will know to multiply, if not I can tell students that parentheses can be used as another symbol to multiply. After getting the answer: 24. I will ask my students if there could have been another way to solve this problem besides adding the two numbers first. After knowing that the parentheses symbol can mean to multiply maybe theyll discover the distributive property. If students get too frustrated trying to figure it out or say no. I will say: we will be learning another way to solve this problem. And go straight into the lesson presented in Go Math! If students get the other way to solve the problem I will say: Awesome job figuring that out, This is what we call the distributive property, and we will be learning more about it today and go into the lesson presented in Go Math!

____________________________________________________________________________

Lesson #2.6


Multiply Using Expanded Form

Go Math! Objective: use expanded form to multiply a multidigit number by a 1-digit number.

Go Math! Focus: students use expanded form and the Distributive Property to multiply a multidigit number by a 1-digit number. They use the area model representing the Distributive Property to help record the multiplication. By using the area model and expanded form, students are able to gain a deeper understanding of the multiplication process.

Main Task(s)

I will follow the Go Math! Lesson the way it is presented in the book in regards to multiplying by using expanded form. However, the context of the word problems that occur for the remainder of the lesson will be modified to match what is contextually relevant for my students.

Evans Word Problems:

Example 2:

To prepare for the construction of the 3D Bearcat Paw, Ms. Conn the integrative arts teacher orders 3 boxes of legos. Each box of legos contains 1,250 pieces. How many lego pieces does Ms. Conn order for the project?

On Your Own:

6. Between the 4 boys: Brody, Thatcher, Charles, and Brady they each have 128 pokemon cards. If Raines joins in, he makes the total number of pokemon cards between the 5 of them 334 pokemon cards, how many pokemon cards does Raines have?

7. Peter noticed the new Dimondale Bearcat sweaters for sale in the office. He decides he wants to buy 2 of the extra fleece sweaters for $119 each and 3 regular sweaters for $44 each. How much will Peter spend on the five sweaters?

8. Cierra wanted to make something special for her teammates in class. She thought that friendship bracelets or necklaces would be a cool thing to give them. Already she has 36 inches of thread. She needs 5 times that much to make some of these necklaces and 3 times that amount to make some bracelets. How much thread does Cierra need to make her friendship necklaces and bracelets?

9. To prepare for Annie's Big Nature lesson, Mr. Cotter and Mr. Woodys students walked through the trails of the DODC together 3 times last week. Each time they walked through the trails they walked 1,760 yards. How many yards did the students walk in 3 days?

Kristens Word Problems:

Example 2:

To prepare for the construction of the 3D Bearcat Paw, Ms. Conn the integrative arts teacher orders 3 boxes of legos. Each box of legos contains 1,250 pieces. How many lego pieces does Ms. Conn order for the project?

On your own:

6. Between the 4 boys: Leightin, Nick, Damario, and Braylon they each have 128 pokemon cards. If Cooper joins in, he makes the total number of pokemon cards between the 5 of them 334 pokemon cards, how many pokemon cards does Cooper have?

7. Laila wants get ready for the cold weather of fall coming up by buying some new sweaters. She wants to buy 2 purple sweaters for $119 each and 3 pink sweaters for $44 each. How much will Laila spend on the five sweaters?

8. Myleesa wanted to make something special for her teammates in class. She thought that friendship bracelets or necklaces would be a cool thing to give them. Already she has 36 inches of thread. She needs 5 times that much to make some of these necklaces and 3 times that amount to make some bracelets. How much thread does Mylessa need to make her friendship necklaces and bracelets?

9. To prepare for Annie's Big Nature lesson Ms. Brown and Ms. Kaufmanns students walked through the trails of the DODC together 3 times last week. Each time they walked through the trails they walked 1,760 yards. How many yards did the students walk in 3 days?

____________________________________________________________________________

Lesson #2.7


Multiply Using Partial Products

Objective: Use place value and partial products to multiply a multidigit number by a 1-digit number.

Main Task(s)

To extend on student understanding of multiplication, specifically place value and partial products, I will engage in a number talk. Students will be able to make connections from previous lessons surrounding the Distributive Property along with other strategies used to solve multiplication problems. To initiate this conversation, I will pose the math problem of 2 x 32 on the board. I will then have students get out their small whiteboards and markers so they can show their work for solving the problem. Students will have about two to three minutes to work through the problem. I will remind students that they are to try their best and to not get frustrated, as we will discuss this as a class afterwards. Students will be prompted to raise their hand to signify that they have worked through the problem and found a solution. Once a majority of hands have been raised, students will then begin to share out their strategies used for finding the solution to the problem posed. I will call on a few students to share their ways in solving the problem and write those strategies on the board. We will then have a discussion on what they took from previous lessons to solve this problem. This number talk will help students connect previous lessons to what they are about to learn in the lesson today (using place value and partial products), and it also gets them thinking of other strategies that can work when multiplying (repeated addition).After completing this task, I will teach the rest of the lesson the way it is presented in the GO Math curriculum.

_________________________________________________________________________

Lesson #2.8

Description/Overview of the lesson:

Multiplication Using Mental Math

Objective: Use mental math and properties to multiply a multidigit number by a 1-digit number.

The focus of this lesson is strategies for mental math. While one student may be able to perform a computation mentally, another student may need to use paper and pencil to perform the same computation. Students need lots of experience breaking numbers apart to develop number sense. This building of number-sense skills will help students develop mental math strategies that work for them. Properties are also an important part of developing mental math skills. Knowing how to change the order and grouping of numbers will help students recognize situations where mental math can be used instead of paper and pencil. Mental math is a real-world skill, not just a math class skill.

Main Task(s)

In order to deepen students understanding of mental math, it is imperative to discover the multitude of strategies in which students use when performing multiplication. The lesson provided by the Go Math curriculum does not give students a chance to unpack some of their strategies used to solve multiplication problems before engaging in the actual lesson. Thus, before unlocking the problem set forth by GO Math I will have students participate in a number talk focused on multiplication to look at some of the strategies in which they use for solving problems. To do exactly this, I will select 3 different numbers to multiply (ex. 9x10x2). This number will be displayed on the board so students can see what it is they are multiplying. Students will then have about three to five minutes to use any strategy previously learned or already known to solve the problem. This time, however, students will not have whiteboards as a resource since the goal is all about using mental math. As a whole group, we will then discuss the multitude of strategies used to determine the answer. In doing so, students can actually have a chance to explore multiplication more in their own terms, and begin to understand the various strategies generated by other students to see the value of using mental math to problem solve. Students can also come to a better understanding of the commutative property when engaging in the number talk as well. This task alone is used to reinforce student use of mental math and is centered around combining what they have been learning in the unit so far (repeated addition, models, place value, etc.). This number talk task shows us (the teachers) what patterns they have picked up on/learned from previous lessons to apply it to this particular problem. After completing this task, I will teach the rest of the lesson the way it is presented in the GO Math curriculum.

_________________________________________________________________________

Lesson #2.9


Problem solving: multistep multiplication problems

Go Math Objective: Use the draw a diagram strategy to solve multistep problems

Go Math Focus: This lesson involves the problem solving strategy draw a diagram

A diagram organizes information in a problem and helps students visualize the problem.

Grid paper is a useful tool for students to use when they are drawing diagrams.

The problems in the lesson are multistep problems. It is helpful for students to record the steps of the problem in the order they should be performed.

Main Task(s)

In the Go Math! Lesson, it has students solve a multistep multiplication problem. One of the steps in the problem is having the students draw a diagram, but it already has the diagram drawn out for the students. I want to have students create this diagram on their own, because I feel it will give students a better understanding of this step in the problem if they do it themselves vs. having the book just give it to them. We will create the diagram together as a class.

Go Math! Multistep problem:

At the sea park, one section in the stadium has 9 rows with 18 seats in each row. In the center of each of the first 6 rows, 8 seats are in the splash zone. How many seats are not in the splash zone?

____________________________________________________________________________

Lesson #2.10


Multiply 2-digit numbers with regrouping

Go Math Objective: Use regrouping to multiply a 2-digit number by a 1-digit number

Go Math Focus: There are two ways that students experience modeling as they learn mathematics: they learn to model and they learn with models.

Learning to model

Students may draw or build models to reflect the mathematical problem.

Learning with models

In this lesson, students observe and discuss how base-ten blocks can model multiplying a 2-digit number by a 1-digit number. The models are tools that help make the process obvious. They provide a road map to the solution.

Students also discuss how the models relate to the traditional multiplication algorithm.

Main Task(s)

I will go over the Go Math lesson the way it is presented in the book, for teaching how to multiply 2 digit numbers with regrouping. After teaching the lesson mandated by the curriculum, I will have students participate in an activity, where they work in pairs to solve problems using both partial products, which they previously learned in lesson 2.7 and regrouping which they learned in this lesson (2.10). This will allow students to compare both methods and possibly help them pick a method/strategy that makes the most sense to them when computing multiplication problems in the future. This activity also considers the importance of place value and how it is carried out in each of the methods (partial products and regrouping). After solving and comparing the problems below, students will return to their seats to finish the GO Math! lesson as stated in the book.

Problems:

1)

35 (show partial product method and regrouping method)

x 3

2)

31

x 7

3) 26

x 8

4) 52

x 5

kristenkaufmann.weebly.comkristenkaufmann.weebly.com/uploads/5/3/1/2/53122747/… · web viewmath...

Documents