TE Math Support – Summer 2012 – Content Overview
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Session 1: 5/17/12
Math Content Focus: Multi-digit Addition and Subtraction Strategies
Activities
o Reflection & Sharing
 High point and low point in your experiences with math
 Something you hope or want to learn about teaching mathematics
 Something fun you can share to help us get to know you better
o Mental Math: 48 + 25, 86 – 32, 72 – 47
 Sharing & discussing strategies
o Reading cases from Developing Mathematical Ideas: Building a System of Tens
 Case 1: Do my students think flexibly? Do I? (Ann, Grade 6)
 Case 2: Creative thinking in subtraction (Ann, Grade 6)
 Case 3: Children inventing their own addition problems (Sandra, Grade 2)
 Case 4: Learning math while teaching (Emily, Grade 2)
o Case Discussion:
 In Ann’s Case 1 (on addition), examine the methods presented by Janae, Tom, Bert, and
Betsy. Apply their methods to this problem: 57 + 24.
 In Ann’s Case 2 (on subtraction), examine the methods presented by Jason, Bert, Holly, and
Joe. Apply their methods to this problem: 83 – 56.
 What did the student do on the original problem (in the case)?
 What do you think the student would do with the new problem (57 + 24 or 83 – 56)?
 What is the logic behind each student’s strategy?
o Using Games in Math Instruction
 Close to 100 Game
o Mental Math Revisited
 After our work today, do you have any new mental math strategies you would add to our
list?
o Exit Questions
 What is something that you are thinking about from the work we have done today?
 What questions or concerns do you have?
 Any other feedback?
Session 2: 5/24/12
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Math Content Focus: Place Value
o Recognizing and keeping track of groups of 10 while operating on numbers
Activities
o Reflection and Sharing: What does it mean to be “smart” in math?
o Mental Math:
 40 – 26 & 35 – 16
o Overview of subtraction strategies
 Connection to MTH 201: Go over four thinking strategies for subtraction
 Counting down
 Counting up
 Four fact families
 Compensation
o Video: Subtraction in 2nd grade
 Watch the video and take notes on what each student says and/or does
 Try each student’s strategy with a new problem (54 – 38) and choose one problem to put
on a poster for discussion
o Math Manipulatives: Base Ten Blocks, Unifix Cubes, and Cuiseniare Rods
 Model different numbers with the manipulatives (17, 45)
 Solve the problem 17 + 8 using Base Ten Blocks
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TE Math Support – Summer 2012 – Content Overview
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 Solve the problem 45 + 39 using Unifix Cubes
 Solve the problem 38 + 59 using Cuisenaire Rods
 Solve the problem 40 – 26 using all three types of manipulatives
Reading cases from Developing Mathematical Ideas: Building a System of Tens related to the use of
manipulatives to help students make sense of place value
 Case 5: Thinking about tens (Base Ten Blocks)
 Case 6: Keeping it straight (Unifix Cubes)
 Case 3: This is confusing, this 8 and 9 thing (Cuisenaire Rods)
 Case 4: Learning math while teaching (Emily, Grade 2)
Discussion of math manipulatives
 How are they similar? How are they different?
 What are the benefits and constraints of using each one?
Math Group Activity: Hundred Chart Hunt
Exit Questions
 Did you learn anything new today? If so, what? If you didn’t learn anything new today,
what is something you would like to learn about in future sessions?
 Is there anything we talked about or did today that you would like to explore further?
 What questions or concerns do you have about using manipulatives with your students?
Session 3: 6/7/12
Math Content Focus: Multiplication and Division
Activities
o Modeling Multiplication Math Activity
 Use 3 x 5 to do the following:
 Write a word problem
 Draw a picture
 Use manipulatives to represent (Multi-Link Cubes, Unifix cubes, Base Ten Blocks,
Cuisenaire Rods, Graph Paper)
o Review Multiplication Models (from MTH 201 textbook)
 Set model
 Measurement model
 Rectangular array model
o Repeat Modeling Multiplication Activity for 16 x 18
 Write a word problem
 Draw a picture
 Use manipulatives to represent
o Discussion of the use of manipulatives for multiplication concepts
 Which ones were better for single digit multiplication?
 Which ones were better for multi-digit multiplication?
o Review Properties of Multiplication (from MTH 201 textbook)
 Multiplicative Identity, Commutative Property, Associative Property, and Distributive
Property
o Examining Students’ Strategies for Multiplication – Written Case from Developing Mathematical
Ideas: Building a System of Tens
 Case 18: 27 x 4, or dogs looking for scraps
 Focus questions for reading and discussion
 In Eleanor’s case 18, Mark, Joel, Stephan, Jen and Mika each offer strategies for
computing 27 x 4. For each student, do the following:
o Show what the student did to solve 27 x 4.
o Choose one of their strategies to use to solve 34 x 6.
o Examining Students’ Strategies for Multiplication – Video Case from Developing Mathematical Ideas:
Building a System of Tens
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TE Math Support – Summer 2012 – Content Overview
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Video shows some 3rd grade students working on 29 x 4 and some 5th grade students
working on 36 x 17
 Focus Questions:
 What do the students seem to understand about multiplication? How do they
think about multiplication?
 What do these strategies highlight about multiplication?
Multiplication Algorithms
 Go through each algorithm
 Partial Products
 Box Method
 U.S. Traditional Algorithm
 Lattice Method
 Try each method for the following problems
 12 x 18
 16 x 18
 36 x 17
 Look for connections between the different algorithms
 What are the advantages and disadvantages of each
Exploring Common Misunderstandings in Multidigit Multiplication
 For each example, figure out what is incorrect about the suggested procedure.
Session 4: 6/14/12
Math Content Focus: Multiplication and Division
o Note: I only had one student attend Session 4 and she had not been at Session 3, so I tried to review
some things we had done in Session 3
Activities
o Multiplication Algorithms
 Review three types of models for measurement (set, measurement & array)
 Review multiplication algorithms (partial product, box method, U.S. traditional, lattice
method)
 Solve 28 x 65 using all four methods
o Factor Game
 Model and play game
 Discuss how teachers could use the game for instruction and assessment
o Problem Solving Task: Missing Key Dilemma
 Oh no!! My calculator does not have a 3 key that works! I need your help! How can I use
my broken calculator to do the following problem: 23 x 25? Try to find at least three
different ways to do the problem. Feel free to use graph paper, manipulatives, drawings or
anything that will help you make sense of the problem.
o Product Game
 Model and play game
 Discussion how teachers could use the game for instruction and assessment
o Problem Solving Task: Carpet Caper
 I would like to carpet my basement and I need your help. My basement is 23 feet long and
13 feet wide. The carpeting comes in rolls that are 100 square feet. How many rolls of
carpeting do I need to buy to cover the floor? Remember that carpeting is very expensive
(100 square feet including the pad is on sale for $200), so I want to buy the least number of
rolls needed to do the job. How should I cut the 100-square-foot rolls of carpet so that I get
the least number of seams?
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TE Math Support – Summer 2012 – Content Overview
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Session 5: 6/18/12 & 6/20/12
Math Content Focus: Measurement
o Perimeter & Area
o Decomposing space into component parts and then recomposing the parts into a coherent whole
Activities
o Reflecting on Key Ideas in Measurement
o Math Activity: Ordering Rectangles by Perimeter and Area
 Part 1 – order the rectangles without measuring
 Part 2 - use any available tools to put the rectangles in order
 Part 3 – reflecting on ideas about perimeter, area, and/or measuring from the task
o Examining Student Thinking: Ordering Rectangles
 Read case from Developing Mathematical Ideas: Measuring Space in One, Two, and Three
Dimensions
 Case 4, Rectangles and Chocolate Bars
 Reflection Questions
 What did the teacher learn about the students’ thinking related to measurement
after day one?
 What did the teacher learn about the students’ thinking related to measurement
after day two?
 What are some possible advantages of using the open-ended version of the task
with students?
 Think of at least one way to adapt the task.
o Problem Solving Task: Shannon’s Puppy Problem
 Shannon just got a new puppy named Clover. Clover is very energetic and loves to play
outdoors, so Shannon decided to build a dog run (pen) to allow Clover to be outside while
she is at school. Shannon happens to have 50 feet of fencing that a friend gave her to use
for the dog run. What are some of the different ways that Shannon can set up the dog run
(pen) that would use all the fencing? What are the dimensions of the dog run (pen) with the
most space available for Clover to play?
o Math Activity: Quick Images
 Directions:
 Everyone needs 10-12 interlocking cubes
 Look at image for 3 seconds
 Build the structure as best you can
 Look at image again for 3 seconds
 Make any necessary changes or addition
 Repeat for two more images
 Examining Student Thinking: Quick Images (video)
 Elementary students explain their ways to visualize each of the quick images
o Math Activity: Crazy Cakes
 Directions:
 Divide each of the “strange” cakes into two parts with equal area.
 Examining Student Thinking: Crazy Cakes (video)
 Elementary students explain their thinking on how to divide up the crazy cakes
Session 6: 6/28/12
Math Content Focus: Geometry
Activities – For this session we explored six different hands-on geometry activities for a range of grade levels
that focused on important concepts.
o Activity 1: Shape Families (Prekindergarten-Kindergarten)
 Identifying and naming 2-dimensional shapes
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TE Math Support – Summer 2012 – Content Overview
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 Identifying attributes of shapes
Activity 2: Inside or Outside? (1st grade)
 Identifying attributes of 2-dimensional shapes
 Identifying lines of symmetry in shapes
 Naming triangles, squares, quadrilaterals, pentagons, and hexagons
Activity 3: Cut It Apart, Put It Together (3rd grade)
 Analyze characteristics and properties of 2- and 3-dimensional shapes
 Decomposing polygonal regions and recomposing their parts to make other polygonal
regions
Activity 4: Tetrominoes Cover-Up (3rd grade)
 Identifying all possible arrangements of 4 squares
 Using transformations to completely cover the area of a grid
Activity 5: Build What I’ve Created (3rd – 5th grade)
 Construct a geometric design from oral directions
 Use precise geometric vocabulary in giving directions
 Recognize geometric shapes and patterns in designs
Activity 6: Roping in Quadrilaterals (4th – 5th grade)
 Sort quadrilaterals on the basis of specific attributes
 Use Venn diagrams to classify quadrilaterals
 Determine the common attributes of a set of quadrilaterals
Session 7: 7/12/12
For this session, I only had one student who could attend. Since she had missed Session 5 (focused on
Measurement), I just repeated the plan that I used for Session 5.
Session 8: 7/18/12
Math Content Focus: Fractions
Activities
o Reflections on Fractions
 What makes sense to you about fractions? What is confusing to you about fractions?
 What fraction concepts are you most worried about teaching? What would you like to
learn? What would be most helpful for you?
o I Have, Who Has Game – Fraction Models
o Exploring Fraction Manipulatives
 Pattern Blocks, Cuisenaire Rods, Fraction Circles, Fraction Squares
o Creating Fraction Kits
 Using strips of colored paper, we created fraction strips for a variety of fractions
o Fraction Kit Games/Activities
 Cover Up, Uncover Version 1, Uncover Version 2, Cover the Whole
 Comparing Pairs and What’s Missing Worksheet
 Pick Two, Pick Three, Roll Five, Make a Whole
Session 9: 7/25/12
Math Content Focus: Fractions
Activities
o Fraction Squares Exploration
 Using the blue square to represent one whole, figure out what each of the other fraction
square pieces represents
o Fraction Circle Exploration
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TE Math Support – Summer 2012 – Content Overview
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Using the blue circle to represent one whole, figure out what each of the other fraction
circle pieces represents
Capture Fractions Game & Assessment
Order Up Fraction Game & Assessment
Math Activity: Thinking about Fractional Amounts
 Use diagrams, graph paper, and/or manipulatives to help you solve the problems
Examining Student Thinking: Sharing Brownies
 Read case from Developing Mathematical Ideas: Making Meaning of Operations –Case 20,
Sharing brownies or adding fractions
 Focus questions:
 Focus on Maribel, Alejandro, and Jackson in the case. What did each student do?
What does each student understand?
 What questions or tasks would you like to give to each student to learn more
about his/her thinking? What more is there for the student to understand?
 What is the difference between using fractions as labels and understanding the
addition of fractions?
 What are ideas about fractions that students must consider when they begin to
add fractions with unlike denominators?
 When dealing with fractions, how does a child’s understanding of addition have to
change?
Smaller to Larger Game & Assessment
Session 10: 8/2/12
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Math Content Focus: Fractions
Activities
o Multiplication with Fractions
 Create a visual model for each problem
 Try to write a mathematical equation that goes with each model
o Modeling Multiplication with Fractions using Paper Folding
o Discussion: Multiplication and Division with Fractions
 Making sense of what it means
 Review of partitive and measurement division with whole numbers
 Partitive and measurement division with fractions
o Math Activity: Multiplying and Dividing with Fractions
 Draw a diagram to model the problem
 Find the arithmetic phrase that corresponds to each problem
 Label what each number represents in the arithmetic phrases
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