Carroll School August 18 & 19, 2016 by: Graham Fletcher email: - - PowerPoint PPT Presentation

▶
carroll school
SMART_READER_LITE
LIVE PREVIEW

Carroll School August 18 & 19, 2016 by: Graham Fletcher email: - - PowerPoint PPT Presentation

Sep 26, 2022 363 likes •1.59k views

Carroll School August 18 & 19, 2016 by: Graham Fletcher email: gfletchy@gmail.com twitter: @gfletchy blog: www.gfletchy.com Broken Squares Designate shape keeper Share the shapes as evenly as possible between the group All the

slide-1
SLIDE 1

by: Graham Fletcher email: gfletchy@gmail.com twitter: @gfletchy blog: www.gfletchy.com

Carroll School

August 18 & 19, 2016

slide-2
SLIDE 2

Broken Squares

  • Designate shape keeper
  • Share the shapes as evenly as possible between the

group

  • All the shapes will make 6 congruent squares with no

shapes leftover

  • Everyone is encouraged to OFFER a shape. No one

may TAKE or SNATCH. You may RECEIVE a shape but only if it’s OFFERED

  • No “community square”
slide-3
SLIDE 3
slide-4
SLIDE 4
slide-5
SLIDE 5
slide-6
SLIDE 6
slide-7
SLIDE 7

@gfletchy

slide-8
SLIDE 8
slide-9
SLIDE 9
slide-10
SLIDE 10
slide-11
SLIDE 11
slide-12
SLIDE 12
slide-13
SLIDE 13
slide-14
SLIDE 14

Packages Used

58

slide-15
SLIDE 15
slide-16
SLIDE 16

The answer IS NOT 812!

slide-17
SLIDE 17

The 8 Standards for Mathematical Practice

  • 1. Make sense of problems and persevere in solving them.
  • 2. Reason abstractly and quantitatively.
  • 3. Construct viable arguments and critique the reasoning
  • f others.
  • 4. Model with mathematics.
  • 5. Use appropriate tools strategically.
  • 6. Attend to precision.
  • 7. Look for and make use of structure.
  • 8. Look for and express regularity in repeated reasoning.
slide-18
SLIDE 18

The 8 Standards for Mathematical Practice

  • 1. Make sense of problems and persevere in solving them.
  • 2. Reason abstractly and quantitatively.
  • 3. Construct viable arguments and critique the reasoning
  • f others.
  • 4. Model with mathematics.
  • 5. Use appropriate tools strategically.
  • 6. Attend to precision.
  • 7. Look for and make use of structure.
  • 8. Look for and express regularity in repeated reasoning.
slide-19
SLIDE 19

The 8 Standards for Mathematical Practice

  • 1. Make sense of problems and persevere in solving them.
  • 2. Reason abstractly and quantitatively.
  • 3. Construct viable arguments and critique the reasoning
  • f others.
  • 4. Model with mathematics.
  • 5. Use appropriate tools strategically.
  • 6. Attend to precision.
  • 7. Look for and make use of structure.
  • 8. Look for and express regularity in repeated reasoning.
slide-20
SLIDE 20

Missing the Modeling Mark

  • The use of manipulatives does not ensure that

modeling with mathematics is taking place.

  • If the mathematics is not contextualized, modeling

with mathematics cannot exist.

  • Modeling with mathematics does not mean, “I do,

we do, you do.”

slide-21
SLIDE 21

Model with Mathematics Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw

  • conclusions. They routinely interpret their mathematical results

in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

slide-22
SLIDE 22

Model with Mathematics Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw

  • conclusions. They routinely interpret their mathematical results

in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

slide-23
SLIDE 23

#4 Model with Mathematics in the Elementary Grades

slide-24
SLIDE 24

3 Things on the road to modeling…

  • Identify the problem, or pose a question.
  • Make an estimate.
  • Identify the variables needed to solve, and

answer the problem or question posed.

slide-25
SLIDE 25

3-Act Tasks

Act 1:

  • Real world problem or scenario presented
  • What do you notice? What do you wonder?
  • Make estimates

Act 2:

  • Identify missing variables and missing variables to solve
  • Define solution path using variables

Act 3:

  • Solve and interpret results of the solution
  • Validate answer
slide-26
SLIDE 26

5 Practices for Orchestrating Productive Mathematical Discussions

slide-27
SLIDE 27
  • 1. Anticipating student responses to challenging mathematical tasks;

5

The practices are:

Anticipate student solutions for the Whopper Jar task. Identify and record the types of strategies students will use to solve the task.

slide-28
SLIDE 28
slide-29
SLIDE 29
  • 1. Anticipating student responses to challenging mathematical tasks;
  • 2. Monitoring students’ work on and engagement with the tasks;
  • 3. Selecting particular students to present their mathematical work;
  • 4. Sequencing the student responses that will be displayed in a specific
  • rder and;
  • 5. Connecting different students’ responses and connecting the responses

to key mathematical ideas.

5

The practices are:

MTMS: Vol. 14, No. 9, May 2009-5 Prac8ces for Orchestra8ng Produc8ve Mathema8cs Discussions

slide-30
SLIDE 30
  • Look at the student work samples
  • Select the solutions you want to highlight in the closing
  • Sequence how you’ll share them
  • Discuss the connection focus you’re after

5 Moves Planning

slide-31
SLIDE 31
slide-32
SLIDE 32

Our next step as the teacher is….?

  • identify student misconceptions
  • identify common strategy
  • are you surprised that a strategy wasn’t used?
  • discuss your next moves as a teacher
slide-33
SLIDE 33
slide-34
SLIDE 34

Procedural Fluency Conceptual Understanding Application

slide-35
SLIDE 35

Closest to 1000

1. The starting number must be between 11 and 30. 2. This number must be multiplied by a number between 1 and 10.

  • 3. The product must then be multiplied by another number

between 1 and 10.

  • 4. The goal is to obtain a final result of 1,000.

3 rounds without a calculator AND 3 rounds using a calculator What’s different? What stays the same?

slide-36
SLIDE 36

Questions for discussion…

  • 1. What strategies did you use to get closest to

1,000?

  • 2. How did you decide when you had gotten as

close as possible to 1,000?

  • 3. What do you know about the numbers for

which it’s possible to get a final result of 1,000?

slide-37
SLIDE 37
slide-38
SLIDE 38

Strip Model Diagramming for Division

slide-39
SLIDE 39
slide-40
SLIDE 40

Water Rate

slide-41
SLIDE 41

What additional information do you need?

slide-42
SLIDE 42
slide-43
SLIDE 43
slide-44
SLIDE 44

Most asked questions:

  • How often should we use 3-Act Tasks?
  • When should we use 3-Act tasks? How do they fit

into the scope of a unit?

  • How long does one task usually take?
  • What if we don’t have the time?
  • Any others?
slide-45
SLIDE 45

Got Cubes?

slide-46
SLIDE 46
slide-47
SLIDE 47
slide-48
SLIDE 48

Using the digits 0 through 9, create two different shapes with a volume that is equal. Each digit can only be used once.

Open Middle

MCC5.MD.5

slide-49
SLIDE 49
slide-50
SLIDE 50
slide-51
SLIDE 51
slide-52
SLIDE 52
slide-53
SLIDE 53
slide-54
SLIDE 54
slide-55
SLIDE 55
slide-56
SLIDE 56
slide-57
SLIDE 57
slide-58
SLIDE 58
slide-59
SLIDE 59

NUMBER SENSE TRAJECTORY

  • 1. Cut and separate all the headers and descriptors
  • 2. Match the header to the correct descriptor
  • 3. Place them in order and glue to chart paper
  • 4. Explain the stage and what student thinking would

look like in each stage (use number, pictures, and/or words). Kindergarten 2nd Grade

slide-60
SLIDE 60
slide-61
SLIDE 61

Subitizing war: one card is flipped over and the first player to say the card gets to keep it More or less: each player flips over a cards and players must say the number on the card that is MORE or LESS +/- 1 and 2: one card is flipped over and players must say the number that is 1 more Addition war: 2 cards flipped over and students must say the sum

  • f the 2 cards

Part-Whole-Head: 3 players needed. 2 players flip over a card and without looking at it they place it on their forehead. The third player says the sum of the cards and each player tries to solve for the number value that is on their head.

PURPOSEFUL WITH DOT CARDS

slide-62
SLIDE 62
slide-63
SLIDE 63

8 8 1 7 5 4

slide-64
SLIDE 64

Becoming a good estimator takes practice What are you currently doing to promote number sense through estimation in your classroom?

slide-65
SLIDE 65

low actual high

slide-66
SLIDE 66

28 ?

slide-67
SLIDE 67

www.estimation.com

slide-68
SLIDE 68

Estimation Station

slide-69
SLIDE 69
slide-70
SLIDE 70

estimation jar

slide-71
SLIDE 71

16 100 20 20 1002 50 14 19 200 20 32

slide-72
SLIDE 72
slide-73
SLIDE 73
slide-74
SLIDE 74
slide-75
SLIDE 75

Dots Claps

Do more dots or claps in a minute?

slide-76
SLIDE 76
slide-77
SLIDE 77

What do you notice? What do you wonder?

slide-78
SLIDE 78
slide-79
SLIDE 79

?

Questions

slide-80
SLIDE 80
slide-81
SLIDE 81

3 minutes

individual work time

slide-82
SLIDE 82
slide-83
SLIDE 83
slide-84
SLIDE 84
  • 1. Anticipating student responses to challenging mathematical tasks;
  • 2. Monitoring students’ work on and engagement with the tasks;
  • 3. Selecting particular students to present their mathematical work;
  • 4. Sequencing the student responses that will be displayed in a specific
  • rder and;
  • 5. Connecting different students’ responses and connecting the responses

to key mathematical ideas.

5

The practices are:

MTMS: Vol. 14, No. 9, May 2009-5 Prac8ces for Orchestra8ng Produc8ve Mathema8cs Discussions

slide-85
SLIDE 85

Student 1 Student 7 Student 6 Student 2 Student 3 Student 4 Student 5 Student 8

Select and sequence student work in the order

  • f least efficient to

most efficient

slide-86
SLIDE 86

In a particular condominium community 2/3 of all of the men are married to 3/5 of all of the women. What fraction of the entire condominium community are married?

The Condominium Problem

slide-87
SLIDE 87

Task Instruction For each part of the problem, start with a square sheet of paper and make folds to construct a new shape. Then, explain how you know the shape you constructed has the specified area.

  • 1. Construct a square with exactly ¼ the area of the original square.
  • 2. Construct a triangle with exactly ¼ the area of the original

square.

  • 3. Construct another triangle, also with ¼ the area, that is not

congruent to the first one you constructed.

  • 4. Construct a square with exactly ½ the area of the original square.
  • 5. Construct another square, also with ½ the area, that is oriented

differently from the one you constructed in 4.

slide-88
SLIDE 88

PROBLEM TYPE SORT

  • Cut the page apart (11 problems and 4 headers).
  • Write an equation that matches the story

problem directly on each card. Use a ☐ (box) as unknown variable. Be sure the equation accurately match the context.

  • Match each of the 11 problems to the

corresponding header.

slide-89
SLIDE 89

Unit Fractions

slide-90
SLIDE 90
slide-91
SLIDE 91

Representation of a Fraction

1 a

unit fraction —

slide-92
SLIDE 92
slide-93
SLIDE 93
slide-94
SLIDE 94
slide-95
SLIDE 95
slide-96
SLIDE 96

https://www.random.org/integers/

slide-97
SLIDE 97
slide-98
SLIDE 98

Choose a standard/concept and create an Open Middle Problem

slide-99
SLIDE 99
slide-100
SLIDE 100
slide-101
SLIDE 101
slide-102
SLIDE 102

Fair Share

RIBBONS

slide-103
SLIDE 103
  • 1. Macey, Jeremiah and Bryson have 8 cookies. If they

share the cookies equally, how many cookies would each person get?

  • 2. 12 children in art class have to share 8 packages of clay

so that everyone gets the same amount. How much clay can each child have?

Fair Share

Taken from Epson and Levi’s book Extending Children’s Mathematics: Fractions and Decimals

Before you start:

  • Solve using only drawings.
  • Numbers can only be used to label drawings.
  • Share your solution with the group or with a partner.
  • Write an equation to match your model.
slide-104
SLIDE 104

the Big Pad

slide-105
SLIDE 105
slide-106
SLIDE 106

What do you notice? What do you wonder?

slide-107
SLIDE 107

need more?

slide-108
SLIDE 108
slide-109
SLIDE 109
slide-110
SLIDE 110
slide-111
SLIDE 111

Multiple Group Problems

GECKO

slide-112
SLIDE 112

Multiple Groups

Taken from Epson and Levi’s book Extending Children’s Mathematics: Fractions and Decimals

Before you start:

  • Solve using only drawings.
  • Numbers can only be used to label drawings.
  • Share your solution with the group or with a partner.
  • Write an equation to match your model.
  • 1. Emma drinks 2/3 cups of water for every mile she hikes.

Her water bottle holds 4 cups of water. How many miles can she hike before her water runs out?

  • 2. It takes 3/5 yard of ribbon to make a bow. How many

bows could you make with 7.5 yards of ribbon?

slide-113
SLIDE 113

model with manipulatives or drawings NO NUMBERS ALLOWED be prepared to explain and justify your model

slide-114
SLIDE 114
slide-115
SLIDE 115
slide-116
SLIDE 116
slide-117
SLIDE 117
slide-118
SLIDE 118
  • 1. David used exactly 24 cups of flour to make 8 loaves of
  • bread. How many loaves of bread can he make with 6

cups of flour?

  • 2. Socks are selling for $5 for 4 pairs. How much will 9

pairs of socks cost at this rate?

  • 3. Who gets more popcorn? A person in a group where 3

people are sharing 2 small bags of popcorn or a person in a group where 6 children are sharing 4 small bags of popcorn? Equivalencing Problems

Taken from Epson and Levi’s book Extending Children’s Mathematics: Fractions and Decimals

slide-119
SLIDE 119
slide-120
SLIDE 120

www.gfletchy.com

slide-121
SLIDE 121
slide-122
SLIDE 122

EMAIL: gfletchy@gmail.com TWITTER: @gfletchy EMAIL: www.gfletchy.com WEBSITE: https://gfletchy.com/nctm-2016/