**Number Talks**

**Common Core State Standards**

for Mathematics

for Mathematics

**SEDOL's Transition to the Common Core**

**Counting, Order and Compare, and Number Sense**

**Objectives:**

Know how to read the SEDOL Curriculum Framework

Understand the new Instructional Planning Form (IPF) for math

Locate and understand the SEDOL Scope and Sequence and Alignment Document

Comprehend Number Talks

Know the progression of number sense development

Know how to read the SEDOL Curriculum Framework

Understand the new Instructional Planning Form (IPF) for math

Locate and understand the SEDOL Scope and Sequence and Alignment Document

Comprehend Number Talks

Know the progression of number sense development

**Grades 6-8**

**The Math Practice Standards**

**SEDOL's Curriculum Framework**

**SEDOL's IPF**

What are the Common Core State Standards?

**SEDOL's Scope and Sequence & Alignment Document**

**Conceptual Understanding**

Designed with focus, coherence, and rigor in mind

Narrows the scope of content in each grade

Domain

Cluster

Standard

How math should be taught

1. Make Sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively

3. Construct viable arguments and critique the reasoning of 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

Read the article at your table.

Counting

Order and Compare

Fractions

Rational numbers

Irrational Numbers

What does it mean to have $200?

What does it mean to have $-200?

What does it mean to be -25 feet below sea level?

What does it mean to be 25 feet above sea level?

Find the distance a train is from a station

when the stations location is at mile 375 and

the trains current location is p.

**PARCC**

Assessment

Assessment

Think of the problems you encounter in your everyday life,

Are you given what chapter in a textbook to find an answer?

Are you always given all the information you need to solve the problem?

Does the problem always indicate where to begin?

Developing that "puzzlers" disposition requires allowing students to learn through experience.

For example, take a common word problem like

George had 45 green pepper seedlings and 32 tomato seedlings. He planted 52 of them. How many more does he have to plant?

You might leave off some numbers and ask children how they'd solve the problem if the numbers were known.

For example, George started with 45 green pepper seedlings and some tomato seedlings. He planted 52 of them. If you knew how many tomato seedlings he has in all, how could you figure out how many seedlings he still has to plant?

Or, you might keep the original numbers but drop off the question and ask what can be figured out from that information, or what questions can be answered.

George has 45 green pepper seedlings and 32 tomato seedlings. He planted 52 of them. (I could ask "how many seedlings did he start with?" or "How many seedlings did George not plant?" or "What is the smallest number of tomato seedlings he planted?"

Take a problem situation and put it into number.

1 + 2 + 3 + 4 + 3 + 2 + 1

6 + 10

Students need to communicate about mathematics.

The intent of this standard is to have students see math in the real world.

We want students to see that math is not just a collection of skills whose only use is to demonstrate that one has them.

Modeling with mathematics also involves understanding how to interpret situation in the real-world that involve mathematics.

For example:

Does the situation require an exact answer or is estimation okay?

Are there multiple correct answers to the problem?

Are there multiple ways to arrive at an answer?

What are math tools?

This standard also stresses the importance of students deciding when a tool will be helpful, and recognizing the limitations certain tools may have in a particular situation.

In order for students to learn the benefits and drawbacks of particular tools, a variety of tools need to be used in instruction.

Number lines and Area models!

How do you interpret this standard?

The primary focus of this standard is precision of communication, in speech, written symbols, and in specifying the nature and units of quantities in numerical answers, graphs, and diagrams.

Recognize patterns and structures

Encourage students to notice key features, such as identifying defining characteristics of shapes or noticing whether the order in which you add numbers changes the sum.

1 ¾ – ⅓ + 3 + 1/4 – ⅔

Discovering patterns or shortcuts to solving problems.

This standard allows for students to discover strategies rather than be taught them.

e.g., adding 9 is one less than adding 10

The Problem with using number charts to teach skip counting.

5 10 15

20

25

30

35

40

45

50

55

60

65

70

75

80

85

90

95

100

105

110

115

120

125

130

135

140

145

150

5

10

15

20

25

30

Cardinality: The last number counted is the number of items in a set.

Denominator: the unit we are counting

Numerator: The number of units that we have

IMPORTANT:

Make sure to always refer to the whole

Be sure students are aware of what is meant by equal parts

The goal is for students to see unit fractions

as the basic building blocks of fractions, in the

same sense that the number 1 is the basic building

block of the whole numbers; just as every whole

number is obtained by combining a sufficient number

of 1s, every fraction is obtained by combining a

sufficient number of unit fractions.

Important:

Limit denominators to 2, 3, 4, 6, and 8 (3rd grade)

Limit denominators to 2, 3, 4, 6, 8, 10, 12, and 100 (4th grade)

Key Idea: A fraction does not say anything about the size of the whole or the size of the parts. A fraction tells us ONLY about the RELATIONSHIP between the part and whole.

What is the formula?

What if p = 452

0

1

2

3

4

-1

-2

-3

-4

Lets try some problems in a calculator...

3/9

17/99

765/999

This means that students understand cardinality

Though not explicitly stated, students are now determining "how many more/less"

MODELS

Algorithm develops in 4th grade after

more experience

with models

After several examples that 8/12 = 2/3, one would make an argument that each was divided or multiplied by 4

(Through reasoning - they haven't learned about fraction multiplication)

Misconception:

Students at this stage, again, have not learned fraction multiplication or how to find a common denominator.

They should reason about the fractions they are comparing. Using benchmark fractions such as 0, 1/2, and 1 is a beneficial strategy, along with using models

Lets try some examples. Which is Greater?

4/5 or 4/9 (same numerator)

4/7 or 5/7 (same denominator)

3/8 or 4/10 (different numerator & denominator)

4/6 or 7/12

Which is Greater

5/3 or 7/4 (remember we are always going to work with

fractions greater than 1)

Writing decimals as base-ten fractions allows for easier comparisons.

For example:

.13 or .2

.134 or .12

.301, .031, .003, .31

Magnitude vs. value

-8 or -4

-3 or -7

What day was it warmer, the day it was -5 degrees below zero, or the day it was -3 degrees below zero.

While it is impossible to find the exact placement of an irrational number on a number line students can learn to approximate its location based on a comparison to rational numbers.

Where would pi be located on a number line?

What about square root of 3?

Lets do a number talk

http://www.parcconline.org/samples/mathematics/grade-6-mathematics

Children's progression to understanding beginning fractions:

1. Partitioning squares and circles into 2 and 4 equal shares and

name

how many shares.

2. Partitioning squares and rectangles into 2, 3, and 4 equal shares and

name

how many shares.

Introduce concept through real-world problems

William’s class had a pizza party on the last day of school. One of the pizzas

was divided into 6 pieces. William ate 2 of the pieces. What fraction of the

pizza did William eat?