Transitioning to the Common Core State

Standards – Mathematics

5th Grade Session 3Pam Hutchison

pam.ucdmp@gmail.com

AGENDA

Multi-Step and Other Word Problems Review Math Practice Standards Operations and Algebraic Thinking

Algebraic Expressions Coordinate Graphing

Volume

Multi-Step Word Problems

Bao saved $179 a month. He saved $145

less than Ada each month. How much

would Ada save in three and a half

years?

Multi-Step Word Problems

The baker pays $0.80 per pound for

sugar and $1.25 per pound for butter.

How much the baker will spend if he

buys 6 pounds of butter and 20 pounds

of sugar?

Multi-Step Word Problems

Ava is saving for a new computer that

costs $1,218. She has already saved half

of the money. Ava earns $14.00 per hour.

How many hours must Ava work in order

to save the rest of the money?

Multi-Step Word Problems

A load of bricks is twice as heavy as a

load of sticks. The total weight of 4 loads

of bricks and 4 loads of sticks is 771

kilograms. What is the total weight of 1

load of bricks and 3 loads of sticks?

CCSS Mathematical Practices

REASONING AND EXPLAINING2. Reason abstractly and quantitatively3. Construct viable arguments and critique the reasoning of others

MODELING AND USING TOOLS4. Model with mathematics5. Use appropriate tools strategically

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SEEING STRUCTURE AND GENERALIZING7. Look for and make use of structure8. Look for and express regularity in repeated reasoning

Math Practice Standards

Using the MP descriptions from the 5th Grade Flipbook, describe how you are developing each of these practices in your students. Be ready to share an example for each

of the 8 Math Practices Standards. Which standard is the hardest to

implement?

Engage NY Fluency Practice

Designed to promote automaticity of key concepts

Daily Math is another form of fluency practice

Application Problem Designed to help students understand how

to choose and apply the correct mathematics concept to solve real world problems

Read-Draw-Write (RDW): Read the problem, draw and label, write a number sentence, and write a word sentence

Engage NY Concept Development

Major portion of instruction Deliberate progression of material, from

concrete to pictorial to abstract Student Debrief

Students analyze the learning that occurred

Help them make connections between parts of the lesson, concepts, strategies, and tools on their own

OA.1

Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

OA.2

Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.

Engage NY

Module 2 Lesson 3: Write and interpret numerical expressions and compare expressions using a visual model.

OA.3Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.

G.1Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).

G.2Represent real-world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.

Planning – Day 1

Word Problem (embedded in opening activity)

Opening Activity Number Lines Locating Points

Student Page

Day 1

| | | |0 1 2 3

_

3_

2_

1 _

x

y___, ___ x y2 3

(2, 3)

Plotting Points

(4, 6) – Square

(3, 8) – Triangle

(7, 2) – Star

(5½, 7) – Circle

6, 4½) – Heart

3½, 2½) – Happy Face

Plotting Points

Practice Page 1

Practice Page 2

Day 2

Review (TBD) Opening Activity Activity 1

Draw an -axis so that it goes through points and , and label it -axis.

Draw the -axis so that it goes through points and , and label it -axis.

Day 2, cont.

Label 0 at the origin On the -axis, we’re going to label the

whole numbers only. The length of one square on the grid represents 1 fourth. How many whole numbers will be represented?

Count by fourths as we label the whole number grid lines.

What is the -coordinate of ? What is the -coordinate of ?

Day 2, cont.

Label the -axis the same way Count by fourths as you label the whole

number grid lines. What is the -coordinate of ? What is the -coordinate of ?

Day 2, cont.

Now let’s name the points Put your finger on point A. We know the -

coordinate is 1. What is the -coordinate? So the point should be labeled (1, 0) Do the same for point B. Now put your finger on point C. We know

the -coordinate is 2. What is the -coordinate?

How should the point be labeled? BE CAREFUL!

The point should be labeled (0, 2) Do the same for point D.

Naming Points

Put your finger on point E How do we find the -coordinate for point

E ?What is the -coordinate for point E ?Write the -coordinate as part of a coordinate

pair. How do we find the -coordinate for point

E ?What is the -coordinate for point E ?Write the -coordinate as part of a coordinate

pair.

What are the coordinates for point E ? Write that coordinate pair above point on

your plane.

Naming and Locating Points

Find the coordinates for points F and G. Name the point located at (1, 0). Name the point located at (0, ). Name the point whose distance from

the -axis is . Which point lies at a distance of from

the -axis?

Naming and Locating Points

Plot a point at (3, 2 ). What is the distance between and ?

How did you find it? Plot a point so that the - and -

coordinates are both Find the distance between and .

Naming and Locating Points

Coordinate Practice 2 page 1 Coordinate Practice 2 page 2

Engage NY Module 6 Topic A Lessons 1, 2, and 3 Lesson 4 – Battleship

Lesson 5

Lesson 6

Solving Problems

Module 6 Topic B

Hexagons in a Row

Module 6 Topic D

Patterns and Graphs 1

Volume

Module 5 Topic A and Topic B