Download Multi-Step Word Problems

Transitioning to the
Common Core State
Standards – Mathematics
5th Grade Session 3
Pam Hutchison
[email protected]
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?
1. Make sense of problems and perseveres in solving
them
6. Attend to precision
OVERARCHING HABITS OF MIND
CCSS Mathematical
Practices
REASONING AND EXPLAINING
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the reasoning of
others
MODELING AND USING TOOLS
4. Model with mathematics
5. Use appropriate tools strategically
SEEING STRUCTURE AND GENERALIZING
7. Look for and make use of structure
8. 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.3
Generate 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.1
Use 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., xaxis and x-coordinate, y-axis and y-coordinate).
G.2
Represent 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
y
___,
2 ___
3
x
y
_
3_
(2,
3)
|
2
|
3
2_
1
_
|
0
|
1
x
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 𝑥-axis so that it goes through points 𝐴
and 𝐵, and label it 𝑥-axis.
 Draw the 𝑦-axis so that it goes through points 𝐶
and 𝐷, and label it 𝑦-axis.

Day 2, cont.
Label 0 at the origin
 On the 𝑥-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 𝑥-coordinate of 𝐴?
 What is the 𝑥-coordinate of 𝐵?

Day 2, cont.
Label the 𝑦-axis the same way
 Count by fourths as you label the whole number
grid lines.
 What is the 𝑦-coordinate of 𝐶?
 What is the 𝑦-coordinate of 𝐷?

Day 2, cont.

Now let’s name the points
Put your finger on point A. We know the 𝑥coordinate is 1. What is the 𝑦-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 𝑦coordinate is 2. What is the 𝑥-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 𝑥-coordinate for point E ?
is the 𝑥-coordinate for point E ?
 Write the 𝑥-coordinate as part of a coordinate pair.
 What

How do we find the 𝑦-coordinate for point E ?
is the 𝑥-coordinate for point E ?
 Write the 𝑥-coordinate as part of a coordinate pair.
 What

What are the coordinates for point E ?

Write that coordinate pair above point 𝐸 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,
1
4 ).
4
Name the point whose distance from the 𝑦1
axis is 4 .
4

Which point lies at a distance of
𝑥-axis?
1
4
from the
Naming and Locating Points

Plot a point 𝐽at (3, 2
3
).
4
What is the distance between 𝐽 and 𝐹? How
did you find it?
 Plot a point 𝐾 so that the 𝑥- and 𝑦1
coordinates are both 1

4

Find the distance between 𝐾 and 𝐺.
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