powerteaching i3: grade 6 mathematics - johns hopkins...

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Scope and Sequence

The grade 6 PowerTeaching Scope and Sequence is a guide for the content covered in each lesson of the Power Teaching grade 6 curriculum. Additionally, the

scope and sequence visually demonstrates the structure of PowerTeaching and shows how the lessons are divided into units and cycles based on math content.

The scope and sequence also provides the Common Core State Standards Mathematical Practice and Content standards that apply to each lesson. It a

lso

provides a picture of when media, tools, and routines are introduced and used within each lesson cycle.

The PowerTeaching Scope and Sequence is a guide to the order in which the PowerTeaching lessons are intended to be taught. This order is provided so that

concepts can be introduced then later reviewed as a part of new skills. Similarly, problem solving strategies are first introduced then applied to later word problems

and real-world math situations.

Sta

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Unit 1 – Start-Up

Cycle 1

1 – Introduction to

Teamwork

1 and 3

n/a

Pre-assessment on

Grade 5 Skills

n/a

Learning routines:

Think-Pair-Share

and Zero Noise

Signal

2 – Team Building

n/a

n/a

n/a

n/a

Learning routine:

Team Huddle

Video: W

orking

Together

3 – Math as a Brain

Workout

1, 3, and 7

n/a

Multiply decimals

(CC 5.NBT.7)

n/a

Learning routines:

Get the Goof and

Team Score Sheet

Video: Team

Cooperation Goals

4 – The Problem

Solving Plan

1, 2, and 4

The Problem

Solving Plan

Adding fractions

(CC 5.NF.1)

The Problem

Solving Plan

Learning routines:

Homework Check

and Team Mastery

5 – Extraneous Data

Problem Solving

1, 4, and 6

Extraneous Data in

Word Problems

Dividing Whole

Numbers (CC

6.NS.2)

Extraneous Data in

Word Problems

Learning routines:

Quick Check

6 – Pose-a-Problem

Problem Solving

2 and 6

Pose Problems for

Given Data

n/a

Pose Problems for

Given Data

Learning routine:

Cool-Down

Strategies

7 – Assessment

Day

1 and 3

Assessment of Unit

1 Math Topics

n/a

n/a

Learning routines:

Assessment Day,

Improvement

Points, Goal Setting

Videos:

Improvement Points

and the Team Score

Sheet

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Unit 2 – Computation Skills

Cycle 1 – Dividing Whole

Numbers

1 – Mental Math

3 and 6

Use the Distributive

Property to mentally

divide whole

numbers (CC

6.NS.4)

Divide by multiples

of 10 (CC 5.NBT.2)

n/a

Videos: Active

Listening 1 and

Mental M

ath

2 – Estimation

3, 5, and 6

Estimating quotients

and products

Mental Math

Strategies (CC

6.NS.4)

One-step word

problems

n/a

3 – Whole Number

Division 1

3, 4, and 6

Divide two multi-

digit whole numbers

with no remainder

(CC 6.NS.2)

Multiply two multi-

digit whole numbers

(CC 5.NBT.5)

One-step word

problems

n/a

4 – Whole Number

Division 2

3, 4, and 6

Divide two multi-

digit whole numbers

with remainders (CC

6.NS.2)

Write answers to

word problems as

mixed numbers (CC

5.NF.3)

One-step word

problems in which

students choose the

best way to

represent the

answer

n/a

Cycle 2 – Decimal Operations

5 – Estimating

Decimals

3, 5, and 6

Estimate sums,

differences,

products, and

quotients with

decimal numbers

Estimate the value

of decimal numbers

One-step word

problems

Video: Active

Listening 2

6 – Adding and

Subtracting

Decimals

3, 4, and 6

Find the sum and

difference of multi-

digit decimal

numbers (CC

6.NS.3)

Fractions represent

division of two

numbers (CC

5.NF.3)

One-step word

problems

n/a

7 – Multiplying

Decimals

3, 4, and 6

Find the product of

multi-digit decimal

numbers (CC

6.NS.3)

Estimate to check

computation

One-step word

problems

n/a

8 – Dividing

Decimals

3, 4, and 6

Find the quotient of

multi-digit decimal

numbers (CC

6.NS.3)

Estimate to check

computation

One-step word

problems

n/a

9 – Decimal

Computation

1, 2, and 4

Use decimal

computation to

answer complex,

real-world math

problems (CC

6.NS.3

Use whole

estimation and

inverse operations

to check

computation and

use whole number

computation to

solve real-world

problems (CC

6.NS.2)

Complex, multi-step

math problems in

which data is

presented in text

and in diagrams

n/a

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Unit 3 – Fractions

Cycle 1 – GCF and

LCM

1 – Greatest

Common Factor

3, 4, and 6

Find the greatest

common factor of

two whole numbers

(CC 6.NS.4)

Finding factors (CC

4.OA.4)

One-step word

problems; drawing

models for word

problems

Video: Help and

Encourage Others 1

2 – Least Common

Multiple

3, 4, and 6

Find the least

common multiple of

two whole numbers

(CC 6.NS.4)

n/a

One-step word

problems

n/a

3 – Problem Solving

with GCF and LCM

1, 2, and 7

Use GCF and LCM

to answer complex

math problems

n/a

Complex, real-world

math problems with

data in words and in

diagrams

n/a

Cycle 2 – Fraction Concepts

4 – Estimating

Fractional Values

3, 5, and 6

Estimate the value

of complex fractions

in relation to 0, ½,

and 1.

Reason about the

size of a fraction

using a number line

(CC 3.NF.2)

n/a

Video: Help and

Encourage Others 2

5 – Ordering

Fractions, Mixed

Numbers, and

Decimals

3 and 6

Compare and order

fractions, mixed

numbers, and

decimals

Fractions represent

division of two

numbers (CC

5.NF.3)

n/a

n/a

6 – Multiplying

Fractions

3 and 6

Multiply fractions

and mixed numbers

Multiply fractions

and whole numbers

(CC 5.NF.4a)

Multiply fractions by

fractions (CC

5.NF.4b)

One-step word

problems

n/a

Cycle 3 –

Dividing

Fractions

7 – Dividing Whole

Numbers and

Fractions

3 and 6

Divide whole

numbers by

fractions and mixed

numbers (CC

6.NS.1)

Multiply fractions

and whole numbers

(CC 5.NF.4a)

One-step word

problems

Videos: E

veryone

Partic

ipates 1 and

Dividing with

Fractions is Hot

8- Divide Fractions

by Fractions

3 and 6

Divide fractions by

other fra

ctions (CC

6.NS.1)

Multiply fractions by

fractions (CC

5.NF.4b)

One-step word

problems

Video: Reciprocals

and Division of

Lasagna


with Multiplying and

Dividing Fractions

1, 2, and 4

Multiply and divide

fractions, whole

numbers, and mixed

numbers to solve

complex word

problems (CC

6.NS.1)

Problem Solving

Steps

Complex, real-world

math problems with


diagrams

n/a

Ratio

s a

nd

Pro

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ela

tion

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Unit 4 – Rational Numbers

Cycle 1 – Understanding

Integers

1 – Exploring

Integers

3 and 6

Use integers to

represent real-world

concepts and

amounts (CC

6.NS.5)

Sequence and

comparing

quantities on a

number line

n/a

Video: Everyone

Partic

ipates 2

2 – Graphing

Ordered Pairs in All

Quadrants

3, 4, and 8

Locate and plot

points in all

quadrants of a

coordinate plane

(CC 6.NS.6b)

Plotting and locating

points in Quadrant I

(CC 5.G.1)

n/a

Tools: graphing

calculator or

desmos.com

3 – Exploring

Graphing

1, 2, and 4

Use the coordinate

plane and the

properties of

polygons to solve

problems (CC

Properties of

polygons (CC 5.G.3

and CC 5.G.4)

Geometric problem

solving on the

coordinate grid

Tools: graphing

calculator or

desmos.com

Cycle 2 – Integers and Problem

Solving

4 – Compare and

Order Integers

3 and 6

Use a number line

and number sense

to compare and

order integers in

real-world and

mathematical

context (CC 6.NS.7)

n/a

n/a

Video: E

xplain

Ideas 1

Tool: number line

5- Absolute Value

3 and 6

Find the absolute

value of given

rational numbers

and order absolute

values (CC 6.NS.7)

n/a

Simple context

problems

n/a


with Coordinates

1, 2, and 4

Solve real-word

problems involving

plotting points on

and calculating

distance on

coordinate planes

(CC 6.NS.8 and

6.G.3)

Line of symmetry

(CC 4.G.3)

Complex, real-world

math problems with


diagrams

Tools: graphing

calculator or

desmos.com

Video: Distance on

the Coordinate

Plane

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Unit 5 – Introduction to

Ratios and Rates

Cycle 1 – Introduction to Rates

and Ratios

1 – What are

Ratios?

3 and 6

Write ratios in three

ways and use ratio

language (CC

6.RP.1)

n/a

Problems with

simple context

Videos: Explains

Ideas 2 and What

are Ratios Anyway?

2 – Ratios and

Tables

3, 4, and 6

Use tables to find

equivalent ratios

(CC 6.RP.3)

Analyze number

patterns within a

table (5.OA.3)

One-step word

problems

n/a

3 – Rate and Unit

Rate

3, 4, and 6

Use double number

lines, tables, and

fractions to find the

unit ra

te (CC

6.RP.2)

Equivalent fra

ctions

(CC 4.NF.1)

One-step word

problems

n/a

4 – Comparing

Rates

1, 2, and 4

Compare rates,

ratios, and unit rates

in the context of

real-world problems

(CC 6.RP.3)

Find the unit ra

te

(CC 6.RP.3)

Comparing fractions

(CC 4.NF.2)

One- or two-step

word problems

Video: Unit P

ricing

or W

hose Bargain is

Better?

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Unit 6 – Ratios and Percents

Cycle 1 – Problem Solving with Ratio and Rate

1 – Converting

Measurements

4, 5, and 6

Determine

conversion rates

and use given rates

to convert m

easures

(CC 6.RP.3)

n/a

One-step word

problems

Video: Complete

Tasks 1


with Unit Rates

3, 4, and 8

Solve complex unit

rate and unit price

word problems (CC

6.RP.3)

Find equivalent

ratios (CC 6.RP.2)

One- to two-step

word problems

n/a

3 – Ratios and

Graphing

3, 4, 5, and 6

Make tables of

equivalent ratios

and graph the ratios

as ordered pairs

(CC 6.RP.3)

Plot ordered pairs

(CC 6.NS.6)

One- to two-step

word problems

Tools: graphing

calculator or

desmos.com

4 – Ratios and Tape

Diagrams

1, 2, and 4

Use tape diagrams

to answer questions

about rates and

ratios (CC 6.RP.3)

n/a

Two-step word

problems

n/a

5 – Ratio and Rate

Problem Solving

1, 2, and 4

Use rate and ratio

reasoning to solve

complex, real-world

problems (CC 6.NS

1–3)

Problem Solving

Strategies

Fraction

computation (CC

6.NS.1–4)

Complex, real-world

math problems with


diagrams

Tools: graphing

calculator or

desmos.com

Cycle 2 –

Percents

6 – Understanding

Percents

3 and 6

Write a percent to

represent a simple

situation and

convert between

fractions, decimals

and percents (CC

6.RP.3)

Convert between

fractions and

decimals (CC

5.NF.3)

Simple context

problems

Video: C

omplete

Tasks 2

7 – Comparing and

Ordering Percents,

Fractions, and

Decimals

3 and 6

Compare and order

percents, fra

ctions,

and decimals in

mathematical and

real-world contexts

(CC 6.RP.3)

Compare fractions

and decimals

Simple context

problems

Tool: number line

8 – Solving Percent

Problems

1 and 2

Solve one-step word

problems involving

percents, such as

finding the percent

of a number (C

C

6.RP.3)

n/a

One-step word

problems

n/a


with Percents

1, 2, and 4

Solve complex, real-

world problems

involving percents,

decimals, and

fractions (CC

6.RP.3)

Problem solving

with fractions and

decimals (CC

6.NS.1 and 3)

Complex, real-world

math problems with


diagrams

n/a

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Unit 7 – Writing and Evaluating Expressions

Cycle 1 – Numeric

Expressions

1 – Understanding

Exponents

3, 4, and 6

Use real-world

examples, such as

area and arrays, to

make sense of and

simplify exponents

(CC 6.EE.1)

Area of a square

(CC 4.MD.3)

One-step word

problems; drawing

models for word

problems

n/a

2 – Order of

Operations

3 and 6

Use the full Order of

Operations to

simplify and

evaluate numeric

expressions (CC

6.EE.1)

Evaluate

expressions with

parentheses (CC

5.OA.1)

n/a

Video: O

rder of

Operations or The

Mystery Caller

3 – Write and Solve

Numeric

Expressions

1, 2, and 4

Write numeric

expressions to solve

complex, real-world

math situations (CC

6.EE.1)

The Problem

Solving Steps

Complex, real-world

math problems with


diagrams

n/a

Cycle 2 – Writing Algebraic

Expressions

4 – Introduction to

Variables

2 and 4

Define variables,

then identify and

name variables in

math stories (CC

6.EE.2 and 6)

n/a

Simple context

problems

Video: In

troduction

to Variables or

Maxed Out!

5 – Algebraic

Expressions and

Vocabulary

3 and 6

Understand and

identify the key

parts of algebraic

expressions

(variable, constant,

term, etc)

n/a

n/a

n/a

6 – Writing

Expressions 1

2

Write one-step

algebraic

expressions to

represent math

phrases (CC

6.EE.2)

Translate word

problems into

number sentences

On-step math

phrases

n/a

7 – Writing

Expressions 2

2

Write multi-step

algebraic

expressions to

represent math

phrases (CC

6.EE.2)

Translate word

problems into

number sentences

Two-step math

phrases

n/a

Cycle 3 – Evaluating Expressions

8 – Evaluate

Expressions 1

2

Evaluate single- and

multi-step

expressions for

specific values. (CC

6.EE.2)

Order of Operations

(CC 6.EE.1)

One- and two-step

math phrases

n/a

9 – Evaluate

Expressions 2

2

Use geometric

formulas to explore

and evaluate

algebraic

expressions with

exponents (CC

6.EE.2)

Order of Operations

(CC 6.EE.1)

Multi-step math

phrases and

diagrams

n/a

10 – Expressions

and Patterns

3, 4, and 7

Use a table of

values to determine

how changing the

value of the variable

affects the value of

the expression. (CC

6.EE.2)

Order of Operations

(CC 6.EE.1)

n/a

n/a

11 – Write and

Evaluate

Expressions

1, 2, and 7

Write and evaluate

algebraic

expressions for real-

world math

situations (CC

6.EE.2)

Order of Operations

(CC 6.EE.1)

Real-world math

problems with data

in words and in

diagrams

Video: W

rite and

Evaluate

Expressions

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Unit 8 – Equivalent Expressions

Cycle 1 – Properties of Addition

1 – Properties of

Addition 1

3, 6, and 7

Identify the

Properties of

Addition and use

them to rewrite

expressions (CC

6.EE.3)

Order of Operations

(CC 6.EE.1)

n/a

n/a

2 – Combining

Variables

2, 3, and 6

Simplify algebraic

expressions with

one variable. (CC

6.EE.3)

Properties of

Addition and Order

of Operations

n/a

n/a

3 – Proving

Expressions

Equivalent 1

3, 6, and 7

Evaluate two

expressions to

prove if th

ey are

equivalent and use

the Properties of

Addition to describe

why (CC 6.EE.4)

Properties of

Addition and Order

of Operations

n/a

Tools: proofs

Cycle 2 – Properties of

Multiplication

4 – Properties of

Multiplication

3, 6, and 7

Identify the

Properties of

Multiplication and

use them to rewrite

expressions (CC

6.EE.3)

Order of Operations

(CC 6.EE.1)

n/a

n/a

5- Greatest

Common Factors

3, 6, and 7

Identify the GCF of

algebraic terms in

an expression (CC

6.EE.3)

Greatest Common

Factor of two hole

numbers (CC

6.NS.4)

n/a

n/a

6 – The Distributive

Property

3, 6, and 7

Use the Distributive

Property to rewrite

expressions (CC

6.EE.3)

n/a

n/a

n/a

7 – Proving

Expressions

Equivalent 2

3, 6, and 7

Evaluate two

expressions to

prove if th

ey are

equivalent and use

the Properties of

Multiplication to

describe why (CC

6.EE.4)

Properties of

Multiplication (CC

6.EE.3)

n/a

n/a

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Unit 9 – Solving Equations

Cycle 1 – Expressions and Equations

1 – Defining

Equations

2 and 4

Understand and

model that

equations must

remain balanced by

definition (CC

6.EE.5)

Properties of

Addition and

Multiplication (CC

6.EE.3)

Use models and

contextual examples

to represent

equations

n/a

2 – Solutions to

Equations and

Inequalities

2, 3, and 6

Substitute given

values into the

variables of

equations and

inequalities to

determine if th

ey are

possible solutions

(CC 6.EE.5)

Order of Operations

(CC 6.EE.1)

n/a

n/a

3 – Solving

Equations

2, 3, and 6

Use mental math

and quess-and-

check to solve one-

step equations (CC

6.EE.5)

Order of Operations

(CC 6.EE.1)

n/a

n/a

4 – Geometry and

Equations

2 and 4

Solve geometric

equations using

mental math, guess-

and-check, and

visual estimation

(CC 6.EE.5)

Perimeter, Area,

and Volume

Geometric word

problems or

diagram problems

n/a

Cycle 2 – One-Step

Equations

6 – Inverse

Operations

3 and 6

Define and identify

inverse operations

and use them to

solve equations

equal to 0 (CC

6.EE.7)

Opposite integers

(CC 6.NS.6)

Simple context

problems

Video: In

verse

Operations

7 – Solving Addition

and Subtraction

Equations

2 and 4

Use inverse

operations to solve

one-step addition

and subtraction

equations with

whole numbers (CC

6.EE.7)

Inverse Operations

(CC 6.EE.7)

Simple context

problems

Video: Solving

Equations

Tool: balance or

scale

8 – Solving

Multiplication and

Division Equations

2 and 4

Use inverse

operations to solve

one-step

multiplication and

division equations

with whole numbers

(CC 6.EE.7)

Inverse Operations

(CC 6.EE.7)

Simple context

problems

Tool: balance or

scale

9 – Solving

Equations to

Answer Questions

1 and 2

Solve a given one-

step equation to

answer a real-world

math problem (CC

6.EE.7)

n/a

Real-world math

situations with one-

step solutions

n/a

Cycle 3 – Equations and Problem Solving

10 – Choose the

Correct Equation 1

2 and 4

Given a choice of

addition and

subtraction

equations, choose

the one that

correctly represents

the math situation

(CC 6.EE.7)

The Problem

Solving Steps

One-step word

problems

n/a

11 – Choose the

Correct Equations 2

2 and 4

Given a choice of

multiplication and

division equations,

choose the one that

correctly represents

the math situation

(CC 6.EE.7)

The Problem

Solving Steps

One-step word

problems

n/a

12 – Write and

Solve Equations

1, 2, and 4

Write an equation to

represent a real-

world problem, then

solve the equation

to answer the

question. (CC

6.EE.7)

The Problem

Solving Steps

One-step word

problems

n/a

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esso

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Unit 10 – Inequalitities

Cycle 1 – Simple Inequalities

1 – Equations and

Inequalities

3 and 6

Understand the

differences and

similarities between

equations and

inequalities. (CC

6.EE.8)

Understand and

solve equations.

(CC 6.EE.7)

n/a

Tool: balance or

scale

2 – Graphing

Inequalities

3, 4, and 6

Graph simple

inequalities on a

number line and

answer questions

about the

inequalities. (CC

6.EE.8)

Ordering rational

numbers (CC

6.NS.7a, 5.NBT.5)

n/a

Tool: number line

3 – Write and Graph

Inequalities

1 and 4

Write and graph

simple inequalities

to represent real-

world problems. (CC

6.EE.8)

The Problem

Solving Steps

Simple context

problems

Tool: number line

4 – Solutions to

Inequalities

3 and 6

Substitute given

values for the

variables in

inequalities to

determine if th

ey are

a possible solution.

(CC 6.EE.8)

Evaluate

expressions (CC

6.EE.2)

n/a

n/a

5 – Solving

Inequalities

1 and 2

Use number sense

and guess-and-

check to define a

solution set for an

inequality. (CC

6.EE.8)

Solving equations

(CC 6.EE.7)

Simple context

problems

n/a

L

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Math

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Unit 11 – Patterns, Equations, and Graphs

Cycle 1 – Independent and Dependent

Relationships

1 – Dependent and

Independent

Relationships

2 and 4

Understand the

definition for

dependent and

independent events.

(CC 6.EE.9)

n/a

Simple context

problems

n/a

2 – Patterns and

Number Tables

3, 4, and 6

Write an expression

to represent the

pattern in a number

table using

variables. (CC

6.EE.9)

Write algebraic

expressions (CC

6.EE.2)

Construct models

for patterns in a

table

n/a

3 – Dependent and

Independent Data

1 and 2

Name the

dependent and

independent

variables in a real-

world relationships,

then use the table to

describe the

relationship. (CC

6.EE.9)

n/a

Construct models

for patterns in a

table that represents

a real-world

situation

n/a

Cycle 2 – Graph and Write

Equations to Solve Real-

World Problems

4 – Tables and

Equations 1

3, 4, and 6

Make a table of

values from a linear

equation and write

an equation to

represent a given

table of values. (CC

6.EE.9)

Write equations (CC

6.EE.8)

Construct models

for patterns in a

table

n/a

5- Tables and

Equations 2

2, 4, and 8

Use a table of

values to

understand and

write formulas for

area, perimeter, and

volume. (CC

6.EE.9)

Perimeter, area, and

volume (CC 5.MD.5,

3.MD.7 and 8)

Construct geometric

formulas for

patterns in a table

Tools: shapes

6 – Tables and

Graphs

2 and 4

Use tables of values

to graph a

relationship

between two

variables. (CC

6.EE.9)

Graph ordered pairs

on a coordinate

plane (CC 6.NS.6c)

n/a

Tools: graphing

calculator or

desmos.com

7 – Linear

Relationships

1, 4, and 8

Given a real-world

situation, make a

table of values, write

an equation, and

graph the

relationship. (CC

6.EE.9)

Use coordinate

planes to solve real-

world problems (CC

6.NS.8)

Complex, real-world

problems.

Video: Linear

Relationships

Tools: graphing

calculator or

desmos.com

Geo

metry

an

d M

easu

rem

en

t

L

esso

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Math

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Unit 12 – Measurement

Cycle 1 – Measurement and Conversion

1 – Estimate

Measures of Length

3, 5, and 6

Choose the

appropriate tools to

measure length.

Estimate customary

and metric

measures.

Name the number of

smaller measures in

a larger measure

(CC 4.MD.1)

Estimation and

mental math

Tools: ruler, yard

stick, tape measure

2 – Estimate

Measures of Weight

3, 5, and 6

Choose the


measure weight.

Estimate the

customary and

metric measure of

weight.

Name the number of

smaller measures in

a larger measure

(CC 4.MD.1)

Estimation and

mental math

Tools: scale and

balance

3 – Estimate

Measures of

Capacity

3, 5, and 6

Choose the


measure capacity.

Estimate the

customary and

metric measure of

capacity.

Name the number of

smaller measures in

a larger measure

(CC 4.MD.1)

Estimation and

mental math

Tools: ruler and cup

measures

4 – Convert M

etric

Units of Measure

7 and 8

Use the four

operations and ratio

reasoning to convert

between metric

units. (CC 6.RP.3d)

Convert between

units of measure

(CC 5.MD.1)

Simple context and

geometric problems

Tools: tools of

measure

Video: Convertin

g

Units of M

easure

5 – Convert

Customary Units of

Measure

7 and 8

Use the four

operations and ratio

reasoning to convert

between customary

units of measure

(CC 6.RP.3d)

Convert between

units of measure

(CC 5.MD.1)

Simple context and

geometric problems

Tools: tools of

measure

Video: Convertin

g

Units of M

easure

6 – Measurement in

Problem Solving

1, 2, 7, and 8

Answer complex,

real-word problems

involving estimating,

finding, and

converting

measures of length,

weight, and

capacity. (CC

6.RP.3d)

Convert between

units of measure

(CC 5.MD.1)

Complex real-world

problems

Tools: tools of

measure

Cycle 2 – Area

7 – Properties of

Polygons

5 and 8

Identify two-

dimensional shapes

based upon the

measures and

characteristics of

their sides and

angles. (CC 5.G.3)

Identify two-

dimensional shapes

based upon the

measures and

characteristics of

their sides and

angles. (CC 5.G.3)

n/a

Tools: tools of

measure

8 – Area of

Rectangles and

Triangles

4, 5, and 8

Review the formula

for area of a

rectangle and derive

the formula of a

triangle from a

rectangle. (CC

6.G.1)

Area of a rectangle

(CC 4.MD.3)

Derive one formula

from another

Tools: tools of

measure

9 – Area of

Quadrilaterals

4, 5, and 8

Find the area of

special

quadrilaterals by

composing or

decomposing them

into rectangles and

triangles.

Extrapolate

formulas for finding

the area of each

shape. (CC 6.G.1)

Area of a rectangle

(CC 4.MD.3) and

Area of a triangle

(CC 6.G.1)

Derive one formula

from another

Tools: tools of

measure

10 – Area on the

Coordinate Plane

3, 4, and 6

Use a coordinate

plane to find the

area of tria

ngles and

quadrilaterals. (CC

6.NS.8 and 6.G.1)

Find distance on the

coordinate plane

(CC 6.NS.7)

n/a

Tools: graphing

calculator or

desmos.com

11 – Problem

Solving with Area

1, 2, and 5

Use the formulas for

area of tria

ngles and

quadrilaterals to

solve real-world

problems. (CC

6.G.1)

Area of a rectangle

(CC 4.MD.3) and

Area of a triangle

(CC 6.G.1)

Complex, real-world

problems

Tools: tools of

measure

L

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Math

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Unit 13– Volume and Surface Area

Cycle 1 – Independent and Dependent Relationships

1 – Finding Volume

1

3, 4, and 6

Estimate the volume

of a container/

rectangular prism in

fractional unit

cubes, then find the

actual volume in

fractional unit

cubes. (CC 6.G.2)

Find the volume of

rectangular prisms

in whole units (CC

5.G.4 and 5)

n/a

Tools: fra

ctional unit

cubes

2 – Derive the

Formula

4 and 8

Derive the formula

for volume (V = lwh)

by making a data

table. (CC 6.G.2)

Find the volume of

rectangular prisms

in whole units (CC

5.G.4 and 5)

Derive a formula

from collected data

n/a

3 – Finding Volume

2

3 and 6

Estimate and find

the volume of

rectangular prisms

with fractional side-

lengths using the

formulas for volume.

(CC 6.G.2)

Find the volume of

rectangular prisms

in whole units (CC

5.G.4 and 5)

n/a

Video: Finding

Volume

4 – Volume and

Problem Solving

1 and 2

Solve complex, real-

world problems

related to finding

volume. This will

include additive and

subtractive

problems. (CC

6.G.2)

Find the volume of

rectangular prisms

in whole units (CC

5.G.4 and 5)

Complex, real-world

problems

n/a

Cycle 2 – Surface Area 5 – Solid Figures

and Nets

4, 5, and 7

Name a solid figure

for a given net and

construct or draw a

net when given a

solid figure. (CC

6.G.4)

Identify two-

dimensional shapes

based upon the

measures and

characteristics of

their sides and

angles. (CC 5.G.3)

Spatial, geometric

problem solving.

Video: Solid Figures

and Nets

Tools: Nets

6 – Surface Area of

Rectangular and

Triangular Prisms

4 and 5

Construct and use

nets to find the

surface area of

prisms. Extrapolate

the process to find

the surface area

without nets. (CC

6.G.4)

Area of a rectangle

(CC 4.MD.3) and

Area of a triangle

(CC 6.G.1)

Derive a

formula/process

from collected data

Tools: Nets

7 – Surface Area of

Pyramids

4 and 5

Construct and use

nets to find the

surface area of

pyramids.

Extrapolate the

process to find the

surface area without

nets. (CC 6.G.4)

Area of a rectangle

(CC 4.MD.3) and

Area of a triangle

(CC 6.G.1)

Derive a

formula/process

from collected data

Tools: Nets


with Surface Area

1, 4, and 5

Use nets or

processes to find

surface area in

order to solve

complex, real-world

problems. (CC

6.G.4)

Area of a rectangle

(CC 4.MD.3) and

Area of a triangle

(CC 6.G.1)

Complex, real-world

problems

Tools: Nets

Sta

tistic

s a

nd

Pro

bab

ility

L

esso

n

Co

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Co

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(s) o

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Pra

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Main

Math

C

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Rev

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Math

C

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Pro

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Unit 14 - Introduction to Statistics

Cycle 1 – Statistical Questions

1 – Collecting Data

3 and 6

Students will use

given survey

questions to collect

and organize data.

They will start

talking about good

and bad questions.

(CC 6.SP.1)

n/a

Simple reasoning

about good and bad

survey questions

Tools: Various data

collecting and

organizing tools like

spreadsheets

2 – Variability and

Statistical Questions

3 and 6

Students will use

the data they

collected to talk

more in depth about

good and bad

statistical questions

and the reasons

organizations ask

questions. (CC

6.SP.1)

n/a

Simple reasoning

about good and bad

survey questions

Tools: Various data

collecting and


spreadsheets

3 – Writing

Statistical Questions

3 and 6

Students construct

their own statistical

questions, conduct

a survey, and

organize the data in

a list. They will

begin to make

simple observations

about the data. (CC

6.SP.1)

n/a

Simple reasoning

about good and bad

survey questions

Tools: Various data

collecting and


spreadsheets

Cycle 2 – Displaying Data

4 – Displays of

Categorical Data

4 and 5

Define categorical

data and introduce

bar graphs and

circle graphs. (CC

6.SP.4)

Make a line plot to

display data (CC

4.MD.4)

n/a

Tools: Various data

collecting and

displaying tools

such as

spreadsheets and

graphs

5 – Displays of

Numerical Data

4 and 5

Define numerical

data and introduce

histograms, line

plots, box plots,

histograms, and

stem-and-leaf plots.

(CC 6.SP.4)

Make a line plot to

display data (CC

4.MD.4)

Use a coordinate

plane to display

real-world data )CC

5.G.1 and 2)

n/a

Tools: Various data

collecting and

displaying tools

such as

spreadsheets and

graphs

6 – Line Graphs

4 and 5

Understand that line

graphs represent a

special case for

displaying numerical

data (CC 6.SP.4)

Make a line plot to

display data (CC

4.MD.4)

n/a

Tools: Various data

collecting and

displaying tools

such as

spreadsheets and

graphs

7 - Histograms

4 and 5

Create histograms

for given data using

appropriate tools.

Make a line plot to

display data (CC

4.MD.4)

n/a

Tools: Various data

collecting and

displaying tools

such as

spreadsheets and

graphs

Unit 15 – Describing and Using Data

Cycle 1 – Distribution of Statistical Data 1 – Shapes of Data

Sets

1, 2, and 4

Compare the

shapes of

categorical data

sets on similar and

different data. (CC

6.SP.2)

n/a

Analyze the shape

of data sets.

Tools: Various data

collecting and

displaying tools

such as

spreadsheets and

graphs

2 – Numerical Data

Sets

1, 2, and 4

Compare the

shapes of numerical

data sets on similar

and different data.

(CC 6.SP.2)

Define numerical

data and introduce

histograms, line

plots, box plots,

histograms, and


(CC 6.SP.4)

Analyze the shape

of data sets.

Tools: Various data

collecting and

displaying tools

such as

spreadsheets and

graphs

3 – Box Plots

1, 2, and 4

Construct and

analyze box plots.

(CC 6.SP.2)

Define numerical

data and introduce

histograms, line

plots, box plots,

histograms, and


(CC 6.SP.4)

Analyze the shape

of data sets.

Tools: Various data

collecting and

displaying tools

such as

spreadsheets and

graphs

Video: Box Plots

4 – Comparing Box

Plots

1, 2, and 4

Compare box plots

on similar and

different data. (CC

6.SP.2)

Define numerical

data and introduce

histograms, line

plots, box plots,

histograms, and


(CC 6.SP.4)

Analyze the shape

of data sets.

Tools: Various data

collecting and

displaying tools

such as

spreadsheets and

graphs

Cycle 2 – Measures of Center

and Variability

5 – Measures of

Center 1

3 and 6

Calculate mean,

median, and mode

of a given data set.

(CC 6.SP.3)

Calculate with whole

and decimal

numbers. (CC

6.NS.2 and 3)

n/a

Tools: spreadsheets

to calculate various

measures of center

Video: You know

what I M

EAN?!

6 – Measures of

Center 2

4 and 7

Analyze what the

mean, median, and

mode of a data set

tell you about the

data. (CC 6.SP.3)

n/a

Analyze data sets

Tools: spreadsheets


measures of center

Video: Displaying

Data

7 – Measures of

Variability

3, 6, and 7

Calculate

interquartile range

and mean-absolute

deviation and

analyze what these

measures of

variability tell you

about a data set.

(CC 6.SP.3)

Calculate with whole

and decimal

numbers. (CC

6.NS.2 and 3)

Analyze data sets

Tools: spreadsheets


measures of

variability

8 – Describing Data

Sets

4 and 7

Use the shape of

the data, the

measures of center,

and the measures of

variability to

describe (CC

6.SP.3)

n/a

Analyze data sets

Tools: Various data

collecting and

displaying tools

such as

spreadsheets and

graphs

Cycle 3 – Complete a Data Project

9 – Define the

Investigation

1–6

Write a statistical

question and find a

data set that

answers it. (C

C

6.SP.5)

CC 6.SP.1–4

Analyze data sets

Tools: Various data

collecting and

displaying tools

such as

spreadsheets and

graphs

10 – Present the

Data

1–6

Choose an

appropriate

graphical display for

your data and justify

your choice. (CC

6.SP.5)

CC 6.SP.1–4

Analyze data sets

Tools: Various data

collecting and

displaying tools

such as

spreadsheets and

graphs

11 – Reporting 1

1–6

Calculate the

measures of center

and measures of

variability to

describe your data

set (CC 6.SP.5)

CC 6.SP.1–4

Analyze data sets

Tools: Various data

collecting and

displaying tools

such as

spreadsheets and

graphs

12 – Reporting 2

1–6

Reflect and report

on what your graph

and various

measures tell you

about the data set,

what questions you

have answered, and

what questions you

might still h

ave. (CC

6.Sp.5)

CC 6.SP.1–4

Analyze data sets

Tools: Various data

collecting and

displaying tools

such as

spreadsheets and

graphs

Pro

ble

m S

olv

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Problem solving in PowerTeaching is addressed in two main ways. The first is through problem-solving strategy lessons. These lessons

are designed to give students basic problem solving skills and strategies that will help them understand and solve any word problem or

real-world math situation. These lessons are distributed throughout the PowerTeaching curriculum to provide consistent points of

problem-solving discussion and practice.

The second way in which PowerTeaching addresses problem solving is through the math content lessons. These lessons often include

simple one- or two-step problem solving examples or complex, real-world situations and applications of the math being taught in that

cycle. Students will use their problem solving strategies to solve these word problems that are spread throughout each cycle of

PowerTeaching.

Through the balance of consistent practice and targeted strategy instruction, students are immersed in problem solving throughout

PowerTeaching and consistently apply the Common Core State Standards for Mathematical Practice.

Pro

ble

m S

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Stra

teg

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L

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Lesso

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Co

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ech

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Problem

Solving

The Problem-Solving Plan

Unit 1, Day 4

Understand the steps of the problem

solving process, and use those steps to

solve math word problems.

n/a

Problem Solving and

Extraneous Data

Unit 1, Day 5

Identify extraneous data in word

problems and math situations, then

solve the problems.

n/a

Pose-a-Problem

Unit 1, Day 6

Pose a problem for given mathematical

data. Ask a question that you could

answer using given data.

n/a

Sort and list

Unit 3, Cycle 3, Lesson 10

Sort lis

t data in word problems and

math situations to better answer

questions about the data.

n/a

Model the Problem


Use number sentences, expressions,

and drawings to model what is

happening in a problem and to find the

solution.

Video: M

odel th

e Problem

Find a Pattern


Look for patterns within word problems

and math situations to find solutions or

make predictions about what will

happen next.

n/a

Guess and Check


Use the guess and check strategy to

solve complex math situations and

readjust your guess based on your

previous guesses.

n/a

Solve a Simpler Problem


Use simpler numbers to solve multi-step

problems, then substitute the original

numbers to find the actual answer.

Video: Solve a Simpler

Problem

Work Backwards


Recognize problems and situations in

which working backwards is the

appropriate strategy to solve and

successfully use the strategy to solve

given problems.

Video: W

ork Backwards

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