Prerequisite Unit (3 days)6.NS.2

Investigations Notes1. Multiplying Numbers

I can fluently multiply numbers. Review multiplying multi-digit numbers, making sure they

understand this before leading to division Emphasize place value

2. Dividing multi-digit numbers I can fluently divide numbers.

Students have worked with division in 5th grade, they were limited to 4-digit numbers, divided by 2-digit numbers and used concrete models and other methods to solve – the extension in 6th grade is to fluently divide all types of numbers using the standard algorithm

Emphasizing estimating before working to solve and then can check answer with multiplication

NY Engage Activity – The activity for dividing whole numbers starts on page 109

Prime Time – Unit 1 (23 days) 6.NS.4, 6.EE.1, 6.EE.2b

Investigations ACE ?’s Notes1. Building on Factors and MultiplesProblem 1.1 – Playing the Factor Game Finding proper factors I can find all of the factors/divisors of a number.

1-7, 34-35, 41

Want to play a few hands as a class so they get the hang of it

This game is not meant to last all class period, it’s to get them thinking and playing with factors

Problem 1.2 – Playing to Win Prime and composite numbers I can find out information about a number by looking at its

factors.

8-13, 37-38, 42

Problem 1.3 – The Product Game Finding multiples I can find another factor of a number if I know one factor.

14-21, 36, 39-40, 43-

44Problem 1.4 – Rectangles and Factor Pairs I can prove when I have found all of the factors of a

22-23, 45-49

This is laying the foundation for students to think of area models, which they will be using

number. throughout middle and high school2. Common Multiples and Common FactorsProblem 2.1 – Riding Ferris Wheels Choosing Common Multiples or Common Factors I can discover when it is useful to find common multiples

or factors.

1-15, 35-39, 44-58

Remember the limitations in the standards – find the GCF of two whole numbers less than or equal to 100 and the LCM of two whole numbers less tan or equal to 12

Problem 2.2 – Looking at Cicada Cycles Choosing Common Multiples or Common Factors I can find the least common multiple.

16-29, 40-41, 59-61

Problem 2.3 – Bagging Snacks I can find the greatest common factor of two numbers.

30-34, 42-43, 62-69

Here is a nice visual for students to work out finding GCF and LCM - GCF and LCM

3. Factorizations: Searching for Factor StringsProblem 3.1 – The Product Puzzle Finding factor strings I can find the prime factorization of a number.

1-4

Problem 3.2 – Finding the Longest Factor String I can determine how many unique prime factorizations of

a number there are.

5-20, 31-36, 51-53

Problem 3.3 – Using Prime Factorization I can utilize the prime factorization of a number to find the

LCM and GCF of two or more numbers.

21-27, 37-42, 54-55

Problem 3.4 – Unraveling the Locker Problem I can find special characteristics about numbers. 28-30, 43-

50, 56

This problem can be difficult and time consuming, if you are short on time, you can skip this problem and supplement with some more practice on prime factorization, GCF, and LCM

4. Linking Multiplication and Addition: Distributive Property

Problem 4.1 – Reasoning With Even and Odd Numbers I can determine when a number is even or odd 1-6, 66, 80-

87

This problem seems really simple, it lays the foundation for factoring and the distributive property, can keep it short and sweet to save time

Problem 4.2 – Using the Distributive Property I can create equivalent expressions using the Distributive

Property.

7-23, 67-74, 88-90

Problem 4.3 – Ordering Operations I can decide what order to preform operation in a number

sentence.24-60, 75-

79

Order of operations will come back in Variables and Patters, this in just an intro

Reason for Order of Operations, if you wrote everything in expanded form, everything goes back to just addition and subtraction

Problem 4.4 – Choosing an Operation I can decide what operations are needed in a given

situation.61-65, 91

Students will probably need a little more practice after this, so bring out the whiteboards, a game, etc. and have them practice

Comparing Bits and Pieces – Unit 2 (25 days)6.RP.1, 6.RP.2, 6.RP.3, 6.NS.5, 6.NS.6, 6.NS.7

Investigations ACE ?’s Notes1. Making Comparisons – 6.RP.1, 6.RP.3, 6.NS.6 Another resource could use: Mathshell - LCM and

GCFProblem 1.1 - Fundraising Comparing with fractions and ratios I can compare numbers given in different forms.

1-2, 35-40

Can split up between groups to save time, assign groups different ones in A – it’s fine if they do not get to C

Students do NOT have to know how to carry on calculations, this is to get them thinking about different numbers and making sense of them, laying the foundation

Problem 1.2 – Fundraising Thermometers Introducing rations I can show ratio comparison in “for every” statements.

3-4, 41-43, 65-70

The bar models are essential in understand fractions, decimals, and percents

Problem 1.3 – On a Line Equivalent fractions and the number line I can see a relationship between numerators and

denominators of equivalent fractions. 5-18, 44-46, 52-53, 55-64, 71-80

Essential for students to see how fractions, decimals, and percents relate to one another, can have large number line up on the wall and reference throughout the school year

Have students make their own fraction strips so they can have them for the year, nice to have each strip a different color paper or let students color them with a pre-assigned color for each different fraction

Problem 1.4 – Measuring Progress Finding fractional parts I can use fraction strips to help find part of a number.

18-28, 47, 81

Problem 1.5 – Comparing Fundraising Goals Using fractions and ratios I can understand what it means for fractions and ratios to

be equivalent.

29-34, 48-51, 54, 82

2. Connecting Ratios and Rates – 6.RP.3, 6.RP.3a, 6.RP.3b DPI - Lessons for Learning – Bake Sale Brownies DPI - Lessons for Learning – Paper Clip Comp.

Problem 2.1 – Equal Shares Introducing unit rates I can interpret a unit rate comparison statement.

1-6, 25-26, 31-33

Problem 2.2 – Unequal Shares Using rations and fractions I can relate part-to-part relationships to part-to-whole

fractions.

7-15, 27-28, 34-35

Problem 2.3 – Making Comparisons With Rate Tables I can use rate tables to help find equivalent ratios.

16-24, 29-30, 36-37

3. Extending the Number Line – 6.NS.5, 6.NS.6a, 6.NS.6c, 6.NS.7b, 6.NS.7cProblem 3.1 – Extending the Number Line Integers and mixed numbers I can use the number line to think about fractions greater

than 1 and less than 0.

1-15, 20-22, 24, 89-91

Opposites and absolute value, focus first with whole numbers – 1 day

Then move to the fractions and mixed numbers – 2 days

Problem 3.2 – Estimating and Ordering Rational Numbers Comparing fractions to benchmarks I can compare two rational numbers.

16-19, 23, 25-52, 94-96, 98-99

Again, great to have a large number line on the wall (vertical or horizontal) to reference throughout school year

Do a few from A together as a classProblem 3.3 – Sharing 100 Things Using tenths and hundredths I can use what I know about fractions to help understand

decimals.

53-69, 93

Exponents not the focus here

Problem 3.4 – Decimal on the Number Line I can use what I know about fractions to estimate and

70-84, 88, 97

compare decimals.Problem 3.5 – Earthquake Relief Moving from fractions to decimals I can divide fractions to get the equivalent decimal.

85-87, 92, 100-105

4. Working With Percents – 6.RP.2, 6.RP.3c, 6.RP.3dProblem 4.1 – Who Is the Best? Making sense of percents I can use a percent bar in making comparisons with

decimals.

1-5, 20, 26-31, 34-39

Can have great conversation here around sports, why they do certain plays to certain players, etc.

Problem 4.2 – Genetic Traits Finding percents I can use partitioning to express one number as a percent

of another number.

6-19, 32-33, 40

Essential for students to understand what a percent is – if they can find 10% and 1% (which is easy!) they can find any percent of a number – sometimes it is more useful using this strategy than the actual algorithm

Percent Practice – Finding easy percents Thinking of shopping and tips – using easy percents, focusing on 10%’s to easily estimate discounts, tips, marl-ups, etc. but focusing on estimating, not doing it paper and pencil – this is what we do in real life almost every day

Let’s Be Rational – Unit 3 (20 days)6.NS.1, 6.NS.4, 6.EE.2, 6.EE.3, 6.EE.6

Investigations ACE ?’s Notes1. Extending Additions and Subtraction of Fractions – 6.NS.4, 6.EE.7Problem 1.1 – Getting Close Estimating Sums I can use strategies to estimate the sums of fractions.

1-21, 54-57, 62-66,

72-74

Game to start leading ideas with fractions and decimals – just play for about 45 minutes

Problem 1.2 – Estimating Sums and Differences I can use overestimating and underestimating strategies.

22-26, 51

Estimating is HUGE and should be done throughout the school year – in real life this is how we do most problems, by estimating and getting a good idea first

Problem 1.3 – Land Sections 27-29, 52- A, B, and C only

Adding and subtracting fractions I can discover strategies for adding and subtracting

fractions.

53, 67-70, 75-76

Problem 1.4 – Visiting the Spice Shop Adding and subtracting mixed numbers I can discover strategies for adding and subtracting mixed

numbers.

30-50, 58-61, 71, 77

Traditional Practice – Adding and Subtracting Fractions I can add and subtract fractions.

Easy place to being out whiteboards, worksheets, games, etc. to practice

Making sure to include word problems Variety of practice

2. Building on Multiplication With Fractions – 6.NS.1, 6.EE.3Problem 2.1 – How Much of the Pan Have We Sold? Finding parts of parts I can use an area model to relate to multiplying fractions.

1-2, 28-29

The representational/pictures are huge for students to make sense, this is the same things as using area models for multiplication, we have to teach students how to represent math in pictures

Problem 2.2 – Modeling Multiplication Situations I can discover strategies to multiply all combinations of

numbers (whole, fractions, mixed).

3-12, 30-38, 54-55

Problem 2.3 – Changing Forms Multiplication with mixed numbers I can utilize number properties and equivalent fractions to

multiply rational numbers.

13-27, 39-53, 56-57

Traditional Practice – Multiplying Fractions I can multiply fractions.

Easy place to being out whiteboards, worksheets, games, etc. to practice

Making sure to include word problems Variety of practice

3. Dividing With Fractions – 6.NS.1, 6.EE.2bProblem 3.1 – Preparing Food Dividing a Fraction by a Fraction I can understand what it means to divide a fraction by

another fraction and use strategies to solve.

1-2, 36-39

Could replace this investigation with the “Bean Party”

Having students always verbalize “How many _____ are in _____?”

Problem 3.2 - Into Pieces 3-12, 40, 54

Whole numbers or mixed numbers divided by fractions I can understand what it means to divide a whole or mixed

number by a fraction and use strategies to solve.Algorithm for Dividing Fractions I can divide fractions.

CPALMS - Discovering Dividing Fractions Important for students to understand what is

happening first and then work on the procedure, here is where the procedure comes into play

After they discovered some on their own, this video is a good reference tool - Flocabulary - Dividing Fractions

Problem 3.4 – Examining Algorithms for Dividing Fractions I can divide fractions.

Can use questions to practice traditional or just provide traditional practice problems, make sure to include word problems

Variety of practice 4. Wrapping Up the OperationsProblem 4.3 – Becoming an Operations Sleuth I can analyze a word problem to determine what

operations will need to be preformed.

Good questions to practice how to read word problems

Can practice reading the beginning ones as a class and discussing how and why you are picking what operations and utilize Pinch Cards

Decimal Ops – Unit 4 (23 days)6.RP.1, 6.RP.2, 6.RP.3, 6.NS.1, 6.NS.3, 6.EE.3, 6.EE.5, 6.EE.6

Investigations ACE ?’s Notes1. Decimal Operations and Estimation – 6.RP.1, 6.RP.2, 6.RP.3b

2 days max for investigation, this is to get them thinking about decimals before performing actual operations with them

Problem 1.1 – Out to Lunch Matching operations and questions I can analyze a word problem and decide what operation I

will use to solve.

1-7, 27-34, 60-61

Estimation

Problem 1.2 – Getting Close Estimating decimal calculations

8-23, 35-51, 62

Only A and B

I can estimate answers when working with decimals computations.

Problem 1.3 – Take a Hike Connecting rations, rates, and decimals I can express a unit rate as a decimal.

24-26, 52-59, 63-64

2. Adding and Subtracting Decimals – 6.NS.3Problem 2.1 – Getting Things in the Right Place Adding Decimals I can use place value to add decimals.

1-9, 21-27, 42-44

Can use beginning with the store to start thinking about how to do this – give time for students to develop ideas, but then teach them how to do it and practice

Traditional – Adding and Subtracting Decimals I can add and subtract decimals.

Easy way – give students numbers like 1.5 and 2.05 and tell them to add together, to just see what they get. Then can relate it to money and ask how much money they would have, easy for them to see they must line up the decimals

Good questions with analyzing problems – 2.1F and 2.2C

Plenty of practice questions in the ACE ?’s3. Multiplying and Dividing Decimals – 6.NS.1, 6.NS.2, 6.NS.3Problem 3.1 – It’s Decimal Time(s) Multiplying decimals I can find the product of any two decimal numbers.

1-8, 48-55, 65

Can use beginning with the store to start thinking about how to do this – give time for students to develop ideas, but then teach them how to do it and practice next

Traditional – Multiplying Decimals I can multiply decimals.

Plenty of practice in the ACE ?’s Practice

Traditional – Dividing Decimals I can divide decimals.

Plenty of practice in the ACE ?’s Practice

4. Using Percents – 6.RP.3c, 6.NS.3 Unit project fits in well hereProblem 4.1 – What’s the Tax on This Item? I can find the tax and total cost of an item.

1-3, 14-21, 28-30

Can bring in actual receipts or look up ordering items online

Problem 4.2 – Computing Tips I can find the tip and total cost of a meal.

4-6, 22-23, 31-38

Bring in real menus from restaurants and let students plan their own menu and calculate

Problem 4.3 – Percent Discounts I can find the discount and total cost of an item. 7-13, 24-27,

39-40

This is one of the biggest real life topics, can do so many things here – bring in catalogs or shop online and make students come up with the costs.

Practice – Using Percents I can solve real life problems dealing with percents.

Percents in real life Can pull Problem 4.4 as well for more practice This is one of the biggest real life aspects of math

that we use every day, so make sure students have a good grasp mentally – students can find 10% in their head and use that as a benchmark for other percents

Variables and Patterns – Unit 5 (26 days)6.RP.3, 6.EE.2, 6.EE.3, 6.EE.5, 6.EE.6, 6.EE.7, 6.EE.8, 6.EE.9, 6.NS.6, 6.NS.8

Investigations ACE ?’s Notes1. Building on Factors and Multiples – 6.RP.3a, 6.RP.3b, 6.EE.9Problem 1.1 – Getting Ready to Ride Data tables and graphs I can construct a graph from a table of data.

1-3, 14-15, 20

Problem 1.2 – From Atlantic City to Lewes Time, rate, and distance I can determine advantages and disadvantages of tables

and graphs.

4-9, 16-19, 23

Can do quickly as a class, just rough sketch the graph a class, or start them off as a class and have them finish with a partner

Problem 1.3 – From Lewes to Chincoteague Island Stores, tables, and graphs I can determine which representations of data are better

to show change in distance over time.

10-11, 21, 24-26

Video of horses

Problem 1.4 – From Chincoteague to Colonial Williamsburg Average speed I can calculate the average speed of a trip.

12-13, 22

2. Analyzing Relationships Among Variables – 6.NC.6b, 6.NS.6c, 6.NS.8, 6.EE.6

Problem 2.1 – Renting Bicycles Independent and dependent variables I can analyze and compare the relationship between

variables given in different forms.

1-3, 17-19

Problem 2.3 – Predicting Profits Four-quadrant graphing I can plot data points in all four quadrants.

8-9, 23

3. Relating Variables With Equations – 6.EE.2, 6.EE.2c, 6.EE.7, 6.EE.9Problem 3.1 – Visit to Wild World Equations with one operation I can write real life situations in an equation.

1, 22-25

Problem 3.2 – Moving, Texting, and Measuring Using rates and rate tables I can find useful information from an equation.

2-5, 26-30, 36

Problem 3.3 – Group Discounts and a Bonus Card Equations with two operations I can calculate values by plugging them into equations.

6-9, 31-35

Problem 3.4 – Getting the Calculation Right Expressions and order of operations I can apply the order of operations.

10-21, 37-42

4. Expressions, Equations, and Inequalities - 6.EE.3, 6.EE.5, 6.EE.7, 6.EE.8Problem 4.1 – Taking the Plunge Equivalent Expressions I can determine if it is possible to have two different, but

equivalent, expressions for the same situation.

1-14, 21-25

Problem 4.2 – More Than One Way to Say It Equivalent Expressions I can understand what t means for two expressions to be

equivalent.

5-6, 26-38

Problem 4.3 – Putting It All Together Equivalent expressions I can rewrite expressions in equivalent forms.

7-11, 39-52, 65, 67

Problem 4.4 – Finding the Unknown Value Solving Equations I can discover strategies to solve one-step equations.

12-19, 53-58, 68

Traditional - Practice Solving Equations I can solve one-step equations.

Be careful when pulling problems so students do not have to preform operations with negative numbers

Can bring out whiteboards, relay race, etc for a fun traditional practice

Variety of practice worksheets Problem 4.5 – It’s Not Always Equal Solving inequalities I can represent and find solutions for inequalities.

20, 59-64, 66, 69

Traditional - Practice Solving Inequalities I can solve one-step inequalities.

Making sure to include shading on the number line

Variety of practice worksheets

Covering and Surrounding – Unit 6 (23 days)6.NS.8, 6.EE.3, 6.EE.4, 6.EE.6, 6.EE.9, 6.G.1, 6.G.2, 6.G.3, 6.G.4

Investigations ACE ?’s Notes1. Extending and Building on Area and Perimeter – 6.NS.8, 6.EE.3, 6.EE.9Problem 1.1 – Designing Bumper Car Rides Area and perimeter I can explain how the formulas work for the area of

perimeter of rectangles.

1-24, 37-54

Use A for launch together

Problem 1.2 – Building Storm Shelters Constant area, changing perimeter I can discover how area and perimeter are related and

how they affect each other.

25-30, 55-57

Problem 1.3 – Fencing in Spaces Constant Perimeter, changing area I can discover how area and perimeter are related and

how they affect each other.

31-36, 58-69, 70-78

Can bring out square tiles for students to manipulate

2. Measuring Triangles – 6.EE.2a, 6.G.1Problem 2.1 – Triangles on Grids Finding area and perimeter of triangles I can discover the formula for finding the area of a triangle.

1-6, 27-32

Think of how to rearrange these triangles to make rectangles, because we can easily find the area of those, use this idea to derive formula for area of triangle

Problem 2.2 – More Triangles Identifying base and height I can analyze triangles to find the base and height.

7-21, 33-35

Problem 2.3 – Making Families of Triangles Maintaining the base and height I can compare triangles that have the same base and

height.

22-23, 36-39

3. Measuring Parallelograms – 6.NS.8, 6.G.1, 6.G.3Problem 3.1 – Parallelograms and Triangles Finding area and perimeter of parallelograms I can discover a strategy for finding the area of

parallelograms.

1-9, 39

Only A, B, and C, can model part C

Problem 3.2 – Making Families of Parallelograms Maintaining the base and height I can compare two parallelograms that have the same base

and height.

10-21, 40-42

Supplement – Trapezoids Area and perimeter of trapezoids I can calculate the area and perimeter of trapezoids

Do not have to know the formula, using the method of composing the polygons into triangles and rectangles to combine to get the area

Look at the unpacking documents for examples to give guidance

Finding area of trapezoid Problem 3.4 – Polygons on Coordinate Grids I can find the area of polygons on coordinate grids.

34-38, 43, 44-48

Perimeter and Area of Complex Shapes I can find the area and perimeter of complex shapes.

4. Measuring Surface Area and Volume – 6.EE.4, 6.G.2, 6.G.4

Can rearrange if you prefer to do volume before surface area

DPI - Lessons for Learning – Block Part-y

Problem 4.1 – Making Rectangular Boxes I can develop a strategy for finding surface area of a

rectangular prism.1-14, 47-51

Problem 4.3 – Designing Gift Boxes Finding surface area I can develop a strategy for finding the surface area of a 3D

object.

31-46, 52-55, 66-71

Practice – Surface Area I can solve problems involving surface area.

Can pull from unpacking questions Making sure to include word problems Variety of surface area worksheets

Problem 4.2 – Filling the Boxes Finding volume I can develop a strategy for finding the volume of a

rectangular prism.

15-30, 56-65

Practice –Volume I can solve problems involving volume.

Can pull from unpacking questions Making sure to include word problems Variety of volume worksheets

Data About Us – Unit 7 (20 days)6.SP.1, 6.SP.2, 6.SP.3, 6.SP.4, 6.SP.5

Investigations ACE ?’s Notes1. Organizing, Representing, and Describing Data – 6.SP.2, 6.SP.4, 6.SP.5a

Grades is always item to bring in for data analysis, can use students’ progress reports to analyze

Problem 1.1 – How Many Letters Are in a Name? I can collect, represent, and analyze data.

1-4, 15-16

Problem 1.2 – Describing Name Lengths What are the shape, mode, and range? I can measure central tendencies and variability in data.

5-8, 17-18, 24-28

Problem 1.3 – Describing Name Lengths What is the median? I can identify and use the median.

9-14, 19-23, 29-30

2. Supplement – Mean – 6.SP.3, 6.SP.4, 6.SP.5Data Collection Grades are always a good place, can track their

I can collect, organize, and evaluate data. progress through class, 9 weeks, etc. Fruit Loops vs. Cheerios – Activity where students

compare and analyze data About Our Class – collect data from their own class

Real Life I can analyze data.

Baseball stats activity

Mean, Median, Mode, and Range I can represent and analyze data.

Representing variability with mean, median, mode, and range

3. What’s You Favorite…? Measuring Variability – 6.SP.1, 6.SP.3Problem 3.1 – Estimating Cereal Serving Sizes Determining the IQR I can describe what the IQR tells us about a data set.

1-3, 12-13 Students might need a little more practice with this

topic before moving on

Problem 3.2 – Connecting Cereal Shelf Location and Sugar Content Describing variability using the IQR I can use the IQR to make comparisons among

distributions.

4, 17-20, 26

Problem 3.3 – Is It Worth the Wait? Determining and describing variability using the MAD I can determine what the MAD is telling me about how

data varies.5-11, 14-16, 21-25,

27

DPI - Lessons for Learning – How MAD are you? A and B only, another practice or two with MAD

(teach what the word means – MAD, mean absolute deviation, mean (already know average), absolute (absolute value), deviation (change from)) – this also helps to not worry about negative numbers, since it is “how far away from mean?”

4. What Numbers Describe Us? Using Graphs to Group Data – 6.SP.4, 6.SP.5a, 6.SP.5c, 6.SP.5dProblem 4.1 – Traveling to School Histograms I can use a histogram to help interpret data.

1-9, 27, 31

Practice – Histograms I can create and use histograms to interpret data.

DPI - Lessons for Learning – Shakespeare vs. Rowling

Virtual histogram

Representing Data Problem 4.2 – Jumping Rope Box-and-whisker plots I can interpret data using a box-and-whisker plot.

10-16, 28-29

Practice - Box and Whisker Plots I can create and analyze data in box-and-whisker plots.

Virtual box and whisker plot