U8  Accentuate the Negative, Inv. 1 & 2: Adding and Subtracting Rational Numbers

Review Questions

• How can you find the total value of a combination of positive and negative numbers?
• What are zero pairs, and how are they used when combining positive and negative numbers?
• How can you use a number line to represent addition and subtraction? A chip model?
• How are the algorithms for addition and subtraction of integers related?

Practice Tasks

• Model the following equations with chip models and number lines, then solve.

5 + -8 =       -4 + -6 =        -5 - 4 =         -9 - -3 =

• Restate the following addition problem as subtraction problem:  5 + -4 =
• Restate the following subtraction problem as an addition problem:  12 - -9 =
• Describe the algorithms (rules) for adding and subtracting integers.
• True or False?

• The sum of two negative numbers is always negative.
• The difference of two negative numbers is always negative.

Reinforcement (I need some extra help to get it)

• Understand the additive inverse (zero pairs) (LZ QC 1021)
• Adding positive and negative numbers on a number line (LZ QC 673)
• Subtract integers using number lines (LZ QC 3082)
• Subtract integers using distance on a number line (LZ QC 3064)
• Using CHIP MODELS 

Enrichment (I get it and I want to challenge myself)

• Brain Stretchers
• Making Zero
• Connect Three

U8  Accentuate the Negative, Inv. 3: Multiplying and Dividing Rational Numbers

Review Questions

• How is multiplication of two integers represented on a number line and a chip board?
• What algorithm can you use for multiplying integers?
• What algorithm can you use for dividing integers? How are multiplication and division of integers related?

Practice Tasks

• Model the following equations with chip models and solve:   -7(2) =         -3(-3) =        
• Model the following with chip models and solve:  -14/2 =        -8/-2 =
• Describe the algorithms (rules) for multiplying and dividing integers.
• Write the fact family for:  -8 * -4 = 24
• Find a value for n that makes the number sentence true:  24/n = -12  
• Give an example of a multiplication problem in which the product is less than zero.
• Give an example of a division problem in which the quotient is less than zero.

Reinforcement (I need some extra help to get it)

• Use chip models to model multiplication
• Dividing integers using integer tiles
• Using chip models to divide integers
• Multiplying negatives (text, Math is Fun)

Enrichment (I get it and I want to challenge myself)

• Brain Stretchers

U8  Accentuate the Negative, Inv. 4: Property of Operations

Review Questions

• Does the Order of Operations work for integers? Explain.
• How can you use the Distributive Property to expand or factor an expression that involves integers?

Practice Tasks

• Find each value:      -8*(4-(-5+3))

                                                -16  8 * 2^3 + (-7)

• Write these expressions in expanded form:   5(3 + -2)         x(-3 + 5)
• Write these expressions in factored form:      6(2) + 6(3)     5(x)+ 5(2)

Reinforcement (I need some extra help to get it)

• Write equivalent expressions using the distributive property (LZ QC 649)
• Khan Video on order of operations

Enrichment (I get it and I want to challenge myself)

• Brain Stretchers

U7  Data About Us, Inv. 1: Organizing, Representing, and Describing Data

Review Questions

• What are ‘data’? How do you represent data using a frequency table or a line plot?
• What words can you use to describe the distribution, or shape, of data?
• What are some measures of central tendency? of spread?
• How do you compute and use median, mode, and range?

Practice Tasks

• A class of students recorded the number of years their families had lived in their town. Here are two graphs that students drew to summarize the data. Which graph gives a more accurate representation of the data? Why?

What is the range of this data? the mode? the median?

Do you see any clusters or gaps in the data?

Is this data skewed?

Reinforcement (I need some extra help to get it)

• Frequency Tables and Dot Plots (Khan)
• Find the median by elimination (LZ)
• Describe the shape of a dot plot (LZ QC 3109)
• Use and find the range of a data set (LZ QC 535)

Enrichment (I get it and I want to challenge myself)

• Class 5 Names (nrich)

U7  Data About Us, Inv. 2: Measures of Center: Mean, Median, Mode

Review Questions

• How do you interpret, compute, and use the mean?
• How do you choose which measure of center to use when describing what is typical?

Practice Tasks

• The weekly salaries of six employees at McDonalds are $140, $220, $90, $180, $140, $200.  For these six salaries, find: (a) the mean (b) the median (c) the mode

• Which do you think is the best measure for the ‘typical’ salary? Why?

• Create a data set of 10 salaries which has:

• a minimum of $90
• a maximum of $200
• a median of $140
• and a mode of $160.
• Create a line plot for this data set.

• Create two different data sets of five values that have a mean of 50.

Reinforcement (I need some extra help to get it)

• Find the mean by equally distributing objects (LZ QC 2482)
• Summarize the center of data with a single number using mean, median, and mode (LZ QC 538)
• Summarize a data set using mean, median, and mode (LZ QC 3797)

Enrichment (I get it and I want to challenge myself

• Searching for the Mean (nrich)
• Match the Matches (nrich)
• M, M & M (nrich)
• Battling Averages (Figure This!)
• Working Hours (Figure This!)

U7  Data About Us, Inv. 3: Measuring Variability

Review Questions

• What are the measures we use to describe variability?
• What is the interquartile range (IQR)? How do you find it? What information does it provide about how data vary in a distribution?
• How is the IQR used to make comparisons among distributions?
• What is the Mean Absolute Deviation (MAD)?
• What information does the MAD provide about how data vary in a distribution?

Practice Tasks

• For the following data, find:

• Quartile 1
• Quartile 2
• Quartile 3
• Range
• IQR
• MAD

                        65, 51, 47, 86, 88, 75, 66, 51, 88, 57, 69

Reinforcement (I need some extra help to get it)

• Distinguish between measures of center and measures of variance (LZ QC 3491)
• Quartiles/Interquartile Range (Math is Fun)
• How to find an IQR  or try this one

• Calculate the IQR PRACTICE (Khan)

• Mean Deviation (Math is Fun)

• ONLINE MAD PRACTICE

• Summarize the spread of data using range and MAD (LZ QC 539)
• Describe the spread of data by finding the range, IQR, and MAD (LZ QC 544)
• Variability, Range, IQR, MAD (Braining Camp)

Enrichment (I get it and I want to challenge myself)

• Which List is Which? (nrich)
• Will women ever earn as much money as men? (Figure This!)

U7  Data About Us, Inv. 4: Using Graphs to Group Data

Review Questions

• How can you display data using a histogram?
• How can you display and describe data using a box plot?
• How can you use histograms or box plots to compare two sets of data?
• How can you decide when to use a dot plot, histogram, or box plot?

Practice Tasks

1.

Describe the distribution of the data set above. (Remember to comment on spread, center, and variability)

2.

Reinforcement (I need some extra help to get it)

• Choose the best graph for a data set using measures of center (LZ QC 3793)
• Box and Whisker Plots - making and interpreting 
• Create a box and whisker plot (Khan video)

• Create box and whisker plots online tool (Khan)

• Creating histograms (Khan video)

• Create histograms online tool (Khan)

Enrichment (I get it and I want to challenge myself)

• Which List is Which? (nrich)
• Will women ever earn as much money as men? (Figure This!)

U6  Variables & Patterns, Inv. 1: Variables, Tables, and Graphs

Review Questions

• How do we graph data in rate tables onto a coordinate grid?
• What are the advantages and disadvantages of showing patterns with tables? with graphs?
• How can you see the patterns of the speed of moving objects in a table? In a graph?

Practice Tasks

1. Students have a test to see how many sit ups they can do in 10 minutes. Andrea and Ken have plotted their results on the graph below.

• Ken says he did better than Andrea because his points are higher on the graph. Do you agree? Why or why not?
• Make rate tables to show Andrea and Ken’s results.
• In what ways is the data easier to compare in the tables? In what ways is it easier to compare in the graphs?

2.  The red and green lines represent the progress of two different cyclists. How would you describe   and compare the progress of the two cyclists? Which cyclist went farther? Which cyclist went faster?

Reinforcement (I need some extra help to get it)

• Identify how patterns are related by making a chart (LZ QC 3583)
• Graph ordered pairs (LZ QC 3567)
• Identifying numerical patterns by forming and graphing ordered pairs (LZ QC 3602)

Enrichment (I get it and I want to challenge myself)

• Graphing Number Patterns (nrich)
• Do dogs age faster than people? (Figure This! Rate tables)

U6  Variables & Patterns, Inv. 2: Analyzing Relationships Among Variables

Review Questions

• How can relationships between variables be shown in graphs?
• What are independent and dependent variables? How are they related to each other?
• What can you learn from the shape of a graph?

Practice Tasks

• What story could match the following graphs? What are the variables in the story? x-axis? y-axis?

Reinforcement (I need some extra help to get it)

• Identifying variables and their relationships (LZ QC 1654)

• Identifying variables and their relationships given a real world scenario (LZ QC 1654)
• Identifying variables and their relationships in a table (LZ QC 1655)
• Identifying variables and their relationships within a graph (LZ QC 1656)

Positive and Negative Integers and Ordered Pairs on the 4-quadrant plane

• Find the value of a number using its distance and direction from zero (LZ QC 3265)
• Find opposite numbers on the number line (LZ QC 3419)
• Locate a point on the coordinate plane (LZ QC 3470)
• Graphing on a coordinate plane (Khan)
• Practice identifying points - game

Enrichment (I get it and I want to challenge myself)

• Cops and Robbers (game)
• Will women ever earn as much money as men? (Figure this!)
• Who’s on First Today? (Figure This!)

U6  Variables & Patterns, Inv. 3: Relating Variables with Equations

Review Questions

• How are variables used to represent unknown values?
• How can situations be represented in expressions and equations using variables?
• How do you calculate the values of y from an equation like y = x + 3 or y = 3x when x values are given? (Solving one-step equations)
• How can you calculate the values of y from an equation like y = 3x + 5 when values of x are given? (Solving two-step equations)
• How is the order of operations applied to equations and expressions?

Practice Tasks

• The 6th grade Save Club plans to sell T-shirts to raise money. The club must pay $5.50 per T-shirt for the sale.

• Write an equation to show the relationship between total cost (C) and the number of T-shirts the club buys for the sale.
• How much will it cost the club to buy 12 T-shirts?

• The cost of renting a bike is $20 for the bike plus $10 per hour for the amount of time it is used.

• Write an equation that shows the relationship between total cost (C) and the number of hours a bike is rented.

• Use the Order of Operations to evaluate each expression when n = 5.

• 5n + 7
• 63 - 2n
• 3(4n + 6) - 8
• 2(n+7)+ 3

Reinforcement (I need some extra help to get it)

• Convert real-world situations into equations using models (LZ 1657)
• Convert a real-world situation into an equation (LZ 1511)
• Write equations of a graph using a table (LZ 1658)
• Write algebraic equations (LZ QC 1249)
• Write algebraic equations using multiplication and division (LZ QC 1504)
• Write the equation of a graph using a table (LZ QC 1658)
• PRACTICE (braingenie)

Enrichment (I get it and I want to challenge myself)

• Body Mass (Figure This! Substitute values for variables to solve equations)

U6  Variables & Patterns, Inv. 4: Expressions, Equations, and Inequalities

Review Questions

• How can we write algebraic expressions in equivalent forms?
• How can you use the relationships between variables to write and solve equations?
• How can you show that two expressions are equivalent?

Practice Tasks

• Claire’s mobile phone plan costs 3 cents per text plus a flat monthly fee of $10 for local calls.

• Write an equation to show the relationship between how many text Claire sends and the her total mobile phone cost each month.
• If Claire’s mobile bill for December was $17.50, how many texts did she send?
• If Claire has $25 to spend each month, what is the maximum number of texts she can send? Write an inequality statement that can be used to solve this problem. Solve and express the solution on a number line.

• Write 2 expressions equivalent to the expression:   2n + 8

• Use the distributive property to find one of your expressions.

Reinforcement (I need some extra help to get it)

• Create equivalent algebraic representations (table, graph, equation, word problem) (LZ QC 1659)
• Solve algebraic equations using inverse operations (LZ QC 1503)
• Write equivalent expressions using the distributive property (LZ QC 649)
• Understand inequalities using a number line (LZ QC 3772)
• Represent the solution set of an inequality using a number line (LZ QC
• Represent the solution set of inequalities using a number line (LZ QC 1506)
• Use a bar model to write and solve equations (LZ QC 1509)
• Represent real-world scenarios involving inequalities with a number line (LZ 1508)
• PRACTICE: Solving for inequalities in word problems (Khan)
• PRACTICE: Solving for inequalities (Prodigi online app)
• PRACTICE SOLVING EQUATIONS (basic skills)

Enrichment (I get it and I want to challenge myself)

• nrich weekly problem - writing equations
• Lauren and Thomas (nrich)
• Your number is… (nrich)

U5  Decimal Ops, Inv. 1: Decimal Operations and Estimation

Review Questions

• How do you decide which operations to use to solve real-world problems?
• When working with decimal computations, what strategies can you use to estimate the results?
• How can unit rates be expressed as decimals?

Practice Tasks

• Estimate:

• 24.5 + 195.89 =
• 247.2 - 6.1 =
• 102.08 x 4.1 =
• 3256.34 8.3 =

• Identify the operation you would need to answer the questions. How do you know? Estimate the answer.

• Ellen wanted to buy the following items: A DVD player for $49.95, a DVD holder for $19.95 and a personal stereo for $21.95. Does Ellen have enough money to buy all three items if she has $90 with her?
• Melissa purchased $39.46 in groceries at a store. The cashier gave her $1.46 in change from a $50 bill. Melissa gave the cashier an angry look. What did the cashier do wrong? how much change should Melissa have gotten?
• School lunches cost $14.50 per week. About how much would 15.5 weeks of lunches cost?
• A member of the school track team ran for a total of 179.3 miles in practice over 61.5 days. About how many miles did he average per day?

• Which is better: 10 pencils for $4 or 6 pencils for $2.70?

Reinforcement (I need some extra help to get it)

• Estimate with Decimals (Khan)
• Practice Identifying Operations & Solving Decimal Word Problems (with explanations)
• Unit Price and Unit Rates (First half of video only)
• Unit Rate Review (Khan, whole numbers)

Enrichment (I get it and I want to challenge myself)

• Repititiously (nrich; hint: look at Mrs. McComb’s Jan 27 blog post on repeating decimals)
• Greater Than or Less Than (nrich)

U5  Decimal Ops, Inv. 2: Addition & Subtraction of Decimals

Review Questions

• How do you use place value to add two given decimal numbers?
• How do you subtract one decimal from another?
• How can you use fact-families relationships to solve addition and subtraction problems?

Practice Tasks

• Solve the following:
• Solve for N:

                  N + 10.21 = 89.51              72.3 - N = 5.29               N - 1.2 = 15.8

Reinforcement (I need some extra help to get it)

• Adding Decimals (Khan)

• Practice

• Subtracting Decimals Example 1 (Khan)

• Practice (Khan)

• Adding and Subtracting Word Problems Practice (Khan)
• Sad Hair Day (For fun addition and subtraction of decimals video)
• Line ‘Em Up Decimal Song

Enrichment (I get it and I want to challenge myself)

U5  Decimal Ops, Inv. 3: Multiplication & Division of Decimals

Review Questions

• How do you find the produce of any two decimal numbers?
• What algorithm can be used to find any decimal product?
• How can a decimal division problem be written in equivalent fraction and whole-number form?
• How can you carry out a decimal division using a method similar to long division of whole numbers?
• How can you complete a long division problem that expresses remainders in decimal form?

Practice Tasks

• Estimate, then solve:
• If 34 x 8 = 272, what is 3.4 x 0.8?  What is 0.34 x 8?

• Rewrite each division problem in whole-number equivalent fraction form. Divide.

• 9.6 0.12 =
• 1.43 1.1 =

• Solve using the long division algorithm.

Reinforcement (I need some extra help to get it)

• Multiply decimal numbers (LZ Quick Code 3003)
• Multiplying Decimals (Khan)

• Practice

• Multiplying Decimals Word Problems (Khan)
• Dividing Decimals (LZ Quick Code 3065)
• Division with Decimal Quotient (Khan)

• Practice

• Dividing Decimals (Khan)

• Practice

Enrichment (I get it and I want to challenge myself)

• Route Product (nrich)
• Decimal Movement
• Forgot the Numbers (nrich)
• Toad in the Hole (nrich)
• Build Decimal Division

U5  Decimal Ops, Inv. 4:  Using Percents

Review Questions

• How do you find the tax and total cost of an item from a given selling price and tax rate? How do you find the base price from a given tax rate and amount?
• How do you find the tip and total cost of a restaurant meal from a given meal price and tip rate? How do you find the meal price from a given tip percent and amount?
• How do you find the discount and the total cost of an item given selling price and discount rate? How do you find the base price from a given discount rate and dollar amount?
• How can you express and change in a given amount as a percent change?

Practice Tasks

• Hamburgers cost $3.99 plus an additional 7% sales tax. What is the total cost of a hamburger?
• 15% of the 318 sixth graders at SAS own iPhones. How many sixth graders own iPhones?
• Gabriel leaves a 10% tip on a meal that costs $15.50. How much does he pay in total? How much does he pay in total if he leaves a 15% tip?
• Mr. Munden and Mr. Hardinge go to dinner. Their meals total $25.75, the tax is 7%, and they pay a 15% tip. What is the total amount that they pay?
• The T-shirt Emporium is having a 30% off sale on all T-shirts. What is the sale price of a T-shirt that originally costs $19.00?

Reinforcement (I need some extra help to get it)

• Convert percent to decimal and fraction (Khan)
• How to use percents to calculate tips
• Sales tax and discounts
• How to calculate sales tax
• How to solve discount problems
• PRACTICE: Finding Percents game
• PRACTICE: Finding Percents practice set
• PRACTICE: Discount and sale prices

Enrichment (I get it and I want to challenge myself)

• Percentage Up
• Which Would You Rather (nrich)
• Are You a Smart Shopper? (nrich)

U4  Let’s Be Rational, Inv. 1: Addition and Subtraction of Fractions

Review Questions

• How do you add and subtract fractions with like denominators? different denominators?
• What is a common denominator?
• How do you add and subtract mixed numbers?    

Practice Tasks

• Solve:       ¼ + ⅔        0.5 + ⅙         ⅓ + 2/9          3 ½ + 7 ⅝
• Solve:       ⅔ + 5/12 + ⅚
• Solve:       ¾ - ⅖          10 ⅔ - 8 9/12          4 - ⅔ - ¼ - ⅚

Reinforcement (I need some extra help to get it)

• Adding fractions with different denominators (LZ Quick Code 973)
• Subtract fractions with different denominators (LZ Quick Code 974)
• Adding Fractions finding LCD (math playground)
• Adding fractions finding least common denominator (Khan)

• Practice

• Subtracting fractions finding common denominator (Khan)

• Practice

• Practice: Soccer shootout game
• Adding & subtracting fractions & mixed numbers explanation video (youtube)
• Subtract mixed numbers with borrowing (interactive teaching and practice)

Enrichment (I get it and I want to challenge myself)

• Keep it Simple (nrich)
• Farey Sequences (nrich)
• Article on the History of Fractions (nrich)

U4 Let’s Be Rational, Inv. 2: Multiplication of Fractions

Review Questions

• What strategies, models, and algorithms can we use to multiply fractions?
• How can I use and area model to represent fraction multiplication?
• What strategies, models, and algorithms can we use to multiply mixed numbers?
• How do we convert a mixed number into an improper fraction and vice versa?

Practice Tasks

• Model and solve:       ⅓ x ¼        ¼ of ¾     5/2 x 8/11      ⅔ x 8 ⅚         3 ¼ X 2 ½  
•    Mr. Smith buys a 2 ½ pound block of cheese. His family eats ⅓ of the block. How much cheese has his family eaten?
• Is ⅔ of ¾ of a pan of brownies the same as ¾ of ⅔ of a pan? Why or why not?

Reinforcement (I need some extra help to get it)

• Review and practice changing mixed numbers to improper fractions (Math Playground)
• Multiply whole numbers by fractions using an area model (LearnZillion QC 1548)
• Multiply a fraction by a fraction using an area model (LZ Quick Code 1459)
• Multiply mixed numbers by converting to improper fractions (Khan)

• Practice

• Review and practice game: multiplication of fractions (Math Playground)
• Multiply using cross cancellation to simplify
• Cross Cancellation and why it works

Enrichment (I get it and I want to challenge myself)

• Fraction Multiplication Challenge

U4 Let’s Be Rational, Inv. 3: Dividing with Fractions

Review Questions

• What strategies, models, and algorithms can we use to divide fractions?

• Think: bar model, number line, multiply by reciprocal, etc...

• What is a reciprocal and how does it relate to division of fractions?
• What does it mean to divide by a fraction?

Practice Tasks

1. Model and solve:

2. Solve the following.  Show all your work and include a number sentence (ex 2+2=4)

• 
• 
• Ms. Waterhouse is buying almonds at the grocery store.  The scoop holds 1 ½ cups of almonds.  If she has a container that holds 5 ⅓ cups, how many scoops will she need to fill the container?  

Reinforcement (I need some extra help to get it)

• Examples on dividing fractions
• Understanding division of fractions  (Start here)
• Video on dividing whole numbers by fractions
• Video on dividing fractions by fractions
• Practice set on dividing fractions by fractions
• Word problem practice
• Series of worked examples and practice problems

Enrichment (I get it and I want to challenge myself)

Some people find it helpful to convert fractions to common denominators before dividing them.  In what situations might this approach be useful?  What do you think?  

U4 Let’s Be Rational, General: Modeling of Fraction Operations

Reinforcement (I need some extra help to get it)

• This video walks you through the Check Ups on multiplication and division and reviews how to model the operations.
• IXL practice on multiplying fractions with models
• This online tool lets you model the fraction multiplication yourself and clearly shows the “overlap”
• Khan explanation of multiplication model
• Khan division model
• Division model Part 2

Multiplication

Division

(The quotient is 10)

Enrichment (I get it and I want to challenge myself)

U3 Covering and Surrounding, Inv. 1: Area and Perimeter of Rectangles and Irregular Shapes

Review Questions

• What is ‘area’? How do you find the area of a rectangle? What is the formula for the area of a rectangle? What types of units are used to measure area?
• What is ‘perimeter’? How do you find the perimeter of a rectangle? What is the formula for the perimeter of a rectangle? What types of units are used to measure perimeters?
• What strategies can be used to find or estimate the area and perimeter of an irregular shape?

Practice Tasks

• Find the area and perimeter of the following rectangle:
• Find the area and perimeter of the following shape:

Reinforcement (I need some extra help to get it)

• Find the area of a rectangle using an algorithm (LZ Quick Code 2535)
• Area of a rectangle: product of dimensions same as counting squares (Khan)
• Measuring area with unit squares practice (Khan)
• Area problems practice (Khan)
• Introduction to perimeter (Khan)
• Perimeter of a shape (Khan)
• Finding perimeter practice (Khan)

Enrichment (I get it and I want to challenge myself)

U3 Covering and Surrounding, Inv. 2: Area and Perimeter of Triangles

Review Questions

• How do you find the area of a triangle? What is the formula for the area of a triangle? What types of units are used to measure area?
• How do you find the perimeter of a triangle? How do you find the perimeter of a triangle? What types of units are used to measure perimeters?

Practice Tasks

• Find the area and perimeter of the following triangles: (A = ½ (b * h) )

Reinforcement (I need some extra help to get it)

• How to find the area of a triangle (Math Playground)
• Area of triangle with excellent visual explanations 

• Area of Triangle Practice (Khan)

• Perimeter of triangle practice (Khan)

Enrichment (I get it and I want to challenge myself)

• Triangle Island  (nrich)
• Isosoceles triangles (nrich)

U3 Covering and Surrounding, Inv. 3: Area and Perimeter of Parallelograms

Review Questions

• How is a parallelogram related to a rectangle?
• How do you find the area of a parallelogram? What is the formula for the area of a parallelogram? What types of units are used to measure area?
• How do you find the perimeter of a parallelogram? What is the formula for the perimeter of a parallelogram? What types of units are used to measure perimeters?

Practice Tasks

• Find the area and perimeter of the following parallelograms:  (A = b x h)

Reinforcement (I need some extra help to get it)

• Area of a parallelogram (Art of Problem Solving - watch until 4:20)

• Area of a parallelogram practice (Khan)

• Find the perimeter of a parallelogram (Khan)

Enrichment (I get it and I want to challenge myself)

Taking the concepts of area and perimeter further...

• Area of a circle video (Yummy Math - watch the video at the bottom)

• What is the formula for the circumference of a circle?
• What is the formula for the area of a circle?

• Practice! (You may use a calculator.)

• Area of a trapezoid (Art of Problem Solving)

• Practice (Khan)

U3 Covering and Surrounding, Inv. 4: Volume of Rectangular Prisms and Surface Area

Review Questions

• How do you find the volume of a rectangular prism? What is the formula for the volume of a rectangular prism? What types of units are used to measure volume?
• How do you find the surface area of a shape? Of a rectangular prism? What types of units are used to measure surface area?

Practice Tasks

• Find the volume of the following rectangular prisms:

• Find the surface area of the following objects or nets:

Reinforcement (I need some extra help to get it)

• Find the volume of a rectangular prism by filling it with unit cubes (LZ Quick Code 1062)
• Find the volume of a rectangular prism by developing a formula (LZ quick Code 1063)
• Volume & surface area tool for practice (Illuminations)
• Net tool for visualizing nets of cubes (Illuminations)

Enrichment (I get it and I want to challenge myself)

• Cuboids (rectangular prisms, nrich)
• Painting cubes (nrich)
• Making Boxes (nrich)
• Cuboid in a Box (nrich)
• All Wrapped Up (nrich)

Comparing Bits and Pieces, Intro and Investigations 1.1 & 1.2: Ratios & Making Comparisons

Review Questions

• What is a ratio?
• What language and notation do we use to describe ratios?
• What does it mean to say ratios represent a multiplicative relationships?
• What tools can be used to solve ratio problems? (double number lines, ratio tables, tape diagrams)
• How can we find equivalent ratios?

Practice Tasks

• To make the right shade of pink, Sami mixes 4 parts white paint with 1 part red paint.

• Write a part:part ratio describing this relationship.
• Write a part:total ratio describing this relationship.

• There are 3 girls for every 4 boys on the soccer team. How many players might be on the team?
• The ratio of blue beads to red beads is 3:7. If there are 15 blue beads, how many red beads are there?
• The ratio of apple candies to grape candies in the jar is 2:3. If there are 100 total pieces of candy in the jar, how many apple candies and how many grape candies are there?
• How could you compare the 7th grade and 8th grade fundraising goals?

Reinforcement (I need some extra help to get it)

Describe a picture using ratio language (LZ Quick Code 1178)

Visualize part-to-part ratios using pictures (LZ, Quick Code 580)

Visualize part-to-total ratios using a picture (LZ Quick Code 581)

Create equivalent ratios using a diagram (LZ, Quick Code LZ606)

Solve ratio problems by using tables and multiplication (LZ Quick Code 587)

Solve ratio problems using double number lines (LZ, Quick Code 588)

Create a number line using benchmark numbers (LZ Quick Code 2349)

Ratio Pairs Interactive Activity (nrch, equivalent ratios)

Rod Ratios Interactive Activity (nrich, use rods to identify ratios)

Brainpop Ratios movie

Enrichment (I get it and I want to challenge myself)

Mixing Paints (nrich challenge)

Comparing Bits and Pieces, Investigations 1.3: Equivalent Fractions and the Number Line

Review Questions

• How do we find equivalent fractions?
• How do the numerators and denominators change to make equivalent fractions?
• How can we reason with equivalent fractions to solve problems?
• How can we use benchmark fractions to solve problems?

Practice Tasks

1. Name 5 fractions equivalent to .

3. Find 3 fractions equivalent to 6/18. Explain how to find equivalent fractions.

4. Is each statement true or false?

                              =                =  

Reinforcement (I need some extra help to get it)

Identify equivalent fractions using a number line (LZ Quick Code 1732)

Identify equivalent fractions using fraction strips (LZ Quick Code 1733)

Generate equivalent fractions using a number line (LZ Quick Code 1735)

Generate equivalent fractions by multiplying numerators and denominators (Khan video)

Enrichment (I get it and I want to challenge myself)

Comparing Bits and Pieces, Investigations 1.4 & 1.5:  Solving Problems Using Fractions and Ratios

Review Questions

• What does it mean for fractions to be equivalent?
• What does it mean for ratios to be equivalent?

Practice Tasks

1. About what fraction of the goal has been reached?

                                                         Goal: $?

             If the shaded part represents $50, what is the total goal?

2. This baseball season Kevin made twice as many homeruns as Nick. Give three possibilities for the distances each could have run.
3. The ratio of the distance Usain ran to the distance that Emil ran was 4:3.

• Who ran the farthest?
• Give three possibilities for the distance each could have run.
• Aditya said that Usain ran 200 meters farther than Emil. Is this possible? How far would each runner have run?

Reinforcement (I need some extra help to get it)

Understand the difference between fractions and ratios (LZ video Quick Code: LZ602)

Create equivalent ratios using a diagram (LZ, Quick Code LZ606)

Solve ratio problems by using tables and multiplication (LZ Quick Code 587)

Solve ratio problems using double number lines (LZ, Quick Code 588)

Enrichment (I get it and I want to challenge myself)

Mixing Paints (nrich challenge)

Mixing Lemonade Interactive Activity (nrich, comparing ratios)

Pattern Clues (challenging!)

Comparing Bits and Pieces, Investigations 1 REVIEW SHEETS

• Investigation 1: RATIOS PRACTICE 1
• Investigation 1: RATIOS PRACTICE 2
• Investigation 1: Double Number Lines (Equivalent Ratios) Practice A
• Investigation 1: Double Number Lines (Equivalent Ratios) Practice B
• Investigation 1: Ratio Tables, Practice A
• Investigation 1: Ratio Tables, Practice B

Comparing Bits & Pieces: Investigations 2.1 - 2.3: Unit Rates

Review Questions

• What is a rate?
• What is a unit rate?
• How do we make a unit rate comparison statement? (use ‘per’, ‘for each’)
• How do rate tables help us to find equivalent ratios? unit rates?

Practice Tasks

1. A dozen cookies costs $4.80. What is the price of one cookie? Express your answer as a unit rate.
2.  5 people want to share 4 pieces of pizza equally. How much will each person get? Express your answer as a unit rate.
3. If Tom runs 1 kilometer in 5 minutes, how far does he run in 1 minute? Express your answer as a unit rate. (Note: 1 kilometer = 1000 meters)

Reinforcement (I need some extra help to get it)

How rates are part of the ratio family (LZ quickcode 839)

***FINDING UNIT RATES CLASS SLIDES***

Unit Rate Interactive Lesson (Braining Camp)

Solving unit rate problems (Khan, using equivalent ratios)

Practice online (Khan)

Video explaining rate tables (youtube)

UNIT RATE EXTRA PRACTICE

UNIT RATE PRACTICE #2

STUDENT vs BEASTS

Video explaining how to convert an animal’s speed into a unit rate (sec per meter)

Thanks Mr. Munden!

Enrichment (I get it and I want to challenge myself)

Gasoline Tanks (Figure This!)

Ratio and Unit Rate ENRICHMENT SHEETS (do the Brain at Work problems!)

Answers

Comparing Bits & Pieces: Investigations 3.1-3.2, Comparing Fractions

Review Questions

• How can we compare fractions? Using logical reasoning & benchmarks? Using Least Common Denominator (LCD)? Using Cross Multiplication?
• When is it better to use one of the above methods over another?
• How can we order fractions on a numberline?

Practice Tasks

1. Which fraction is larger? How do you know?

1. ⅚ or ⅞?    b. ¾ or ⅗?    c. 14/30 or 13/24?   d. ⅔ or 3/9?

2. Place the following fractions in order on the number line:

                                      11/12           ⅗        ⅔         6/8          13/18

Reinforcement (I need some extra help to get it)

Comparing Fractions, class slides

Comparing Fractions (text)

Online practice comparing fractions (Khan)

Online practice, ordering fractions (Khan)

Ordering fractions using cross multiplication (video)

Enrichment (I get it and I want to challenge myself)

Grape Juice Jungle (Figure This!)

Comparing Bits & Pieces: Investigations 3.3-3.5, Decimals

Review Questions

• What are decimals?
• What does it mean to say the decimal system is a ‘base ten’ system?
• How can fractions be converted to decimals? Which fractions are easily converted; which are not?
• How can we find decimals on the number line?

Practice Tasks

1. What is the decimal equivalent of the following fractions (using reasoning only):

1/10     ⅛     ⅙     ⅕     ¼     ⅓     ½    

 ⅜     ⅘      5/20     12/16   (use reasoning only)

2. Which is larger?

0.7 or 0.70     1.45 or 1.382     .35 or .351     0.9  or 0.099

3. Locate these fractions on the number line:

0.8     0.18     0.08     0.32     0.679

Reinforcement (I need some extra help to get it)

Represent decimals to the thousandths using base 10 blocks (LZ Quick code 3330)

Decimal Place Value (Khan)

Compare two decimals to the hundredths place using fractions (LZ Quick code 3217)

Comparing Decimals: Ordering from Smallest to Biggest (Khan Academy)

     PRACTICE: Ordering Decimals (Khan)

Compare decimals using base ten blocks (LZ Quick code 3779)

Convert decimals to simplified fractions (Khan)

     PRACTICE: Converting decimals to fractions (Khan)

Convert fractions to decimals using division (LZ Quick code 1427)

Enrichment (I get it and I want to challenge myself)

Comparing Bits & Pieces: Investigations 4.1 - 4.3, Percentages

Review Questions

• What does ‘percent’ mean?
• How can we reason with fractions in tenth and hundredths to find equivalent percents?
• How can we convert and compare between fractions and decimals, and percents?
• How can we use bar models to solve percent problems? Ratio/rate tables? Fraction/decimal reasoning?

Practice Tasks

1. Find percents equal:

¼       20/25       0.45       ⅓       ⅕       .75       .165  

3. Write each percentage in fraction (simplified) and decimal form:

12 ½%     80%     25%     33 ⅓%     73%    15%  

3. How much is…(use models)

• 30% of 270?
• 52% of 500?
• 20% of 45?

4. What percentages do these represent (use models and the unit rate - 1% - as needed):

• 12 out of 36
• 11 out of 20
• 17 out of 24
• 12 out of 75

Reinforcement (I need some extra help to get it)

• The meaning of percent (Khan)
• Converting percent to decimal and fraction (Khan)

• PRACTICE: Convert percent to decimal (Khan)

• Write a fraction as a decimal (reasoning, Khan)

• Estimate a percent value using a bar model (LZ Quick code 3556)
• Compare ratios using tables and percents (LZ Quick code 595)
• PRACTICE: Finding percents (khan)

Enrichment (I get it and Ihe  want to challenge myself)

Matching Fractions, Decimals and Percentages (nrich)

How much does it cost? (Figure This!)

What percentage does it take to win a vote? (Figure This!)

Prime Time Investigations 1.1 & 1.2: Factors

Review Questions

• What is a multiple
• What is a factor?
• What is a prime number?
• What are composite numbers?
• Is the number 1 prime?  Why or why not?

Practice Tasks

1. Find all the factors of 36. Use two different strategies.
2. Which numbers are prime, and which are composite?

3     49     13     1     9     24     19

Reinforcement (I need some extra help to get it)

Finding Factor Pairs of a Number Using a Rainbow Factor Line

Finding Factor Pairs of a Number Using a T-Chart

Determine Whether a Number is Prime, Composite or Neither

Determine Whether a Number is Prime or Composite Using Area Models

Abundant, Deficient and Perfect Numbers

Enrichment (I get it and I want to challenge myself)

Dozens (nrich - see the challenge question at the bottom of the page)

Additional Resources

If you are still learning the standard algorithm for multiplication:

Learnzillion video

Khan Academy

To learn your divisibility rules for 2, 3, 4, 5, 6, 9:

Investigations 1.3 & 1.4: Multiples & Factor Pairs

Review Questions

• If you know one factor of a number, how can your find another factor of the number? What are factor pairs?
• What does product mean?
• What is a multiple? How do you find multiples of a number?
• Will a number have more factors or more multiples? How do you know?
• What is a square number?
• How do you know when you have found all the factors of a number?

Practice Tasks

3. Find the first 8 multiples of 12.

Reinforcement (I need some extra help to get it)

Determine Multiples Using a Table (LZ)

Find Multiples Using a Number Line (LZ)

Find All the Factors Pairs of a Number Using Area Models (LZ)

The Product Game Interactive (Illuminations)

Enrichment (I get it and I want to challenge myself)

Factors and Multiples Game (nrich)

Intro to Stars (nrich) factors and multiples

Stars Interactive (nrich)

Sticky Numbers (nrich) - squares and primes

Investigations 2.1 - 2.3: Common Multiples and Common Factors

Review Questions

• What are common multiples? Common factors?
• What strategies can you use to find common multiples?
• What strategies can you use to find common factors?
• How do you find Least Common Multiples (LCM)?
• How do you find Greatest Common Factors (GCF)?
• In what type of problem do you need to find a Least Common Multiple (LCM)?
• In what type of problem do you need to find the Greatest Common Factor (GCF)?

Practice Tasks

4. Find the LCM of 8 & 24…. of 12 & 18… of 7 & 13.
5. Find the GCF of  60 & 45…. of 23 & 29…. of  12 & 48.
6. John and Elly are making treat bags for the class party. John brought 32 pieces of gum. Elly brought 40 mints. What is the greatest number of equal treat bags they can make? (Do you need to use GCF or LCM to solve this problem?)
7. Mr. Jones orders pizza every 4 days. His neighbor, Mr. Kimble, orders pizza every 5 days. What is the least amount of days until they will be ordering pizza on the same night? (Do you need to use GCF or LCM to solve this problem?)

Reinforcement (I need some extra help to get it)

Find the GCF of Two Numbers (LearnZillion)

Find the LCM of Two Numbers (LearnZillion)

Use GCF and LCM to Solve Real-World Problems (LearnZillion)

Multiples - a review (youtube)

Square Numbers (youtube)

Prime Numbers (Brainpop)

Solve Word Problems Using LCM and GCF (Khan)

Least Common Multiples Help:

Watch this video, then do these exercises.

Greatest Common Factor Help:

Watch this video, then do these exercises.

Practice with LCM and GCF word problems (Khan Academy)

Playlist for Investigations 1-2

Enrichment (I get it and I want to challenge myself)

Cicada 17  (Numberphile Video)

Stars Interactive (Nrich)

Missing Multipliers (Nrich)

Finding the LCM  using Prime Factorization (mathtrain)

Finding the LCM of 3 numbers (using Prime Factorization)

Investigations 3.1 & 3.2: Factor Strings

Review Questions

• What are factorizations?
• What is a factor string?
• How do you find the prime factorization of a number?
• How many unique prime factorizatons of a number are there?
• What is an exponent?
• How do you read ?  ?   ?
• How can exponents be used to represent a number?
• How do you evaluate numerical expressions involving  whole-number exponents?

Practice Tasks

1. Can you think of 3 numbers that you can multiply to get a product of 24? Can you find a different string of 3 numbers?
2. What numbers can you multiply to get a product of 360? Can you find a string of three numbers? What is the longest possible string of factors that you can find? What method did you use to find the longest string?
3. 81 can be written as 9 x 9, , 3 x 3 x 3 x 3, or . Which factorization is the prime factorization?
4. Write the following without exponents:  x  x 11. What is the number?
5. Write the prime factorization of 18 using exponents.

Reinforcement (I need some extra help to get it)

1. Prime factorization and exponential notation (Khan video)
2. Find the GCF and LCM using Prime Factorization (LZ)
3. How to do prime factorization (text)
4. What are exponents? (text)
5. For practice, try this tool:  Prime Factorization Practice Interactive Tool

Enrichment (I get it and I want to challenge myself)

1. Finding the LCM  using Prime Factorization (mathtrain)
2. Finding the LCM of 3 numbers (using Prime Factorization)
3. Code Breaker (NRich interactive)

Investigations 3.3 & 3.4: Prime Factorization

Review Questions

• What is a factor tree?
• What is factorization? Prime factorization?
• How many unique prime factorizations of a number are there? (one!)
• Why is it helpful to write a number as the product of its primes?
• How can you find the factors of a number using its prime factorization?
• How do you find the prime factorization of a number?
• What are exponents? How can you use exponents to express a prime factorization?
• How do you read expressions written with exponents?
• How can prime factorization be used to find least common multiples and greatest common factors of two or more numbers?
• What other strategies have we learned to find least common multiples and greatest common factors? Which method do you prefer?

Practice Tasks

1. Find three different factorizations of the number 36.
2. Find the prime factorization of the number 36.
3. Write the prime factorization of the number 36 in exponential form.
4. Using prime factorization, find the GCF and LCM of 24 and 36.
5. How can we determine that 24 is not a factor of 60 by looking at its prime factorization?
6. How can we determine that 60 is not the least common multiple of 12 and 18 by looking at its prime factorization?

Reinforcement (I need some extra help to get it)

Class slides: Finding LCM and GCF using prime factorization

Online practice for prime factorization with practice finding LCM and GCF

Find the GCF and LCM Using Prime Factorization

Prime Factorization LCM and GCF Practice, Interactive Tool

Enrichment (I get it and I want to challenge myself)

The Moons of Vuvv (Hint: What investigation are we in? How do you think you could solve this??)

Investigations 4.1 & 4.2: Distributive Property

Review Questions

• What is the distributive property?  
• What do we mean when we say that an expression can either be the sum of two terms or the product of two factors?

Practice Tasks

1. Show the area of the rectangles below as the sum of two terms and the product of two factors.

2. The Area Model of Multiplication (multiplication using modelling and the distributive property)

   Use the Area Model of Multiplication to find the product of 34 and 42

Reinforcement (I need some extra help to get it)

Watch this Khan Academy video.

Area of rectangle and distributive property (Khan)

Rewrite addition problems as a multiplication problems using the distributive property

BrainPop - Distributive Property (username: singapor; password: singapor)

Enrichment (I get it and I want to challenge myself):

Investigations 4.3 & 4.4: Order of Operations

Review Questions

• What are the steps in the order of operations?

Practice Tasks

1. Regents Prep questions

Reinforcement (I need some extra help to get it)

Learn Zillion Video on Order of Operations

Khan Video on order of operations

Order of operations with PEMDAS mnemonic

Chapter Review

Use the textbook and your Check Up 1, Check Up 2, & Partner Quiz as your main Review Material

• There are review videos at the end of each lesson (see above)
• Check the “I Can” list to make sure that you have mastered all of the skills and the Review Questions at the start of each lesson summary
• Here’s a playlist of additional review material - just select the videos that cover the skills that you need to review. Remember that you do not need to master every method for each skill - just master the one that makes sense to you!

http://www.youtube.com/playlist?list=PLgYkqZe1XZaltg7LbbPmRwjcNQHCsiDEv

Review Questions

The following review questions are a great way to self-study.  An answer key is included so you can check your answers.  If you make a mistake make sure you make the appropriate corrections!

• ORGANIZED REVIEW (use first)
• Review questions for factors, multiples, GCF, LCM, factorization
• Review questions for Distributive Property and Order of Operations
• Review questions for Prime Factorization
• Prime Time Unit 1 Assessment Review (Hardinge)