EAST ALLEN COUNTY SCHOOLS

Bundle 1

Grade 6

Math

Big Idea: Unity Fractions, Decimals,

Percents

Enduring Understandings Essential Questions Numbers can be manipulated according to a set of standardized rules. The value of a decimal and a percent are dependent upon the size of the whole when the whole is compared to one hundred. Multiplication does not always result in a larger quantity and division does not always result in a smaller quantity. Decimals and percents can have values of less than 1 and more than 100. Relating money to decimals is a real life application of decimal values.

How are fractions, decimals, and percents related? How can you express values less than 1% and greater than 100%?

In what way does multiplication sometimes result in a product smaller than either factor? In what way does division sometimes result in a quotient larger than either the dividend or the divisor?

What does the decimal point represent?

CC/Learning Targets Core Vocabulary Links to Technology *6.1.4 *6.1.5 *6.1.7 *6.2.3

*6.2.4 *6.2.5 *6.2.8 6.2.9

6.2.10 *6.5.10 6.7 6.EE.7 6.EE.9

approximate solutions calculation interest

-Math!!! (app) -Whiteboard (app) -Show Me (app) -SAS Flashcards (app)

Bundle Performance Task(s) The local electronic and game store will give our school one million dollars IF the Sixth Grade students can make a budget showing how the money will be used to benefit their learning using technology. The money must be budgeted wisely and benefit the whole school. You will work in a group and make decisions about the following:

All one million dollars should be spent for this project to be complete

4 categories for which the money will be used (Each of the four categories can be broken down as the groups see fit for this money.)

Amount of money for each category

Percent of total money used per category with an explanation

Create a table/graph which shows a list of items per category (optional) As an extension, students may work independently or in small groups to research costs of Apple products (MacBook, iPad, etc.) and PCs (Mini Netbook, Tablet, laptops, etc.). Create a chart which shows the products and costs, and investigate pros and cons of both companies. After examining the facts, write a short explanation of your recommendation.

Grade 6 Math Bundle 1

Quarter 1 Aug.-Sept.

Recommended Read-Alouds

L.A. Bundle 1

Read-Alouds Page 2 of 5

Big Idea: Unity

Title Author Relates to…

Pigs Will Be Pigs: Fun with Math and Money Amy Axelrod Money

Sideways Arithmetic form Wayside school Louis Sachar Math

Math Curse Jon Scieszka Money and Problem Solving

Marvelous Math: A Book of Poems Lee Bennett Hopkins Math Poetry Connections

Sold! A Mothematics Adventure Nathan Zimelman Money

Lemonade for Sale Stuart J. Murphy Money/Graphs

The Hershey’s Milk Chocolate Bar Fractions Book Jerry Pallotta Fractions

Clean-Sweep Campers Lucille Recht Penner Fractions

Alexander, Who Used to Be Rich Last Sunday Judith Viorst Money

The Grapes of Math Greg Tang Patterns/Problem Solving

Math Appeal: Mind Stretching Math Riddles Greg Tang Patterns/Problem Solving

Let’s Take a Hike: Converting Fractions to Decimals Holly Cefrey Fractions/Decimals

Math G6 - Bundle 1

CC/Learning Targets Resource of Ideas Evidence of Learning *6.1.4 a. Convert fractions (proper and improper)

and mixed numbers to percents.

b. Convert fractions (proper and improper)

and mixed numbers to decimals.

c. Convert decimals (including those greater

than one) to percents.

d. Convert decimals (including those greater

than one) to fractions.

e. Convert percents (including those greater

than 100%) to fractions.

f. Convert percents (including those greater

than 100%) to decimals.

-Chicken Coop Fractions Game (app) -Percents as fractions or decimals (interactive practice at page bottom) -Percents on a number line (interactive practice at page bottom) -Percent of a number (interactive practice at page bottom) -Percents in shopping (shopping game using percents) -Holt Middle School Math, Lessons 8-7, 8-8, 8-9

-Holt Math Corresponding Lesson Resources -Quiz on converting decimals, percents, and fractions

-Percents on a number line -Quiz on percent of a number -Calculate percent off of sales for items at a given store -Calculate money saved through sales of items at a given store -Calculate percent of utility bills or car loan paid for from a paycheck -Calculate tip at a restaurant

*6.1.5 a. Name the equivalent decimal for a common fraction (halves, thirds, fourths, fifths, tenths) using mental math. b. Select an appropriate form of the number (fraction or decimal) to solve problem situations.

-The Hershey’s Milk Chocolate Bar Fractions Book by Jerry Pallotta (fractions)

-Clean-Sweep Campers by Lucille Recht Penner (fractions) -Convert fractions to decimals to percents lesson (interactive practice at page bottom)

-Convert fractions to decimals lesson (interactive practice at page bottom) -Fraction/decimal/percent conversion visual tool (interactive)

-Convert fractions to decimals to percents quiz (interactive) -Convert fractions to decimals quiz (interactive)

*6.1.7 a. Define common factor and greatest common factor. b. Define common multiple and least common multiple. c. Determine the least common multiple of two or more numbers.

d. Find a common denominator for adding and subtracting fractions by determining the least common multiple of two or more

-LCM and GCM (app) -Factor trees lesson (interactive) -Least common multiple lesson (interactive practice at page bottom) -Least common multiple with factor trees lesson (interactive practice at page bottom)

-Least common multiple -Prime factorization lesson (interactive practice at page bottom) -Greatest common factor lesson (interactive practice at page bottom)

-Least common multiple quiz (interactive) -Least common multiple quiz (interactive) -Least common multiple -Prime factorization quiz (interactive) -Greatest common factor quiz (interactive)

Math G6 - Bundle 1

numbers. e. Write or state the divisibility rules for 2, 3, 4, 5, 6 and 10 to assist in finding factors of numbers. f. Determine the greatest common factor of two numbers. g. Simplify fractions by determining the greatest common factor of two numbers. h. Determine the least common multiple of two or more numbers to solve problems.

-Holt Middle School Math, Lessons 4-2, 4-3, 5-5

-Holt Math Corresponding Lesson Resources

*6.2.3 (6.NS.3)

a. Multiply decimals up to thousandths by a whole number. b. Multiply a decimal number (up to thousandths) by a decimal number (up to thousandths).

c. Divide whole numbers by decimals up to thousandths. Explore quotients with repeating decimals, using the vocabulary of "repeating" and "terminating." d. Divide decimal numbers (up to thousandths) by a whole number. Explore quotients with repeating decimals, using the vocabulary of "repeating" and "terminating."

e. Divide a decimal number (up to

thousandths) by a decimal number (up to

thousandths). Explore quotients with

repeating decimals, using the vocabulary of

"repeating" and "terminating."

Fluently add, subtract, multiply, and

divide multi-digit decimals using the

standard algorithm for each

operation. (Notes: Sufficient practice

-Marvelous Math: A Book of Poems by Lee Bennett Hopkins (math poems)

-Math Potatoes by Greg Tang (math poetry connections) -Adding decimals (interactive) -Adding and subtracting decimals with base blocks (interactive) -Holt Middle School Math, Lesson 3-4 (metric), 3-5 (scientific notation), 3-6, 3-7, and 3-8

-Holt Hands-On Lab pp. 118-119 -Holt Middle School Math, p.120-129, 144-145

-Holt Math Corresponding Lesson Resources

Math G6 - Bundle 1

and support throughout the year are

needed to help students meet this

fluency.)

*6.2.4 (6.NS.1)

Explain orally or in writing how to multiply

and divide fractions and perform the

calculations. Explain why these procedures

make sense.

Interpret and compute quotients of

fractions, and solve word problems

involving division of fractions by

fractions, e.g., by using visual

fraction models and equations to

represent the problem. For example,

create a story context for (2/3) ÷

(3/4) and use a visual fraction model

to show the quotient; use the

relationship between multiplication

and division to explain that (2/3) ÷

(3/4) = 8/9 because 3/4 of 8/9 is 2/3.

(In general, (a/b) ÷ (c/d) = ad/bc.)

How much chocolate will each

person get if 3 people share 1/2 lb of

chocolate equally? How many 3/4-

cup servings are in 2/3 of a cup of

yogurt? How wide is a rectangular

strip of land with length 3/4 mi and

area 1/2 square mi?

-Multiplying Menace: The Revenge of Rumpelstiltskin by Pam Calvert (multiplying fractions) -Dividing fractions lesson (interactive practice at page bottom) -Dividing fractions lesson (interactive practice at bottom of page) -Dividing fractions lesson (interactive practice at bottom of page) -Dividing fractions lesson (interactive practice at bottom of page) -Multiply and divide fractions lesson (interactive lesson at page bottom) -Multiplying fractions visual tool (interactive) -Holt Middle School Math, Lessons 5-1, 5-2, 5-3, 5-4 -Holt Hands-On Lab, pp. 210-211, pp. 220-221

-Dividing fractions(interactive) -Dividing fractions(interactive) -Dividing fractions(interactive) -Dividing fractions(interactive) -Dividing fractions(interactive) -Holt Math Corresponding Lesson Resources

*6.2.5

a. Solve problems involving addition, subtraction of positive fractions and explain why a particular operation was used for a given situation.

-Candy Factory (app) -Add and subtract fractions lesson (interactive practice at page bottom)

-Add and subtract fractions quiz (interactive using story problems) -Multiply and divide fractions quiz (interactive using story problems)

Math G6 - Bundle 1

(6.NS.1)

b. Solve problems involving multiplication,

and division of positive fractions and explain

why a particular operation was used for a

given situation.

Interpret and compute quotients of

fractions, and solve word problems

involving division of fractions by

fractions, e.g., by using visual

fraction models and equations to

represent the problem. For example,

create a story context for (2/3) ÷

(3/4) and use a visual fraction model

to show the quotient; use the

relationship between multiplication

and division to explain that (2/3) ÷

(3/4) = 8/9 because 3/4 of 8/9 is 2/3.

(In general, (a/b) ÷ (c/d) = ad/bc.)

How much chocolate will each

person get if 3 people share 1/2 lb of

chocolate equally? How many 3/4-

cup servings are in 2/3 of a cup of

yogurt? How wide is a rectangular

strip of land with length 3/4 mi and

area 1/2 square mi?

-Addition of mixed numbers lesson (interactive practice at page bottom) -Adding fractions flashcards (interactive) -Adding fractions matching game (interactive) -Adding fractions visual tool (interactive) -Pie graphs as a visual tool for adding fractions (interactive) -Subtraction of mixed numbers lesson (interactive practice at page bottom) -Multiply and divide fractions lesson (interactive practice at page bottom) -Multiplying fractions visual tool (interactive) -Dividing fractions lesson (interactive practice at page bottom) -Dividing fractions lesson (interactive practice at page bottom) -Dividing fractions lesson (interactive practice at page bottom) -Dividing fractions lesson (interactive practice at page bottom) -Holt Middle School Math, Lessons 4-8, 4-9, 5-7, 5-8, 5-9 -Holt Hands-On Lab, pp. 240-241, pp. 250-251 -Holt Middle School Math, pp. 220-224

-Subtraction of mixed numbers quiz (interactive) -Addition of mixed numbers quiz (interactive) -Dividing fractions(interactive) -Dividing fractions(interactive) -Dividing fractions(interactive) -Dividing fractions(interactive) -Dividing fractions(interactive) -Holt Math Corresponding Lesson Resources

*6.2.8

a. Calculate given percentages of a quantity using both decimal and fractional representations of the percent.

b. Solve problems involving discounts at sales given the original price and the discount rate. Solve for both the sale price and the amount saved.

-Alexander, Who Used to Be Rich Last Sunday by Judith Viorst (money) -Math Curse by Jon Scieszka (perception) -Math Appeal by Harry Briggs (problem solving) -Scale ratios lesson (interactive practice at bottom of page at end) -Proportional reasoning and ratios lesson

-Holt Math Corresponding Lesson Resources -Hands-On Lab pp. 396-397 -Ratio, proportion, percent quiz -Sales tax quiz (interactive) -Use sales ads and create a list of

Math G6 - Bundle 1

(6.RP.3b)

c. Solve problems involving simple interest earned given principal and interest rate. Solve for both interest earned and total balance. d. Solve problems involving tips given the cost of the service and the tip percentage. Solve for both the amount of tip and the total cost of the service including tip. Practice using mental math to solve and estimate answers to problems involving 5%, 10%, 15% and 20%.

Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations1. b. Solve unit rate problems

including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? (Notes: The CCSS includes unit rates, the use of tables and the coordinate plane with ratios, solving problems involving finding the whole given a part and the percent, using ratio reasoning to do measurement conversions, and manipulating

-Equal ratios lesson -Ratio, proportion, and percent lesson (lesson on ratio/proportion/percents with interactive practice at bottom of page) -Sales tax lesson (interactive practice at bottom of page at end) -Percentage Calculator (interactive part/whole/percent calculator) -Percent wheel (basic visual for part/whole/percent) -Holt Middle School Math, Lessons 8-7, 8-8, 8-9, 8-10 -Holt Middle School Math, Extension pp.436-437 (simple interest)

purchases, costs, and savings -Use restaurant menu and create a mock dinner party with meals, desserts, prices, coupon, and tip

Math G6 - Bundle 1

(6.RP.3c) (6.RP.3d) (6.5.2)

and transforming units) c. Find a percent of a quantity as a

rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. (Notes: The CCSS includes unit rates, the use of tables and the coordinate plane with ratios, solving problems involving finding the whole given a part and the percent, using ratio reasoning to do measurement conversions, and manipulating and transforming units)

d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. (Notes: The CCSS includes unit rates, the use of tables and the coordinate plane with ratios, solving problems involving finding the whole given a part and the percent, using ratio reasoning to do measurement conversions, and manipulating and transforming units)

-Holt Middle School Math, pp.418-422

6.2.9 a. Estimate to decide whether an answer to a decimal computational problem (all four operations) is reasonable.

-Rounding decimals lesson (interactive practice at page bottom) -Estimating sums and differences with decimals game (interactive) -Estimation lesson (interactive practice at page bottom)

-Rounding decimals quiz (interactive) -Estimation quiz (interactive)

Math G6 - Bundle 1

b. Estimate to decide whether the answer to

a decimal problem is reasonable within the

context of a given problem solving situation.

(any of the four operations) Include both

reasonableness looking at the size of the

number compared to the unit (If 1 computer

costs $899.99, is $90,000 a reasonable cost

for 10 computers?) as well as an

interpretation of the decimal remainder.

-Holt Middle School Math, Lesson 3-2

-Holt Math Corresponding Lesson Resources

6.2.10 a. Compute mentally the solution to addition and subtraction problems using simple fractions (halves, thirds, fourths, fifths, sixths, eighths, tenths).

b. Compute mentally the solution to addition

and subtraction problems using simple

decimals (including decimals added to and

subtracted from whole numbers).

-Five Easy Steps to a Balanced Math Program for Secondary Grades pp. 3-28 -Adding fractions matching game (interactive) -Adding fractions visual tool (interactive) -Holt Mathables, p. 262

-Speed math game (timed, with choice of signs) -Whole class interaction -I Have/Who Has? -Verbal response quiz

*6.5.10 a. Add and subtract with money in decimal notation to solve problems.

b. Multiply and divide with money in decimal notation. Interpret and/or round the results to the appropriate number of digits. c. Solve problems using multiplication and division with money in decimal notation.

-Pigs Will Be Pigs: Fun with Math and Money by Amy Axelrod (money) -Sold! A Mothematics Adventure by Nathan Zimelman (money) -Lemonade for Sale (money/graphs) -Sideways Arithmetic from Wayside School by Louis Sachar (math) -Adding money activity (interactive) -Cashier game (interactive) -Sheppards Software Game Assortment (choice of games and levels of difficulty) -Envision Math Activity (quick multiplication/division game) -Multiplication War (decks of cards needed) -Online flashcards (choice of levels and choice of signs) -Math Problem Generator -Holt Middle School Math, Lesson 3-3 (decimals)

-Holt Math Corresponding Lesson Resources -Dry erase board -Partner work -Keep and maintain a checking account balance -Calculate multiple amounts purchased in a clothing /toy store -Calculate money earned for an hourly rate over many hours in a week -Calculate monthly utility bills subtracted from a working checking account

-Speed math game (timed, with

Math G6 - Bundle 1

choice of signs)

6.7 Problem Solving -The Problem Solver 6: Activities for Learning Problem-Solving Strategies -Five Easy Steps to a Balanced Math Program for Secondary Grades pp.29-73 -Math Curse by Jon Scieszka (problem solving)

-Problem Solver Activities -See Problem Solving Template in Appendix.

6.EE.7 Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.

-Holt Middle School Math, pp. 604-605 -Problem Solver Activities -See Problem Solving Template in Appendix.

6.EE.9 Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.

-Variables (independent/dependent)

-Variables video

-Problem Solver Activities -See Problem Solving Template in Appendix.

Math G6 - Bundle 1

Correlating CC/Learning Targets Teacher Notes

-Problem Solving indicators need to be embedded in each Bundle.

-Nlvm.usu.edu (huge library of virtual manipulatives for all standards!)

-Studyzone.com (huge library of process and content activities; many are interactive)

-Onlinemathlearning (huge library of online videos for all standards)

-Study Jams (huge resource of interactive lessons and activities) -Five Easy Steps to a Balanced Math Program for Secondary Grades, pp. 75-100 -All embedded apps included in this curriculum are free.

Bundle 1 – 6th Grade Performance Task

Worksheet and Instructions Name ______________________________ Goal: You will write a technology budget for one million dollars to enhance the education and learning process of the students of 21st Century School. Your school has 4 math teachers. Each teacher has 5 classes of 30 students combined for 150 students. The school has a total of 600 students. There are 4 categories for which you will be purchasing technology from Best Buy. These categories are computers, camera, audio devices, and gaming devices. The items you will be buying from these categories are as follows. Computers - either an Apple iPad2 with Wi-Fi and 32GB for $599.00 each OR a Dell laptop with Microsoft Office software for $479.99 each Camera - a flip video/camera for $77.99 each Audio Devices- an iPod Touch 16GB w/ headphones for $179.99 each Gaming Devices- a Play Station 3 (160GB) for $249.99 each. For each category, you will need to determine and establish the following criteria*.

A. How will the technology devices be distributed? Who will receive them, certain classes or all students? B. How many of each device will be needed according to how they are distributed? C. What is the total cost for each category? D. What are some things that the devices will be used for or how will they enhance learning at NHMS?

*Complete the Budget Sheet with the information from points A through D. The final part of the project is to determine what percent of the $1,000,000 budget each category represents and then show this on the pie graph located at the bottom of the Budget Sheet. To complete the pie graph, do the following steps in order for each category.

1. Take the total cost of each category and divide by 1,000,000. 2. Round the decimal to the nearest hundredths (the second decimal place). 3. Move the decimal point to the right 2 places. 4. Place a percent sign on the right side.

This percent will be written inside the pie graph. 5. For each category, multiply the decimal by 360° and round to the nearest whole degree.

This will give you how many degrees to measure with a protractor inside the circle. 6. You should have four sections. Color the computer section a light red, the camera section a

light green, the audio device section a light blue, and the gaming section a light yellow. 7. Color the boxes in the key the same colors as the pie sections for each category.

Use this workspace to do steps 1 through 5 from above.

Computers Cameras Audio Devices Gaming Devices ___________÷1,000,000 ___________÷1,000,000 ___________÷1,000,000 ___________÷1,000,000

Rounded = 0.__ __ Rounded = 0.__ __ Rounded = 0.__ __ Rounded = 0.__ __

_____% _____% _____% _____%

________ x 360° ________ x 360° ________ x 360° ________ x 360° Rounded = ____° Rounded = ____° Rounded = ____° Rounded = ____°

21st Century School $1,000,000 Technology Budget

Presented by __________________________________ on _______________ Computers

What: Who:

Individual Cost: $ How this will enhance learning:

How Many:

Total Cost: $

Cameras

What: Who:

Individual Cost: $ How this will enhance learning:

How Many:

Total Cost: $

Audio Devices

What: Who:

Individual Cost: $ How this will enhance learning:

How Many:

Total Cost: $

Gaming Devices

What: Who:

Individual Cost: $ How this will enhance learning:

How Many:

Total Cost: $

Key: Computers Cameras Audio Devices Gaming Devices

Name____________________________________________________

Date assigned _____________________________ Date due __________________________________

Math Project---“Percents, Discounts, & Sales Tax”

(Paste Sale Advertisement Here)

Store _________________________________________________________________________

Item on Sale ___________________________________________________________________

Original Price = ____________________________

Percent off= ____________________________

Discount or Amount Saved = _________________

Original Price _____________________________

---Discount --- _____________________________

Sale Price = _____________________________

X Sales Tax (7%) ___________________________

TOTAL PURCHASE PRICE after Discount and Sale Tax = _________________________________