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 Multiples
Problem 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, 43-44
Problem 1.4 – Rectangles and Factor Pairs
· I can prove when I have found all of the factors of a number. / 22-23, 45-49 / · This is laying the foundation for students to think of area models, which they will be using throughout middle and high school
2. Common Multiples and Common Factors
Problem 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 Strings
Problem 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 GCF
Problem 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.7c
Problem 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 class
Problem 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 compare decimals. / 70-84, 88, 97
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.3d
Problem 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.7
Problem 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
· Adding and subtracting fractions
· I can discover strategies for adding and subtracting fractions. / 27-29, 52-53, 67-70, 75-76 / · A, B, and C only
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.3
Problem 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.2b
Problem 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
· 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. / 3-12, 40, 54
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 Operations
Problem 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
· I can estimate answers when working with decimals computations. / 8-23, 35-51, 62 / · Only A and B
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.3
Problem 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 ?’s
3. Multiplying and Dividing Decimals – 6.NS.1, 6.NS.2, 6.NS.3
Problem 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 here
Problem 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)