Time / 6th Grade ALCOS
ARMT+ Standard / Book:
(Connected Math Book (AMSTI)*In bold* or Go Math!) / Content and Essential Questions
Critical Area: Completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers
The Number System: Compute fluently with multi-digit numbers and find common factors and multiples.
1 week / **Introducing Cluster** / Prime Time
  • Investigation 1.1: Playing the Factor Game
  • Investigation 1.2: Playing to Win the Factor Game
***Discuss Divisibility Rules /
  • Become familiar with the factors of the numbers from 2 to 30
  • Review multiplication and division facts
  • Relate dividing and finding factors of a number
  • Classify numbers as prime or composite
  • Recognize that some numbers are rich in factors, while others have few factors
  • Develop understanding of factors and multiples and the relationships between them
  • Understand that some products are the result of more than one factor pair (for example, 18 = 9 3 2 and 18 5 6 3 3)

3 days / 6.NS.4
Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of twowhole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2). / Prime Time
  • Investigation 2.1: Finding Patterns
  • Investigation 2.2: Reasoning with Even and Odd Numbers
  • Investigation 2.3: Classifying Numbers
/
  • Recognize that factors come in pairs and that once one factor is found, another can also be found
  • Visualize and represent a factor pair as the dimensions of a rectangle
  • Determine whether a number is prime/composite, square/non-square, and even/odd based on its factor pairs
  • Develop an informal sense of what factors must be checked to be sure all the factors of a number are found
  • Make conjectures about the result of operations on odd numbers, on even numbers, and on combinations of odd and even numbers, and create arguments to show which conjectures are valid and which are not
  • Determine whether a product is even or odd based on its factors
  • Determine whether a sum is even or odd based on its addends
  • Classify numbers by their characteristics using Venn diagrams as a tool for sorting and classifying
  • Develop understanding of factors and multiples, common factors and common multiples, and the relationships among them

2 weeks / 6.NS.2
Fluently divide multi-digit numbers using the standard algorithm.
6.NS.3
Fluently add, subtract, multiply, and divide multi-digit decimals using thestandard algorithm for each operation.
6.NS.4
(Also:
6.EE.1
Write and evaluate numerical expressions involving whole-number exponents.)
ARMT+1.Fluently add, subtract, multiply, and divide fractions and multi-digit decimals using the standard algorithm for each operation. [6-NS3]
ARMT+3. Solve problems using numeric and geometric patterns. / Lesson 1.1: Divide Multi-Digit Numbers
Lesson 1.2: Prime Factorization
*Prime Time Investigation 4.2: Finding the Longest Factor String
Lesson 1.3: Least Common Multiple
Lesson 1.4: Greatest Common Factor
Lesson 1.5: Problem Solving- Apply the Greatest Common Factor
Mid-Chapter Checkpoint /
  • 1.1: How to divide multi-digit numbers
  • 1.2: How to write the prime factorization of a number
  • Develop a systematic strategy for finding prime factorizations
  • Recognize that a number may have several different factorizations but, except for order, each whole number greater than 1 has exactly one factorization into a product of prime numbers (the Fundamental Theorem ofArithmetic)
  • 1.3: How to find the least common multiple of two whole numbers
  • 1.4: How to find the greatest common factor of two numbers
  • 1.5: How to solve problems involving the GCF and the Distributive Property.

7 days / 6.NS.3
Fluently add, subtract, multiply, and divide multi-digit decimals using thestandard algorithm for each operation.
ARMT+1.Fluently add, subtract, multiply, and divide fractions and multi-digit decimals using the standard algorithm for each operation. [6-NS3]
ARMT+2.Solve problems involving decimals, percents, fractions, and proportions. / **Make Place Value Foldable
Lesson 1.6: Add and Subtract Decimals
Lesson 1.7: Multiply Decimals
Lesson 1.8: Divide Decimals by Whole Numbers
Lesson 1.9: Divide with Decimals
Chapter 1 Review/ Test /
  • 1.6 How to add and subtract multi-digit decimals
  • 1.7 How to multiply multi-digit decimals
  • 1.8 How to divide decimals by whole numbers
  • 1.9: How to divide whole numbers and decimals by decimals

The Number System: Apply and extend previous understandings of numbers to the system of rational numbers.
4 weeks / 6.NS.6.c
Find and position integers and other rational numbers on a horizontal orvertical number line diagram; find and position pairs of integers andother rational numbers on a coordinate plane.
6.NS.4
6.NS.2
(ALSO:
  • 6.RP.3 (B&P I: Inv. 3)
Use ratio and rate reasoning to solve real-world and mathematicalproblems, e.g., by reasoning about tables of equivalent ratios, tapediagrams, double number line diagrams, or equations.
  • 6.NS.7.a (B&P I: Inv. 1-3)
Interpret statements of inequality as statements about the relativeposition of two numbers on a number line diagram. For example, interpret −3 > −7 as a statement that −3 is located to the right of −7 on a number line oriented from left to right.)
ARMT+1.Fluently add, subtract, multiply, and divide fractions and multi-digit decimals using the standard algorithm for each operation. [6-NS3]
ARMT+2.Solve problems involving decimals, percents, fractions, and proportions. / **Review Place Value Foldable
Bits and Pieces I: Investigation1.2 : Folding Fraction Strips
Bits and Pieces I: Investigation 2: Sharing and Comparing With Fractions
Investigation 2.2: Finding Equivalent Fractions
Investigation 2.3: Comparing Fractions to Benchmarks
Investigation 2.4: Fractions Between Fractions
Bits and Pieces I: Investigation 3: Moving Between Fractions and Decimals
Investigation 3.1: Making Smaller Pieces
Investigation 3.2: Making Even Smaller Pieces
Investigation 3.3: Decimal Benchmarks
Lesson 2.1: Fractions and Decimals
Lesson 2.2: Compare and Order Fractions and Decimals
Lesson 2.3: Multiply Fractions
Lesson 2.4: Simplify Factors
Mid-Chapter Checkpoint
SUPPLEMENT WITH Bits and Pieces II- Investigation 3 /
  • B&P 1.2: Develop strategies to partition fraction strips for halves, thirds, fourths, fifths, sixths, eighths, ninths, tenths, and twelfths
  • B&P 1.2: Explore the role of the numerator and the denominator and the part-to-whole nature of fractions
  • B&P 1.2: Investigate equivalent fractions that result from different partitioning strategies
  • B&P 2.2: Understand that a place on a number line can have more than one fraction name
  • B&P 2.2: Recognize that fractions can represent a location on a number line and the length from one point to another on a number line
  • B&P 2.2: Develop strategies for finding equivalent fractions
  • B&P 2.3: Use benchmarks to estimate the size of fractions and compare fractions
  • B&P 2.3: Develop strategies for comparing and ordering fractions
  • B&P 2.4: Develop a strategy for finding a fractionbetween any two given fractions
  • B&P 2.4: Begin to recognize that by using smallerpartitions one can always find a fractionbetween two given fractions.
  • B&P 3.1: Understand relationship between tenths and hundredths including how tenths are partitioned to create hundredths
  • B&P 3.1: Represent decimals as fractions with denominators of ten and one hundred
  • B&P 3.1: Move between fraction strip models, grid models, and numerical forms for both fraction and decimal numbers
  • B&P 3.2: Read and write fractions and decimal numbers
  • B&P 3.2: Extend understanding of fractions and decimals to include place values greater than hundredths
  • B&P 3.2: Develop ways to find a decimal between any two given decimals
  • B&P 3.3: Represent fractions and decimals with hundredths grids
  • B&P 3.3: Use these representations to find approximate or exact decimal equivalents for fraction benchmarks
  • Lesson 2.1: How to convert between fractions and decimals.
  • Lesson 2.2How to compare and order fractions and decimals
  • Lesson 2.3: How to multiply fractions
  • Lesson 2.4: How to simplify fractional factors by using the greatest common factor

The Number System: Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
3 weeks / 6.NS.1
Interpret and compute quotients of fractions, and solve word problemsinvolving division of fractions by fractions, e.g., byusing visual fractionmodels 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 ¾ of 8/9 is 2/3. (In general, (a/b) °“ (c/d) = d/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many3/4-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?
ARMT+1. Fluently add, subtract, multiply, and divide fractions and multi-digit decimals using the standard algorithm for each operation. [6-NS3]
ARMT+2.Solve problems involving decimals, percents, fractions, and proportions. / **Review fraction strips
Lesson 2.5: Model Fraction Division
Lesson 2.6: Estimate Quotients
Lesson 2.7: Divide Fractions
Lesson 2.8: Model Mixed Number Division
Lesson 2.9: Divide Mixed Numbers
Lesson 2.10: Problem Solving- Fraction Operations
Chapter 2 Review/ Test
SUPPLEMENT WITH Bits and Pieces II- Investigation 4 /
  • Lesson 2.5: How to use a model to show fraction division
  • Lesson 2.6: How to use compatible numbers to estimate quotients of fractions and mixed numbers
  • Lesson 2.7: How to divide fractions
  • Lesson 2.8: How to use a model to show division of mixed numbers
  • Lesson 2.9: How to divide mixed numbers
  • Lesson 2.10: How to use the strategy use a model to help solve a division problem

The Number System: Apply and extend previous understandings of numbers to the system of rational numbers.
2 weeks / 6.NS.5
Understand that positive and negative numbers are used together todescribe quantities having opposite directions or values (e.g., temperature
above/below zero, elevation above/below sea level, credits/debits,positive/negative electric charge); use positive and negative numbers torepresent quantities in real-world contexts, explaining the meaning of 0in each situation.
6.NS.6.a
Recognize opposite signs of numbers as indicating locations on oppositesides of 0 on the number line; recognize that the opposite of the oppositeof a number is the number itself, e.g., −(−3) = 3, and that 0 is its ownopposite.
6.NS.7.a
Interpret statements of inequality as statements about the relativeposition of two numbers on a number line diagram.
For example, interpret −3 > −7 as a statement that −3 is located to the right of −7 on a number line oriented from left to right.
6.NS.7.b
Write, interpret, and explain statements of order for rational numbers inreal-world contexts.
For example, write −3°C > −7°C to express the factthat −3°C is warmer than −7°C. / Lesson 3.1: Understand Positive and Negative Numbers
Lesson 3.2: Compare and Order Integers
Lesson 3.3: Rational Numbers and the Number Line
Lesson 3.4: Compare and Order Rational Numbers
Mid-Chapter Checkpoint /
  • Lesson 3.1: how to use positive and negative numbers to represent real-world quantities
  • Lesson 3.2: How to compare and order integers
  • Lesson 3.3: How to plot numbers on a number line
  • Lesson 3.4: How to compare and order rational numbers

8 days / 6.NS.7.c (3.5)
Understand the absolute value of a rational number as its distance from 0on the number line; interpret absolute value as magnitude for a positiveor negative quantity in a real-world situation.
For example, for an accountbalance of −30 dollars, write |−30| = 30 to describe the size of the debt indollars.
6.NS.7.d (3.6)
Distinguish comparisons of absolute value from statements about order.
For example, recognize that an account balance less than −30 dollars represents a debt greater than 30 dollars.
6.NS.6.c (3.7)
Find and position integers and other rational numbers on a horizontal orvertical number line diagram; find and position pairs of integers andother rational numbers on a coordinate plane.
6.NS.6.b (3.8)
Understand signs of numbers in ordered pairs as indicating locations inquadrants of the coordinate plane; recognize that when two orderedpairs differ only by signs, the locations of the points are related byreflections across one or both axes.
6.NS.8 (3.9 & 3.10)
Solve real-world and mathematical problems by graphing points in allfour quadrants of the coordinate plane. Include use of coordinates andabsolute value to find distances between points with the same firstcoordinate or the same second coordinate.
ARMT+5. Plot coordinates on grids, graphs, and maps.
ARMT+8. Determine the distance between two points on a scale drawing or map using proportional reasoning. / Lesson 3.5: Absolute Value
Lesson 3.6: Compare Absolute Values
Lesson 3.7: Rational Numbers and the Coordinate Plane
Lesson 3.8: Ordered Pair Relationships
Lesson 3.9: Distance on the Coordinate Plane
Lesson 3.10: Problem Solving- The Coordinate Plane
Chapter 3 Review/ Test /
  • Lesson 3.5: How to find and interpret the absolute value of rational numbers
  • Lesson 3.6: How to interpret comparisons involving absolute values
  • Lesson 3.7: How to plot ordered pairs of rational numbers on a coordinate plane
  • Lesson 3.8: How to identify the relationship between points on a coordinate plane
  • Lesson 3.9: How to find the distance between two points that lie on a horizontal or vertical line on a coordinate plane
  • Lesson 3.10: How to use the strategy draw a diagram to help solve a problem on the coordinate plane

Critical Area: Connecting ratio and rate to whole number multiplication and division and using concepts of ratio and rate to solve problems
Ratios and Proportional Relationships: Understand ratio concepts and use ratio reasoning to solve problems.
1 week / 6.RP.1 (4.1 & 4.2)
Understand the concept of a ratio and use ratio language to describe aratio relationship between two quantities.
For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”
6.RP.3.a (4.3, 4.4, 4.5)
Make tables of equivalent ratios relating quantities with whole numbermeasurements, find missing values in the tables, and plot the pairs ofvalues on the coordinate plane. Use tables to compare ratios. / Lesson 4.1: Model Ratios
Lesson 4.2: Ratios and Rates
Lesson 4.3: Equivalent Ratios and Multiplication Tables
Lesson 4.4: Problem Solving- Use Tables to Compare Ratios
Lesson 4.5: Use Equivalent Ratios
Mid-Chapter Checkpoint /
  • Lesson 4.1: How to model ratios
  • Lesson 4.2: How to write ratios and rates
  • Lesson 4.3: How to use a multiplication tables to find equivalent ratios
  • Lesson 4.4: How to use the strategy find a pattern to help compare ratios
  • Lesson 4.5: Understand ratio concepts and use ratio reasoning to solve problems

1 week / 6.RP.2 (4.6)
Understand the concept of a unit rate a/b associated with a ratio a:b withb ≠ 0, and use rate language in the context of a ratio relationship.
For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”
6.RP.3.b (4.7)
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?
6.RP.3.a (4.8)
Make tables of equivalent ratios relating quantities with whole numbermeasurements, find missing values in the tables, and plot the pairs ofvalues on the coordinate plane. Use tables to compare ratios.
ARMT+2.Solve problems involving decimals, percents, fractions, and proportions. / Lesson 4.6: Find Unit Rates
Lesson 4.7: Use Unit Rates
Lesson 4.8: Equivalent Ratios and Graphs
Chapter 4 Review/ Test /
  • Lesson 4.6: How to use unit rates to make comparisons
  • Lesson 4.7: How to solve problems using unit rates
  • Lesson 4.8: How to use a graph to represent equivalent ratios

8 days / 6.RP.3.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.
ARMT+2.Solve problems involving decimals, percents, fractions, and proportions. / Lesson 5.1: Model Percents
Bits and Pieces I: Investigation 4: Working with Percents
Investigation 4.1: Making Sense of Percents
Investigation 4.2: Using Percents to Compare
Lesson 5.2: Write Percents as Fractions and Decimals
Lesson 5.3: Write Fractions and Decimals as Percents
Mid-Chapter Checkpoint /
  • Lesson 5.1: How to use a model to show a percent
  • B&P 4.1: Introduce percents as a part-whole relationshipwhere the whole is not out of 100 but scaled tobe “out of 100”
  • B&P 4.1: Use fraction partitioning and fractionbenchmarks to make sense of percents
  • B&P 4.2Develop strategies, including percents, to use in
comparisons where the whole is less than 100
  • B&P 4.2: Understand that comparing situations with
different numbers of trials is difficult unless weuse percents or some other form of equivalentrepresentation
  • Lesson 5.2: How to write percents as fractions and decimals
  • Lesson 5.3: How to write fractions and decimals as percents

1 week / 6.RP.3.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.
ARMT+2.Solve problems involving decimals, percents, fractions, and proportions.
ARMT+8. Determine the distance between two points on a scale drawing or map using proportional reasoning. / Lesson 5.4: Percent of a Quantity
Lesson 5.5: Problem Solving- Percents
Lesson 5.6: Find the Whole Number From a Percent
Chapter 5 Review/ Test /
  • Lesson 5.4: How to find a percent of a quantity
  • Lesson 5.5: How to use the strategy use a model to help solve a percent problem
  • Lesson 5.6: How to find the whole given a part and the percent

2 weeks / 6.RP.3.d
Use ratio reasoning to convert measurement units; manipulate andtransform units appropriately when multiplying or dividing quantities.
ARMT+2.Solve problems involving decimals, percents, fractions, and proportions.
ARMT+9. Convert units of length, weight, or capacity within the same system (customary or metric). / Lesson 6.1: Convert Units of Length
Lesson 6.2: Convert Units of Capacity
Lesson 6.3: Convert Units of Weight and Mass
Mid-Chapter Checkpoint
Lesson 6.4: Transform Units
Lesson 6.5: Problem Solving- Distance, Rate, and Time Formulas
Chapter 6 Review/Test /
  • Lesson 6.1: How to use ratio reasoning to convert from one unit of length to another
  • Lesson 6.2: How to use ratio reasoning to convert from one unit of capacity to another
  • Lesson 6.3: How to use ratio reasoning to convert from one unit of weight and mass to another
  • Lesson 6.4: How to transform units to solve problems
  • Lesson 6.5: How to use the strategy use a formula to solve problems involving distance, rate, and time