Ratios and Proportional Relationships
Understand ratio concepts and use ratio reasoning to solve problems.
6.RP.1: Understand the concept of a ratio and use ratio language to describe a ratio 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.”
Use Ratio Language:
https://learnzillion.com/lessonsets/114
and
https://learnzillion.com/lessonsets/133
Express Ratios
https://learnzillion.com/lessonsets/53
Understand Ratios
https://learnzillion.com/lessonsets/84

6.RP.2: Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 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.” (Note: Expectations for unit rates in this grade are limited to non-complex fractions.)
https://learnzillion.com/lessonsets/152

6.RP.3: 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 equations.

a. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.
Find Ratio Values and Compare:
https://learnzillion.com/lessonsets/86
Use Tables and Coordinate Plane
https://learnzillion.com/lessonsets/156
and
https://learnzillion.com/lessonsets/164
Missing Proportion:
https://learnzillion.com/lessonsets/57

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?
https://learnzillion.com/lessonsets/157

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.

https://learnzillion.com/lessonsets/181


d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.
Convert Measurements
https://learnzillion.com/lessonsets/87
Solve Ratio Problems Using Tables and Coordinate Plane
https://learnzillion.com/lessonsets/164

The Number System
Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

6.NS.1: 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?
Interpret and Compute Quotients with Fractions
https://learnzillion.com/lessonsets/701
Division of Whole Numbers By Fractions
https://learnzillion.com/lessonsets/12
Solve Word Problems
https://learnzillion.com/lessonsets/288
Divide Fractions by Fractions
https://learnzillion.com/lessonsets/13
Compute and Interpret Quotients of Fractions
https://learnzillion.com/lessonsets/145
Multiply with Fractions
https://learnzillion.com/lessonsets/14


Compute fluently with multi-digit numbers and find common factors and multiples.

6.NS.2: Fluently divide multi-digit numbers using the standard algorithm.
Divide Multipdigit Numbers
https://learnzillion.com/lessonsets/545
Standard Division Algorithm
https://learnzillion.com/lessonsets/368

6.NS.3: Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
https://learnzillion.com/lessonsets/403
and
https://learnzillion.com/lessonsets/586


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 two whole 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).
Understand GCF and LCM
https://learnzillion.com/lessonsets/598
Distributive Property
https://learnzillion.com/lessonsets/424