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 Grade 6 Module 4: Expressions and Equations In Module 4, Expressions and Equations, students extend their arithmetic work to include using letters to represent numbers in order to understand that...

 Grade 6 Mathematics Module 1: Ratios and Unit Rates Students begin their sixth grade year investigating the concepts of ratio and rate. They use multiple forms of ratio language and ratio notation,...

 Grade 6 Module 2: Arithmetic Operations Including Division of Fractions In Module 1, students used their existing understanding of multiplication and division as they began their study of ratios and...

 Grade 6 Module 3: Rational Numbers Students are familiar with the number line and determining the location of positive fractions, decimals, and whole numbers from previous grades. Students extend the...

 Grade 6 Module 6: Statistics In this module, students move from simply representing data into analysis of data. Students begin to think and reason statistically, first by recognizing a statistical...

 Grade 6 Module 5: Area, Surface Area, and Volume Problems In this module, students utilize their previous experiences in order to understand and develop formulas for area, volume, and surface area. ...

 Student Outcomes Students understand that a ratio is an ordered pair of nonnegative numbers, which are not both zero. Students understand that a ratio is often used instead of describing the first...

 Student Outcomes Students reinforce their understanding that a ratio is an ordered pair of nonnegative numbers, which are not both zero. Students continue to learn and use the precise language and...

 Student Outcomes Students develop an intuitive understanding of equivalent ratios by using tape diagrams to explore possible quantities of each part when given the parttopart ratio. Students use...

 Student Outcomes Given a ratio, students identify equivalent ratios. Students use tape diagrams and the description of equivalent ratios to determine if two ratios are equivalent. Students relate...

 Student Outcomes Students use tape diagrams to find an equivalent ratio when given the parttopart ratio and the total of those two quantities. Students use tape diagrams to find an equivalent...

 Student Outcomes Students use tape diagrams to solve problems when given a ratio between two quantities and a change to those quantities that changes the ratio.

 Student Outcomes Students understand the relationship between ratios and fractions. Students describe the fraction A/B associated with the ratio A:B as the value of the ratio A to B. Students...

 Student Outcomes Students understand the value of a ratio A:B is A/B. They understand that if two ratios are equivalent, the ratios have the same value. Students use the value of a ratio to solve...

 Student Outcomes Students understand that a ratio is often used to describe the relationship between the amount of one quantity and the amount of another quantity as in the cases of mixtures or...

 Student Outcomes Students identify both the additive and multiplicative structure of a ratio table and use the structure to make additional entries in the table. Students use ratio tables to solve...

 Student Outcomes Students solve problems by comparing different ratios using two or more ratio tables.

 Student Outcomes Students create equivalent ratios using a ratio table and represent these ratios on a double number line diagram. Students extend and use a double number line diagram to solve ratio...

 Student Outcomes Students restate a ratio in terms of its value; e.g., if the ratio of length A to length B is 3:5 (in the same units), students state that “length A is 3/5 of length B”, “length B is...

 Student Outcomes Students associate with each ratio A:B the ordered pair (A, B) and plot it in the xy coordinate plane. Students represent ratios in ratio tables, equations, and double number line...

 Student Outcomes Students associate with each ratio A:B the ordered pair (A, B) and plot it in the xy coordinate plane. Given a ratio table, students plot the ratios in the plane and observe that...

 Student Outcomes Students recognize that they can associate a ratio of two quantities, such as the ratio of miles per hour is 5:2, to another quantity called the rate. Given a ratio, students...

 Student Outcomes Given a rate, students find ratios associated with the rate, including a ratio where the second term is one and a ratio where both terms are whole numbers. Students recognize that...

 Student Outcomes Students solve problems by analyzing different unit rates given in tables, equations, and graphs.