FACTORS & MULTIPLES
RATIOS & PROPORTIONS
Question 6.2
How can factors and multiples be used with ratios to show proportional relationships?
(and in their reasoning, and use the language of ratios and rates to describe relationships)
(and in their reasoning, and use the language of ratios and rates to describe relationships)
Students build on their work in earlier grades in working with factors and multiples (4.OA.4, 5.NF.4b) as they formalize the concepts and uses of greatest common factor (including the distributive property) and least common multiple. Although students have learned all four operations with multi‐digit whole numbers and decimals in earlier grades, in this unit they formalize the related standard algorithms as they build proficiency and fluency. This unit also introduces students to the concept of a ratio and engages them in using ratio and rate reasoning to solve problems. It builds upon students’ work in earlier grades with whole number multiplication and division. The multiplicative reasoning required for working with proportional relationships cuts across most Grade 6 mathematical content domains.
This unit extends students’ understanding of ratio reasoning as they investigate the idea that every ratio can be associated with unit rates. Students represent rate relationships with tape diagrams, tables, graphs, and equations. Students also are introduced to percent of a quantity as a rate per 100. Rate reasoning is central to the study of algebra and is a critical foundation for understanding slope, which is formalized in grades 7 and 8.
PACING = 5 weeks
🌕Students will use their understanding of factors, multiples, and multiplicative reasoning to work with proportional relationships and ratios. (6.NS.4, 6.RP.1, 6.RP.3) (MP.1, MP.4, MP.6)
I can find the greatest common factor of two whole numbers less than or equal to 100. (6.NS.4)
I can find the least common multiple of two whole numbers less than or equal to 12. (6.NS.4)
I can use ratios to compare data. (6.RP.1)
I can create a table of equivalent ratios and find its missing values. (6.RP.3a)
∎ Students will articulate their reasoning and strategies when solving problems ratios, rate, and proportional relationships. (6.RP.2, 6.RP.3) (MP.1, MP.3, MP.8)
I can identify a unit rate. (6.RP.2)
I can solve unit rate problems. (6.RP.3b)
I can understand percent as a rate per 100 and solve problems involving finding the whole if given a part and the percent. (6.RP.3c)
I can use ratios to convert or to change quantities to appropriate measurement units. (6.RP.3d)
∎ Major Content ⊡ Supporting Content 🌕 Additional Content
New Vocab: ratio, equivalent ratio, per, rate, unit rate, percent
Review Vocab: compare, coordinate plane, ordered pair, x-axis, x-coordinate, y-axis, y-coordinate, equivalent ratios, ratio, convert, equivalent fractions, fraction, factor, multiples, quantity, table, Greatest Common Factor (GCF), Least Common Multiple (LCM), prime numbers
Academic Vocab: graph (noun), graph (verb), determine, comparison, justify, relationship, constant, symbol, survey
*The computational strategies that you practice during number talks does NOT have to align with the core math content. Number talks are meant to practice fluency strategies, not teach new content.
Ready Teacher Toolbox Lesson 6: Find Greatest Common Factor and Least Common Multiple -Sessions 1-4
Assessment Tasks 6th grade bank UPDATED 6.NS.4 Proficiency Rubrics 6.NS.4 IAR sample questions 6.NS.4
Prior knowledge/Just in Time support & Enrichment RTTB Lesson 6 Line 'Em Up
Nearpod Math lessons Open Middle tasks
Interactive manipulatives
Ready Teacher Toolbox Lesson 12: Understand Ratio Concepts -Sessions 1-3
Assessment Tasks 6th grade bank UPDATED 6.RP.1 Proficiency Rubrics 6.RP.1 IAR sample questions 6.RP.1
Prior knowledge/Just in Time support & Enrichment RTTB Lesson 6 Line 'Em Up
Nearpod Math lessons Open Middle tasks
Interactive manipulatives
Ready Teacher Toolbox Lesson 13: Find Equivalent Ratios -Sessions 1-5
Lesson 14: Use Part-to-Part and Part-to-Whole Ratios -Sessions 1-4
Assessment Tasks 6th grade bank UPDATED 6.RP.3 Proficiency Rubrics 6.RP.3 6.RP.3 IAR sample questions 6.RP.3a
Prior knowledge/Just in Time support & Enrichment RTTB Lesson 13 Draw a Line Through It & Lesson 14 Flavorful Science
Nearpod Math lessons Open Middle tasks
Interactive manipulatives
Ready Teacher Toolbox Lesson 15: Understand Rate Concepts -Sessions 1-3
Assessment Tasks UPDATED 6th grade bank 6.RP.2 Proficiency Rubrics 6.RP.2 IAR sample questions 6.RP.2
Prior knowledge/Just in Time support & Enrichment RTTB Lesson 15 Racing Robots
Nearpod Math lessons Open Middle tasks
Interactive manipulatives
Ready Teacher Toolbox Lesson 16: Use Unit Rate to Solve Problems -Sessions 1-5
Lesson 17: Understand Percents -Sessions 1-3
Lesson 18: Use Percents to Solve Problems -Sessions 1-4
Assessment Tasks UPDATED 6th grade bank 6.RP.3 Proficiency Rubrics 6.RP.3 IAR sample questions 6.RP.3
Prior knowledge/Just in Time support & Enrichment Lesson 16 Spin Doctor, Lesson 17 Tesselate a Percent , and Lesson 18 Display Time
Nearpod Math lessons Open Middle tasks
Interactive manipulatives
“Closure in a lesson does not mean to pack up and move on. Rather, it is a cognitive activity that helps students focus on what was learned and whether it made sense and had meaning.” How the Brain Learns Mathematics (2007) P. 104
There are many ways to wrap up and reflect the day's activities but this step is often overlooked or rushed. Purposely plan and allow time for students to have closure each day (even if it means setting a timer or daily alarm so you don't run out of time).
Ideas for closure activities