Download Unit 5 (rev. May 2012)

Jakarta International School
Unit Name: Rates, Ratios, and Proportions
Duration: Week 22, 3 weeks
Grade/Subject: 6 / Mathematics
Summary: In grade 6, students will build on their previous knowledge of fractions to develop an
understanding of ratios, rates, and proportions. Students will focus on understanding how ratios, rates, and
proportions are connected to multiplication and division. The ultimate goal is for students to be able to use
ratio and rate to describe relationships, and use equivalent ratios (proportions) to solve a variety of problems.
LEARNING FOCUS
Standards and Benchmarks (Learning Goals)
NCTM: Curriculum Focal Points, NCTM: Grade 6, Focal Points
Number and Operations: Connecting ratio and rate to multiplication and division
 Students use simple reasoning about multiplication and division to solve ratio and rate problems
 By viewing equivalent ratios and rates as deriving from, and extending, pairs of rows (or columns)
in the multiplication table, and by analyzing simple drawings that indicate the relative sizes of
quantities, students extend whole number multiplication and division to ratios and rates.
 Thus, they expand the repertoire of problems that they can solve by using multiplication and
division, and they build on their understanding of fractions to understand ratios.
 Students solve a wide variety of problems involving ratios and rates.
NCTM: Curriculum Focal Points, NCTM: Grade 6, Connections to the Focal Points
Number and Operations:
 They recognize that ratio tables not only derive from rows in the multiplication table but also
connect with equivalent fractions.
 Students distinguish multiplicative comparisons from additive comparisons.
Enduring Understandings
Essential Questions
Knowledge
Skills
Students will be able to
L.1.
Textbook – 8.1
Standard.
Write ratios and equivalent ratios.
Advanced.
Splitting quantities in a given ratio.
Highly Advanced.
Changing ratios.
Combining ratios.
 Rates, ratios, and proportions are simply
relationships between two units.
 Rates, ratio, and proportions can be
represented by fractions.
 Shapes and objects can be transformed
using scale factors, which are
mathematically constructed by applying
ratios and proportions.
 Determine the difference between ratios and
rates
 Write ratios and equivalent ratios
 Identify the difference between rates,
equivalent rates, and unit rates
 Write and solve proportions
 Use proportions to find measures of objects
 How does comparing quantities describe the
relationship between them?
 How can change be described mathematically?
Jakarta International School
L.2.
Textbook – 8.2
Standard.
Write rates, equivalent rates, and unit rates.
Advanced/Highly Advanced.
More complicated unit conversions.
L.3.
Textbook – 8.3
Standard.
Write and solve proportions.
Advanced.
More complicated unit conversions.
L.4.
Textbook – 8.4
Standard.
Use proportions to find measures of objects.
Use scale drawings to find actual lengths.
Highly Advanced.
Use algebra to solve proportions.
ASSESSMENT
Pre and Post Test
LEARNING PLAN
U5L1. Ratios. (8.1)
U5L2. Rates. (8.2)
U5L3. Proportions. (8.3)
U5L4. Measures and scale drawings. (8.4)