Learning Plans for: E. Pauley Content/Grade: 7th Grade Accelerated Math Overview for the week of: November 3, 2014 Unit Objectives: Enduring Understandings:  Proportions are multiplicative rather than additive comparisons.
 Units rates and rates can be calculated by setting up and solving proportions
 The constant of proportionality (k) is the ratio of y to x.
 Graphs, tables and equations can be used to represent rates of change (proportional vs. nonproportional).
Essential Questions: • When given a rate, how do you determine the unit rate?
• What makes two quantities proportional?
• Why are unit rates needed to make effective comparisons?
• How can I analyze relationships to determine how unit rate is related to rate of change?
• How is being able to express a numerical relationship as a ratio useful?
• How are ratios and proportions related to equivalent fractions?
• How can you express a linear relationship between two quantities in multiple ways?
• How are ratios, unit rates, and proportions used to describe and solve real-world problems?
• How can representations, numbers, words, tables and graphs be used to solve problems?
• How do you use tables and verbal descriptions to describe a linear relationship?
Vocabulary: constant, rate, unit rate, rate of change, linear relationship, proportion, constant of proportionality, direct variation Resources: TRC Math Collaborative, HMH textbook Learner Objectives: 7.1A apply mathematics to problems arising in everyday life, society and the workplace. 7.1E create and use representations to organize, record and communicate mathematical ideas. 7.4 B calculate unit rates from rates in mathematical and real-­‐world problems. Monday, November 3, 2014 *I can calculate proportions, using 4 different methods. *I will complete unit rate stations Wolf Work: IXL Proportions & Unit Rates J5 & J9 (7th Grade) Tuesday, November 4, 2014 Ratios, Rates & Unit Rates EQ: How do you find and use unit rates? *I can calculate unit rates from rates. *I will write C-­‐notes on how to generate unit rates. Sentence Frame: I use __________ method to determine which item was the better deal. Wolf Work: Which is the Better Buy? Teaching Strategies A. Ask students to bring in grocery store advertisements from a local newspaper or from the Internet.
Have them find at least 5 items whose costs are given in terms of size or weight. Then have them
change the costs to unit prices.
B. Have students explain how they simplified rates that appear in complicated situations, such as the
complex fractions in Guided Practice Exercises 6 and 7. Student 1: I rewrote the fractions using
division and then multiplied by the reciprocal.Student 2: I found the unit rate for each one separately
by dividing the numerator by the denominator. Then I chose the unit rate that was greater.
C. The population density of a state is the average number of people per square mile. Write the
population densities of each state. Round your answers to the nearest person per square mile. Then rank
the states from least population density to greatest population density.
7.1E 7.4A 7.4C 7.4D create and use representations to organize, record and communicate mathematical ideas. represent constant rates of change in mathematical and real-­‐world problems given pictorial, tabular, verbal, numeric, graphical, and algebraic representations, including d=rt determine the constant of proportionality (k=y/x), within mathematical and real-­‐world problems. solve problems involving ratios, rates and percents. Wednesday, November 5, 2014 Writing & Solving Proportions EQ: How can you identify and represent proportional relationships? *I can determine the constant of proportionality. *I will use ratio tables to determine proportionality. Sentence Frame: The constant of proportionality is ______. I know this because _______. Wolf Work: Constant of Proportionality Teaching Strategies A. Have students discuss different ways to use a table to draw conclusions about a proportional
relationship. Student 1: I find the constant ratio of y t o x in all table columns and then compare
them.Student 2: I find the ratio of y to x in the first column and then check if every other table
column ratio of y to x is the same.
B. Point out to students that they can represent a proportional relationship with a table, with an
equation, or with words. In the table, the quotient of the y-value and the x-value gives the
y
constant of proportionality, k, that is used in the associated equation of the form _ = k. Students
can also state in words that x and y have a proportional relationship with a constant of
proportionality k.
C. The table shows one pair of values for a proportional relationship. Use the table description and
what you have learned about proportional relationships to describe a possible proportional
relationship that it represents, and identify the constant of proportionality. Then fill in the table
and write an equation for the proportional relationship.
Thursday, November 6, 2014 Proportional Relationships & Graphs EQ: How can you use graphs to represent and analyze proportional relationships? *I can represent proportional relationships in multiple representations. *I will complete a card sort of proportional vs. non proportional graphs. Sentence Frame: ___________ is a proportional relationship because the constant of prortionality is ________. __________ is not a proportional relationship because ________. Wolf Work: Proportional vs. Non Proportional Friday, November 7, 2014 Proportional vs. Non-­‐Proportional EQ: How can you use graphs to represent and analyze proportional relationships? *I can represent proportional relationships in multiple representations. *I will compare the cost of flowers and movie rentals. Sentence Frame: The relationship between _________ and __________ is a proportional/non proportional because ________. Wolf Work: Proportional vs. Non Proportional Day 2