In this unit we will be focusing on developing the conceptual understanding of proportional relationships and direct variation. We will look at what a proportion is and how to sove equations with proportions. Also, students will see how proportions can be used in everyday life.
Standards we will learn:
M6A2. Students will consider relationships between varying quantities.
a. Analyze and describe patterns arising from mathematical rules, tables, and graphs.
b. Use manipulatives or draw pictures to solve problems involving proportional relationships.
c. Use proportions (a/b=c/d) to describe relationships and solve problems, including percent problems.
d. Describe proportional relationships mathematically using y = kx, where k is the constant of proportionality.
e. Graph proportional relationships in the form y = kx and describe characteristics of the graphs.
f. In a proportional relationship expressed as y = kx, solve for one quantity given values of the other two. Given quantities may be whole numbers, decimals, or fractions. Solve problems using the relationship y = kx.
g. Use proportional reasoning (a/b=c/d and y = kx) to solve problems.
M6P1. Students will solve problems (using appropriate technology).
a. Build new mathematical knowledge through problem solving.
b. Solve problems that arise in mathematics and in other contexts.
c. Apply and adapt a variety of appropriate strategies to solve problems.
d. Monitor and reflect on the process of mathematical problem solving.
M6P2. Students will reason and evaluate mathematical arguments.
a. Recognize reasoning and proof as fundamental aspects of mathematics.
b. Make and investigate mathematical conjectures.
c. Develop and evaluate mathematical arguments and proofs.
d. Select and use various types of reasoning and methods of proof.
M6P3. Students will communicate mathematically.
a. Organize and consolidate their mathematical thinking through communication.
b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.
c. Analyze and evaluate the mathematical thinking and strategies of others.
d. Use the language of mathematics to express mathematical ideas precisely.
M6P4. Students will make connections among mathematical ideas and to other disciplines.
a. Recognize and use connections among mathematical ideas.
b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.
c. Recognize and apply mathematics in contexts outside of mathematics.
M6P5. Students will represent mathematics in multiple ways.
a. Create and use representations to organize, record, and communicate mathematical ideas.
b. Select, apply, and translate among mathematical representations to solve problems.
c. Use representations to model and interpret physical, social, and mathematical phenomena.
Standards we will review:
M6A1. Students will understand the concept of ratio and use it to represent quantitative relationships.
M6D1. Students will pose questions, collect data, represent and analyze the data, and interpret results.
a. Formulate questions that can be answered by data. Students should collect data by using samples from a larger population (surveys), or by conducting experiments.
b. Using data, construct frequency distributions, frequency tables, and graphs.
c. Choose appropriate graphs to be consistent with the nature of the data (categorical or numerical). Graphs should include pictographs, histograms, bar graphs, line graphs, circle graphs, and line plots.
d. Use tables and graphs to examine variation that occurs within a group and variation that occurs between groups.
e. Relate the data analysis to the context of the questions posed.