7th Grade Mathematics CurriculumConnected Mathematics Project 
During this school year your student will be working with the following units.  Each unit is designed to increase their understanding of a particular aspect of mathematics.  The units work as a series, building from one to the next in various aspects of mathematics.  You may find out more about this curriculum by logging onto the CMP website at www.math.msu.edu/cmp.
 

Variables and Patterns    THIS UNIT IS BEING TAUGHT AT THE END OF 6TH GRADE AS OF SPRING 09.
An introduction to Algebra
 
* Understand that variables in a situation are those quantities that change, such as time, temperature, feelings, a TV show’s popularity, distance traveled, and speed
* Understand that patterns describe a regular or predictable change in data
* Search for patterns of change that show relationships among the variables
* Select an appropriate range of values for the variables
* Create tables, graphs, and simple symbolic rules that describe the patterns of change
* Understand the relationship among forms of representations—words, tables, graphs, and symbolic rules
* Make decisions using tables, graphs, and rules
* Use a graphing calculator for making tables and graphs to find information about a situation 
 
 

Stretching and Shrinking                 (OUR FIRST UNIT )
Introduction to similarity with 2-dimensional shapes
 
* Enlarge figures by using rubber band stretchers and coordinate plotting
* Informally visualize similar and distorted transformations
* Identify similar figures visually and by comparing sides and angles
* Recognize that lengths between similar figures change by a constant scale factor
* Build larger, similar shapes from copies of a basic shape
* Divide a shape into smaller, similar shapes
* Recognize the relationship between similarity and equivalent fractions
* Learn the effect of a scale factor on length ratios and area ratios
* Discover that areas of similar figures are related by the square of the scale factor
* Observe and visualize ratios of lengths and areas
* Recognize that triangles with equal corresponding sides are similar
* Recognize that rectangles with equivalent ratios of corresponding sides are similar
* Determine and use scale factors to find unknown lengths
* Collect examples of figures and search for patterns in the examples
* Use the concept of similarity to solve real-world problems
* Draw or construct counterexamples to explore similarity transformations
* Make connections between algebra and geometry
* Use geometry software to explore similarity transformations
 
 
Accentuate the Negative
Understand how to use positive and negative integers
 
* Develop strategies for adding, subtracting, multiplying, and dividing integers
* Determine whether one integer is greater than, less than, or equal to another integer
* Represent integers on a number line
* Model situation with integers
* Use integers to solve problems
* Explore the use of integers in real-world applications
* Compare integers using the symbols =, >, and <
* Understand that an integer and its inverse are called opposites
* Graph in four quadrants
* Set up a grid on a graphing calculator by naming the scale and maximum and minimum values of x and y
* Graph linear equations using a graphing calculator
* Informally observe the effects of opposite coefficients and adding a constant to y = ax
* Answer questions using equations, tables, and graphs
 
 
Comparing and Scaling
Use of proportional reasoning with ratios, proportions, rates, and percents
 * Use informal language to ask questions, such as:

“What is the ratio of boys to girls in our class?”
“What fraction of the class is going to the spring picnic?”
“What percent of the girls play basketball?”
“Which model of car has the best fuel economy?”
“Which long-distance telephone company is more popular?”
      “What proportion of the delegates should be from rural areas?”
* Decide when the most informative comparison is to find the difference between two quantities and when it is to form ratios between pairs of quantities
* Develop the ability to make judgments about rounding data to estimate ratio comparisons
* Find equivalent ratios to make more accurate and insightful comparisons
* Scale a ratio or fraction up or d own to make a larger or smaller object or population with the same relative characteristic as the original
* Represent data in tables and graphs
* Apply proportional reasoning to situations in which capture-tag-recapture methods are appropriate for estimating population counts
* Set up and solve proportions that arise in applications
* Look for patterns in tables that will allow predictions to be made beyond the tables
* Connect unit rates with the rule describing the situation
* Begin to recognize that constant growth in a table will give a straight-line graph
* Use rates to describe population and traffic density (space per person or car

 

What Do You Expect?

Probability and Expected Value

Review and come to a deeper understanding of experimental and theoretical probabilities and the relationship between them

Review and further develop an understanding of the possible outcome in a situation

Review and come to a deeper understanding of the distinction between equally likely and non-equally likely outcomes

Understand the distinction between single, specific outcomes and sets of outcomes that comprise an event

Analyze situations involving independent events

Analyze situations involving dependent events

Understand how to use probabilities and equivalent fractions to find expected value

Determine whether games of chance are fair or unfair and find ways to make unfair games fair

Develop a variety of strategies for analyzing probabilities, such as using lists, counting trees, and area models

Use counting trees for finding theoretical probabilities in binomial, or 50-50, probability situations

Determine the expected value of a chance situation

Use probability and expected value to make decisions

Find probabilities in situations that involve drawing with and without replacement


Covering and Surrounding
Reason about 2-dimensional shapes and measurements
* Develop strategies for finding areas and perimeters of rectangular shapes and then of nonrectangular shapes
* Discover relationships between perimeter and area
* Understand how the area of a rectangle is related to the area of a triangle, and of a parallelogram
* Develop formulas, or procedures-stated in words or symbols-for finding areas and perimeters of rectangles, parallelograms, triangles, and circles
* Use area and perimeter to solve applied problems
* Recognize situations in which measuring perimeter or area will answer practical problems
* Find perimeters and areas of rectangular and nonrectangular figures by using transparent grids or tiles to cover the figures and string, straight-line segments, rulers, or other objects to surround the figures
* Cut and rearrange figures-in particular, parallelograms, triangles, and rectangles-to see relationships between them and then devise strategies for finding areas by using the observed relationship
* Observe and reason from patters in data by organizing tables to represent data
* Reason to find, confirm, and use relationships involving area and perimeter
* Use multiple representations-in particular, physical, pictorial, tabular, and symbolic models-and verbal descriptions of data


Moving Straight Ahead

Recognize linear relationships  

Further develop their understanding of variables and patterns (continuing the exploration of the ideas presented in the Variables and Patterns unit) Recognize and represent the relationships among variables in a variety of ways, including the use of words, tables, graphs, and symbols Identify variables and determine an appropriate range of values for independent and dependent variables Collect data and use patterns in tables and graphs to make predictions Use graphing calculators to investigate linear relationships Communicate with and interpret information from a variety of representations Recognize linear situations in all forms of representations: written descriptions, tables, graphs, and symbols Recognize that linearity is associated with a constant rate of change between two variables Recognize a change in the slope or the y-intercept and its effect on the various representations Solve a linear equation of the form y=mx+b using tables, graphs, and equations Find the slope of a line from a graph, a table, or an equation and interpret its meaning Find the y-intercept of a linear equation from its table, graph, or equation and interpret its meaning Write a linear equation given the slope and y-intercept Reason with different representations to interpret linear relationships Find a solution common to two linear equations by graphing or creating tables