Moving Straight Ahead
Standards & Objectives | |
File Size: | 314 kb |
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Goals for Moving Straight Ahead
Students should...
- Recognize problem situations in which two variables have a linear relationship
- Understand that the equality sign indicates that two expressions are equivalent
Investigation 1
Vocabulary | |
File Size: | 157 kb |
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The rates at which students walk and the amount of money per kilometer that sponsors donate for a walkathon are two contexts for this Investigation. Students look at the patterns of change for each relationship and the effect of that change on various representations. For example, they recognize that graphs of linear relationships are straight lines. They begin to see that as the independent variable changes by a constant amount, there is a corresponding constant change in the dependent variable. For linear relationships, this pattern of change is a constant rate. At this point, some students will begin to recognize that rate of change is the coefficient of x in the general equation y=mx+b.
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Investigation 2
Vocabulary | |
File Size: | 243 kb |
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This Investigation continues the theme of walk-a-thons and helps students deepen their understanding of patterns of change. The constant rate of change between the two variables in a linear relationship and the y‑intercept of the graph of a linear relationship are formalized in this Investigation. Students interpret the y‑intercept as a special point on a line, a pair of values in a table, or as the constant b in the equation y = mx + b. They find the constant rate, decide whether relationships are decreasing or increasing, and make connections among ordered pairs on a line, a pair of values in a row of a table, and the solution of a linear equation.
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Investigation 3
Vocabulary | |
File Size: | 334 kb |
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Students continue to make the connection between points on a line, pairs of data values in a table, and solutions to equations. They represent pictorial situations symbolically and encounter equivalent expressions for a given situation. They use the Distributive Property to show that the two expressions are equivalent.
Students use the properties of equality for solving equations in pictorial form and then transition into solving equations in symbolic form. They add or subtract the same number or variable or multiply or divide by the same nonzero number or variable on both sides of an equation. In Problem 3.5, students find the point of intersection of two lines (or the solution of a system of two linear equations) by setting the y‑values equal and then solving for x. They also solve linear inequalities and use their solutions to answer questions about real-world contexts. |
Investigation 4
Vocabulary | |
File Size: | 326 kb |
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Students find the ratio of vertical change to horizontal change between two points on a line. The connection between this ratio and constant rate of change is made explicit. Students find the slope of a line given two points on the line and then find the y‑intercept using either a table or a graph. They write an equation of the form y=mx+b, in which m is the slope and b is the y‑intercept. Students then explore the idea that lines with the same slope are parallel lines, and that two lines whose slopes are the negative reciprocals of each other are perpendicular lines. Graphing calculators help students explore the slopes of many lines before they make their conjectures.
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