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Understanding Equations, Variables, and Relationships in Mathematics

This chapter delves into key mathematical concepts including equations, variables, expressions, and relationships. It introduces the process of substituting variables with numbers, providing an example for clarity. The chapter also explains expressions and the arrangement of data through tables of values. Key terms such as scatter plots, equations, and their solutions are defined, highlighting the importance of independent and dependent variables. Lastly, students are encouraged to grasp number rules and patterns, setting the groundwork for further exploration in mathematics.

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Understanding Equations, Variables, and Relationships in Mathematics

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  1. Chapter 8 Equations and Relationships

  2. Terms • Substituting- replacing a variable (any letter) with a number. example- n=4------ 5n+4------ 5(4)+4=24 we switched the “n” variable with the 4. • Expression- a mathematical sentence (4a+2, 10d+5, 67b+24 and so on). • TableofValues- an orderly arrangement of facts set out for easy reference; an arrangement of numerical values in vertical and horizontal columns. • ScatterPlot- a graph that attempts to show a relationship between two variables by plotting them on a grid.

  3. Terms- continued • Equation- a mathematical statement in which the value on the left side of the equal sign (=) is the same as the value on the right side of the equal sign; for example 5n+4=39 means that 4 more of the product 5 and a numbers equals 39 • Solution to an equation- the value of a variable that makes the equation true; for example in the equation 5n+4=39 the value of “n” is 7 because 5(7)=39

  4. Terms- continued • Variable- a letter or symbol such as a,b,c,d,n, etc that represents a number- an example is the formula for area of shape where a=area, l=length and w=width • Horizontal Axis- the bottom line of a graph which tends to hold the dependent variable • Vertical Axis- the up and down line which tends to hold the independent variable.

  5. Terms- continued • Independent Variable- a specific object that forces other objects to change based on how they change. • Example- students were asked to name their favourite junk food. The independent variable is the student because the type of junk food picked changes based on which student is asked. • Dependent Variable- a specific object that changes based on how other objects change. • Example- students were asked what their favourite sport was. The type of sports is the dependent variable because each student can pick a different sport.

  6. Terms- continued • Value- any size of number which represents a specific figure (diagram) or objects changing in the figure. • Number Rule- is associated with the table of values. Is the formula and rate in which the numbers on the left side either increase or decrease by. • Pattern- discovering what the number rule and writing the formula to represent it.

  7. Task • Pg. 251, Questions 1-6 • Any question which are not done will be for homework. • We will do question 3 together, now.

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