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# Reference - 7th Grade Bundle + Basics + Linear Relationships

Product Description
All of the materials that I am including in this bundled unit download are sold separately on TPT. Below is a complete list of what you will receive. You can click on each link to read a detailed description of each product.

Reference - Operations, Decimals, Fractions, Mixed Numbers, Benchmark Numbers

Reference - Circles, Angles, Protractors, Unique Triangles, Area, Volume

Reference - Rations, Proportions, Unit Rate, Scale Drawings, Similar Figures

Reference - Percent Word Problems, Percent Expressions, Converting

Reference - Integers, Expressions, Equations, Inequalities

Reference - Probability, Statistics, Center and Spread, Surveys, Box-and-Whisker

Reference - Linear Relationships, Slope and Y-Intercept, Equations, Graphs

The following information is covered...

The Five Operations of Arithmetic (yes, five!)

1. Explains what each operation means and if the commutative property holds for that operation. Includes examples written as mathematical expressions and in words.
2. Describes grouping (multiplication) as repeated addition when the number of groups is a whole number and taking a piece when the number of groups is a fraction. Establishes the commutative property for each interpretation.
3. Describes division as two separate operations (hence five operations total), "splitting up" and "fitting into". Explains that both of these operations lead to the same numerical answer, even though they ask different questions, which is why we only use one symbol for both of them.

1. Explains the rules for adding with decimals.
2. Gives a step-by-step example of how to add with decimals.

Subtracting with Decimals

1. Explains the rules for subtracting with decimals.
2. Gives two step-by-step examples of subtracting with decimals including borrowing across zeros.

Multiplying with Decimals - Matrix Method

1. Explains how to multiply with decimals using the matrix method.
2. Gives two step-by-step examples of multiplying with decimals using the matrix method.

Multiplying with Decimals - Traditional Method

1. Explains how to multiply with decimals using the traditional method.
2. Gives a completely worked out example of multiplying with decimals using this method.

Long Division

1. Explains the four steps of the long division algorithm.
2. Explains what to do if there are no more digits to bring down but you didn't get a zero the last time you subtracted.
3. Shows examples of putting the decimal in the same place in the dividend and quotient.
4. Reminds students not to be afraid of putting a zero in the quotient (a lot of my students neglect to put zeros in for some reason).
5. Explains the importance of putting the digits of the quotient in the correct place.
6. Explains to move a decimal if it is in the divisor (and to do the same thing to the dividend).
7. Explains repeating decimals.

Multiplying and Dividing by Powers of 10

1. Explains the rule for multiplying and dividing by powers of 10.
2. Explains what is really happening to the value of the digits when multiplying or dividing by a power of 10.

Introduction to Fractions and Mixed Numbers

1. Explains what a fraction is as well as the difference between proper fractions, improper fractions, and mixed numbers.
2. Reminds students that the fraction bar can also mean division.
3. Reminds students that a fraction with a 1 in the denominator is equivalent to the numerator.
4. Gives examples of writing a number as an improper fraction, mixed number, or whole number plus proper fraction.
5. Explains how to convert between mixed numbers and improper fractions.

Equivalent Fractions

1. Explains what equivalent fractions are.
2. Explains how you can tell if two fractions are equivalent.
3. Explains simple strategy (assuming numbers are multiples of each other) for determining the missing number that would make two fractions equivalent.
4. Explains how to create equivalent fractions.
5. Explains how to reduce fractions.

Operations with Fractions

1. Explains how to add and subtract fractions with like or unlike denominators.
2. Explains how to divide fractions.
3. Explains how to multiply fractions.
4. Explains how to reduce before multiplying.
5. Explains how to cancel before multiplying.

Operations with Mixed Numbers

1. Explains how to add mixed numbers including what to do if you wind up with an improper fraction inside the mixed number.
2. Explains how to subtract mixed numbers including what to do if the fraction part of the subtrahend is larger than that of the minuend.
3. Explains how to multiply and divide with mixed numbers.

Benchmark Numbers

1. Charts all benchmark numbers that students should be familiar with (halves, thirds, fourths, fifths, eighths, and tenths).
2. Explain how to quickly derive the benchmark numbers.

Introduction to Circles

1. Explains radius, diameter, circumference, and area.
2. Explains that radius, diameter, and circumference are all one-dimensional while area is two-dimensional.
3. Explains what pi is.

Circle Equations

1. Derives the circle equations c=pi*d, c=2*pi*r, and a=pi*r^2
2. Explains how to use the circle equations to answer problems such as finding the diameter when given the area, finding the circumference when given the diameter, and so on.

Working with Pi

1. Explains how to write an answer "in terms of pi" and with pi multiplied out.
2. Gives examples of mistakes students often make when solving equations with pi in them.

Introduction to Angles

1. Explains what angles and vertices are.
2. Explains what right angles, obtuse angles, and acute angles are.
3. Explains that angles are measured in degrees and that there are 360 degrees in a full rotation.
4. Explains how to denote right angles.
5. Explains how to name angles using three points.

Measuring Angles with a Protractor

1. Explains how to align the protractor.
2. Explains which set of numbers on the protractor to use.

Angle relationships

1. Explains what complementary, supplementary, congruent, adjacent, linear, and vertical angles are.

Writing Equations to Describe Diagrams

1. Explains how to write and solve equations that describe diagrams.

1. Explains that the sum of the angles of a triangle is always 180 degrees.
2. Explains why you can't have one side of a triangle larger than the sum of the other two sides.

Unique Triangles

1. Creates an analogy between given triangle conditions (SSS, SAS, etc.) and an environment that is possibly too restrictive to move around in, thus creating a unique triangle.

SSA

1. Gives step-by-step instructions on how to determine if SSA conditions determine a unique triangle, two triangles, or no triangles.

Area of 2-Dimensional Shapes

1. Explains what area is.
2. Explains how to find the areas of rectangles, parallelograms, triangles, trapezoids, and irregular polygons.

Volume

1. Explains what volume is.
2. Explains how to find the volume of prisms, pyramids, and spheres.

Negatives

1. This sheet breaks the rules for negative numbers down into three distinct sets: rewriting, adding and subtracting, and multiplying and dividing.
2. It shows how to use a number line or positive and negative circles to add or subtract.
3. It discusses the overall sign of a fraction based on the signs of the numerator and denominator.
4. As any middle school math teacher will know, students will often look at a problem like -99+23 and try to answer it by setting up a subtraction problem with 23 on the top and -99 on the bottom. This page also reminds students not to do that!

Finding the Distance between Two Points

1. Teaches students to use subtraction and absolute value when finding the distance between two points.
2. Explains that the order we subtract does not matter since we will be taking the absolute value anyway.
3. Reminds students that when they are subtracting a negative they should write both the minus sign and negative sign.

Combining Like Terms

1. Explains what like terms are, including terms with exponents and that combining them means to add or subtract.
2. Gives examples of like terms and unlike terms.
3. Explains that even if the variables in two terms are rearranged they could still be like terms because of the commutative property.
4. Reminds students that if they don't see a coefficient in front of a variable, it's 1.
5. Explains why unlike terms can't be combined.
6. Explains that more than two like terms may be combined.

Distribution and Factoring

1. Explains what distribution is and why it works using an area model.
2. Explains how to multiply the terms in one pair of parentheses with those of another.
3. Shows how to distribute within a larger expression.
4. Shows how to distribute just a plus or minus sign in front of the parentheses.
5. Discusses factoring as distribution in reverse.

Solving Equations

1. Reminds students that the goal of solving equations is to get the unknown quantity by itself.
2. Explains that inverse operations bring us back to the number we started with.
3. Explains that whatever is done to one side of an equation must also be done to the other side.
4. Shows students how to solve 10 very similar-looking (and easily confused) simple equations.

Solving Multi-Step Equations

1. While not an exhaustive account of how to solve equations, this page helps students plan their line of attack by thinking of "free" and "trapped" terms. Free terms may be removed immediately. Trapped terms, such as those inside parentheses or inside a fraction, must be freed before they can be removed.
2. Presents students with four different multi-step equations as well as their solutions.

Inequalities

1. Explains what inequality symbols are, referring to the "mouth" and "point" of the symbol as well as the line underneath.
2. Emphatically reminds students that inequality symbols are not arrows. This misunderstanding leads many students in the wrong direction when graphing inequalities.
3. Discusses reading inequalities from left to right or right to left.
4. Gives examples of solving inequalities and reminds students to flip the inequality symbol when multiplying or dividing by a negative number.
5. Explains how to graph inequalities.

Writing Equations for Proportional Relationships

1. Gives two examples of how a verbal description of a proportional situation may be modeled with an equation.

Writing Equations for Linear, Non-Proportional Relationships

1. Gives two examples of how a verbal description of a linear, non-proportional situation may be modeled with an equation.

Ratios

1. Explains what ratios are using the example of marbles in a bag.
2. Explains how ratios can affect taste (ingredients in a soup) and appearance (height to width ratio of a t.v. set).

Proportional Relationships

1. Explains proportional relationships by comparing them with analogies.
2. Shows how to set up equivalent fractions to represent a proportional relationship.
3. Explains that a consequence of two quantities being in a proportional relationship is that if one gets multiplied by a certain number then the other gets multiplied by the same number.
4. Gives an example of using an equation, graph, and table to show a proportional relationship.

How to Tell if a Graph, Table, or Equation Represents a Proportional Relationship

1. Explains how to tell if a graph, table, or equation represents a proportional relationship.

Unit Rate

1. Explains that a unit rate is a ratio for which there is 1 of one of the quantities.
2. Explains how to decode a unit rate word problem to decide what unit rate it is asking for.
3. Explains how to calculate a unit rate.
4. Explains that to find a unit rate we always use division but once we know what the unit rate is we might use another operation.

Unit Analysis

1. Explains how to consider the units in a problem to decide if multiplication or division would be warranted to answer it.
2. Shows how the same units in the numerator and denominator cancel when multiplying just like the numbers in a fraction expression.

Finding the Unit Rate / Constant of Proportionality from Graphs, Equations, and Tables

1. Graphs - Explains how to divide coordinates to find the unit rate or to find the y-coordinate that corresponds to 1 on the x-axis.
2. Explains that the unit rate in an equation is next to the variable.
3. Explains to use division to find the unit rate between two quantities in a table and warns to be careful and pay attention to what you divided by what.

Converting between Tables, Graphs, and Equations (for Proportional Relationships)

1. Explains how to convert between tables, graphs, and equations. Contains every combination.

Scale Drawings

1. Explains how to answer problems regarding scale drawings using either multiplication or proportional reasoning.
2. Explains how to find the unit scale.

Scale Factor

1. Explains what the scale factor is and how to find it.

Scale Figures

1. Explains how to set up a proportion to find the missing side length given two proportional figures.

Converting between Percents, Fractions, and Decimals

1. Explains and gives examples of converting between percents, fractions, and decimals (includes every combination).

Six Types of Percent Word Problems

1. Explains how to find a part given the whole and the percent of the whole.
2. Explains how to find the percent of the whole given the part and the whole.
3. Explains how to find the whole given a part and the percent of the whole.
4. Explains how to find the new value given the original value and percent of change.
5. Explains how to find the percent of change given the original and new values or how to find the percent error given the real value and estimate.
6. Explains how to find the original value given the new value and percent of change.

Six Types of Percent Word Problems - Proportion Strategy

1. Explains how to find all of the above but using proportions.

Percent Expressions

1. Explains how to use variables to write percent expressions that represent an increase, decrease, or percent of a number.

Representing Outcomes

1. Gives examples of representing outcomes using tree diagrams, organized lists, and tables.
2. Discusses the counting principle.

Calculating with Probabilities

1. Explains how to calculate a simple probability and a compound probability.
2. Explains how to make a prediction using multiplication or setting up a proportion.
3. Discusses the difference between theoretical probabilities and experimental or observed probabilities.

Measures of Center and Spread (and Mode)

1. Explains and gives examples of how to calculate mean, median, mode, range, and mean absolute deviation.
2. Explains how to visually compare the center and spread of two data distributions.

Box-and-Whisker Plots

1. Explains how to draw box-and-whisker plots.
2. Gives examples of creating a box-and-whisker plot for an even number of data points as well as an odd number.
3. Explains quartiles and interquartile range.

Surveys

1. Explains that random sampling leads to valid inferences.
2. Gives examples of good and bad sampling methods.
3. Discusses cause for a survey to be invalid such as not asking enough people, bias within the survey, and asking biased people.

Slope and y-intercept

1. Explains what the slope and y-intercept are.
2. Discusses rise over run.

Equation of a Line in Slope-Intercept Form

1. Gives an example of an equation written in standard form, then converted into slope-intercept form, and discusses how the latter form makes it so much easier to determine the slope and y-intercept.
2. Gives examples of using equations to easily determine the slope and y-intercept of a line.

Proofs for m and b

1. Gives a proof of why b in the equation y=mx+b tells you where the line will crose the y-axis.
2. Gives a proof of why m in the equation y=mx+b gives you the rise and run between two points.

Equation to a Graph

1. Explains how to easily graph a line, given its equation.
2. Includes examples where there is only one variable such as y=-5 and x=-5.

Graph to an Equation

1. Explains how to write the equation of a line, given its graph.
2. Gives examples of when the line is horizontal or vertical.

Writing Equations from Points and Slope

1. Explains how to find the slope given two points.
2. Explains how to find the equation of a line given two points.
3. Explains how to find the equation given a point and slope.
Total Pages
58 pages
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Teaching Duration
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