Livingston American School Quarter 3 Plan Concept - Topic To Teach: Variables, Expressions, and Integers: Presenting data in tables Presenting data graphically Statistical measures of data *New pre-algebra level topic Variables, Expressions, and Integers: Expressions and variables Powers and exponents Using order of operations Comparing and ordering integers Adding and subtracting integers Multiplying and dividing integers Plotting integers on the coordinate plane Solving Equations: Properties and operations The distributive property Simplifying variable expressions Variables and equations Solving equations using addition and subtraction Solving equations using multiplication and division Decimal operations and equations with decimals Multi-step Equations and Inequalities: Solving two-step equations Solving equations having like terms and parentheses Solving equations with variables on both sides Solving inequalities using addition or subtraction Solving inequalities using multiplication or division Solving multi-step and inequalities *New pre-algebra level topic *New pre-algebra level topic *New pre-algebra level topic Common Core 7.SP.1 (prep) 7.EE.B.4 7.EE.1 7.EE.1 Standards Addressed: Understand that statistics can Use variables to represent Apply properties of operations Apply properties of operations be used to gain information quantities in a real-world or as strategies to add, subtract, as strategies to add, subtract, about a population by mathematical problem, and factor, and expand linear factor, and expand linear examining a sample of the construct simple equations expressions with rational expressions with rational population; generalizations and inequalities to solve coefficients. coefficients. about a population from a problems by reasoning about 7.EE.2 7.EE.2 13dc-fb6a-ea52-4daa 1 P a g e
sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. 7.SP.2 (prep) Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. Draw informal comparative inferences about two populations. 7.SP.3 (prep) Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. 7.SP.B.4 (prep) Use measures of center and measures of variability for numerical data from random the quantities. Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. 7.EE.B.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. 7.EE.B.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. 13dc-fb6a-ea52-4daa 2 P a g e
Specific Objectives: samples to draw informal comparative inferences about two populations. Understand how data can be organized in tables Understand organizing data in graphs Review statistical measures of data mean, median, mode, range Write expressions using variables Evaluate quantities containing exponents Use the order of operations to evaluate expressions containing multiple operations, exponents, and grouping symbols Apply the properties of addition, subtraction, multiplication, and division to simplify expressions and equations Use the distributive property to rewrite expressions and equations using addition and subtraction using multiplication and division with decimal coefficients Write and solve two-step equations having like terms and parentheses with variables on both sides of the equal sign Write and solve inequalities using addition or subtraction Write and solve inequalities using multiplication or division Solve multi-step inequalities Assessment Based On Objectives: 13dc-fb6a-ea52-4daa 3 P a g e
per assignment) per assignment) per assignment) per assignment) Core Values: Share problems and project work with class Share problems and project work with class Share problems and project work with class Share problems and project work with class Compassionate citizen of the world Compassionate citizen of the world Compassionate citizen of the world Compassionate citizen of the world 13dc-fb6a-ea52-4daa 4 P a g e
Week 21 Week 22 Week 23 Week 24 Concept - Topic To Teach: Factors, Fractions, and Exponents: Factors and prime factorization Greatest common factor Equivalent fractions Least common multiple Rules of exponents Negative and zero exponents Scientific notation Rational Numbers and Equations: Rational numbers Adding and subtracting like fractions Multiplying fractions Dividing fractions Using multiplicative inverses to solve equations Equations and inequalities with rational numbers Ratio, Proportion, and Probability: Ratios and rates Writing and solving proportions Solving proportions using cross products Similar and congruent figures Similarity and measurement Scale drawings Probability and odds Percents: Percents and fractions Percents and proportions Percents and decimals The percent equation Percent of change Percent applications Simple and compound interest *New pre-algebra level topic *New pre-algebra level topic The counting principle *New pre-algebra level topic *New pre-algebra level topic Common Core 8.EE.A.1 7.EE.1 8.G.A.2 7.RP.A.3 Standards Addressed: Know and apply the Apply properties of Understand that a twodimensional figure is congruent to solve multistep ratio and Use proportional relationships properties of integer operations as strategies to exponents to generate add, subtract, factor, and to another if the second can be percent problems. Examples: equivalent numerical expand linear expressions obtained from the first by a simple interest, tax, markups expressions. with rational coefficients. sequence of rotations, and markdowns, gratuities and reflections, and translations; commissions, fees, percent 13dc-fb6a-ea52-4daa 5 P a g e
8.EE.A.2 Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that 2 is irrational. 8.EE.A.3 Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. 8.EE.A.4 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities. Interpret scientific notation 7.EE.2 Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. 7.EE.B.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. given two congruent figures, describe a sequence that exhibits the congruence between them. 8.G.A.4 Understand that a twodimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. 7.SP.C.5 Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. 7.SP.C.6 Approximate the probability of increase and decrease, percent error. 13dc-fb6a-ea52-4daa 6 P a g e
that has been generated by technology a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times. 7.SP.C.7 Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. Specific Objectives: Simplify expressions with exponents using the rules of exponents. Calculate values having negative and zero exponents correctly. Express large and small quantities using scientific Solve equations and inequalities with rational numbers as coefficients using multiplicative inverses. Identify similar and congruent figures Use ratios and proportions to find unknown dimensions of similar figures. Determine probability of volving percent of change (increase and decrease) Solve real-world financial problems involving simple and compound interest. 13dc-fb6a-ea52-4daa 7 P a g e
notation and solve problems involving values written in scientific notation. simple events. Determine probability of compound events. Assessment Based On Objectives: per assignment) per assignment) per assignment) per assignment) Core Values: Share problems and project work with class Share problems and project work with class Share problems and project work with class Share problems and project work with class 13dc-fb6a-ea52-4daa 8 P a g e
Compassionate citizen of the world Compassionate citizen of the world Compassionate citizen of the world Compassionate citizen of the world 13dc-fb6a-ea52-4daa 9 P a g e