MATHEMATICS SUMMER ENRICHMENT ALGEBRA 1

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1 MONTGOMERY VILLAGE MIDDLE SCHOOL MATHEMATICS SUMMER ENRICHMENT ALGEBRA 1 RATIOS AND PROPORTIONAL RELATIONSHIPS Understand unit rates using fractional rates Analyze a table to determine find proportional relationships Determine if two rates are equivalent by graphing How do you find the constant of variation from a direct variation equation? How do you write an equation for direct variation from a table? Evaluate specific points on a graph of a proportional relationship Rate problem using fractions Finding the better buy with unit price Which is the better buy? Analyzing proportional relationships Apply taxes, tips, and discounts using a proportion and scale factor Solve ratio and percent problems using bar models Find the percent of decrease using a proportion Find the perfect of increase using a proportion Calculate percent increase and decrease in context Simple Interest Game Math at the mall Cheesy Goldfish Crackers Application of Proportional Relationships

2 RATIONAL NUMBER OPERATIONS How do you rewrite subtraction as addition Multiply positive and negative integers by noticing patterns Use addition and division to solve real-world problems with rational numbers How do you add and subtract a bunch of numbers with different signs? Rewrite fraction as decimals (repeating) Estimate to check reasonableness Multiply positive and negative integers using the distributive property Multiply a negative by a negative using the distributive property Solve real-world problems involving the four operations with rational numbers Feeding numbers Number line bounce Circle 0 Brain racers: Integers Building understanding of rational number operations Virtual algebra tiles Equivalent expressions with distribution and negative numbers Factor an expression Factoring algebraic expressions using the distributive property Factoring algebraic expressions using the distributive property practice Solving multi-step linear equations Solve multi-step equations Solve an inequality with a negative coefficient by using the multiplication property of equality Jeopardy Lab Integrating rational number operations in expressions and equations

3 EXPRESSING GEOMETRIC RELATIONSHIPS Circles: Calculate Area, Circumference and Diameter Volume Cross sections of a cube Wall of Fire: Cube Volume of Triangular Prism & Cube Volume of Rectangles Inside Rectangles Measurement in two and three dimensions Constructing trinagles from three measures of angles Supplementary, complementary, vertical and adjacent angles Write and solve simple equations for an unknown angle in a figure Corner kick Angle relationships: complementary and supplementary angles Interactive angles teaching tool Supplementary and complementary angles Identify complementary, supplementary, vertical, adjacent and congruent angles Angle relationship Triangle sides and angles Constructing triangles STATISTICS AND PROBABILITY Predict the frequency of an event using results from experiments Probability models practice Find the probability of a compound event by creating a tree diagram Sample space for compound events Find the probability of a compound event by creating an organized list Probability fair Chances Flipping discs Chance events and probability models Identify representative sample Identify random sample

4 STATISTICS AND PROBABILITY Compare two populations using mean absolute value deviation Drawing inferences about a population Use proportional reasoning to make estimates about a population Comparing distributions Do the best movies make the most money? Comparing distributions with dot plots Random sampling REAL NUMBER SYSTEM Scientific notation: Richter scale exponents Negative exponent intuition Use patterns to write equivalent expressions with integer exponents Properties of exponents King long scientific notation game Converting small numbers into scientific notation Magnitude and scientific notation Drawing perfect squares What s a rational number? Solve equations with squares and square roots Intro to rational and irrational numbers How do you turn a repeating decimal into a fraction One wasn t square Compare the values of irrational numbers on a number line by approximating their values Mini-cross number Estimating positive and negative square roots Cycling squares Rational or irrational? Estimating cube roots Rational and irrational numbers

5 FUNCTIONAL RELATIONSHIP AND LINEAR EQUATIONS Stairway slope Ski jumping: understanding proportional relationships Finding math in cake artistry Slope mountain train Cable car mountain slope Understanding slope with similar triangles What does negative slope mean? How do you graph a linear equation using a table? Find the slope of a graph Walk the plank Plotter the penguin Connecting proportional relationships to linear equations Understand one solutions equations Understand infinite solution equations Understand no solution equations Multi-step equations Shipments: multi-step equations with like terms Algebra tiles Determine the number of solutions an equation has by recognizing patterns What does it mean when an equation has no solution? Complete missing values in linear equations according to the number of solutions Linear equations with variables on both sides: decimals and fractions Linear equations with one variables Modeling addition subtraction equations Exploring equations Linear variables in one variable

6 TRANSFORMATIONS AND GEOMETRIC MEASUREMENT Rations, reflections and translations What is a reflection? What is a translation? Describe a sequence Describe translations using coordinates Graph a rotated image using coordinates Graph a reflected image using coordinates Relate angles and transversals How did they make miss pacman? Lateral thinking Geometric translations: transformations of a house Reflections: squiggle reflections Translations, rotations, and reflections: rotate the triangle Perform translations Exploring rotations through block designs Congruence through rigid transformations Shape mods Find the side length of a triangle using angle-angle criterion Indirect measurement: treehouse height Dilations Calculate the scale factor of a dilation Solve word problems by doing dilations Human tree: dilations Prove two figures are similar after a dilation Transtar Geo-gebra dilations What are corresponding parts in similar figures? Volumes of cones, cylinders and spheres Dilating shapes: shrinking Similarity through non-rigid transformations Estimate volume - cones Similar shapes Volume of a sphere Develop and apply volume of a sphere Volume of a cylinder Develop and apply volume of a cone Develop and apply volume of a cylinder Volumes of cones, cylinders and spheres