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1 7 th Grade Mathematics District Curriculum Map Reading and Writing Numbers (30 days) Sensitize students to the many places in which they can find numbers and their different uses which arise naturally from many situations. Different ways to write and represent numbers allow us to convey information and more easily perform some mathematical operations. The order of operations provides rules governing the order in which operations are formed. Numbers in everyday life Positive and negative numbers Rational numbers and their uses Powers of ten and other numbers Order of operations Scientific notation Plotting points on a coordinate graph Graphing data on a graphing calculator Convert powers and word names for numbers and decimals. Understand uses of rational numbers in real situations. Use inequality symbols. Interpret situations with opposite directions. Graph and read numbers on a number line. Understand uses of rational numbers in real situations. Perform arithmetic operations using powers of ten. Use grouping symbols and the rules for the order of operations to evaluate numerical expressions. Perform arithmetic operations using scientific notation. Know the structure of the coordinate grid and how to represent data on it. Know how to graph on a graphing calculator. Write an extended place value chart in journals. Create flashcards for vocabulary words. Make a human number line with fractions, decimals, and integers. Index cards for order of operations. Create deck of number cards and play the game of War. (Class champion.) Fraction/decimal contest. Make room into coordinate grid. Graphing calculator instruction using overhead application. and Small groups and and activities Technology sourcebook, Activity Kit, and Visual aids Math Connections Glatzer; Making Math Real Life Math Mysteries Tyler Math Connections Martin; Extreme Math Tyler 1

2 Using Variables (20 days) Variables are used to describe patterns and to translate expressions from words into mathematical language. Describing patterns with variables Translating words into algebraic expressions Evaluating algebraic expressions Expressions and formulas The Pythagorean theorem Formulas in spreadsheets Open sentences Graphing inequalities Given instances of a pattern, write a description of the pattern using variables. Represent a relationship between two variables using a table. Write a numerical or algebraic expression for an English expression involving arithmetic operations. Evaluate algebraic expressions given the values of all variables in them. Calculate the value of a variable given the the values of the other variables in a formula. Use the Pythagorean Theorem to find distances in real situations. Use a calculator or spreadsheet to construct formulas and apply them to real-life situations. Find solutions to equations and inequalities involving simple arithmetic. Graph solutions to simple inequalities. Practice patterns and writing expressions from extra examples in discussion. Be a secretary translating verbal instructions. Equation activity. Envelopes with different categories for students to organize. Set up to discover Pythagorean Theorem with given triangles. Check hand-made graphs with the graphing calculator. Small groups Basic MI, L/R brain, LS, colors with vocabulary Text with Lesson Masters Technology source book and Math Connections Glatzer; Making Math Real Life Math Mysteries Tyler; Math Connections Martin; Extreme Math - Tyler 2

3 Representing Numbers (20 days) Concentrate on the representations of numbers as decimals, fractions, and percents. All of these representations allow you to express numbers between the integers. Numbers from 0 to 1 can represent both relative frequencies and probabilities. Decimals for numbers between integers Equal fractions Adding and subtracting fractions Estimating by rounding Fraction-decimal equivalence Fractions, decimals, and percents Using percents Square roots Probability Order and compare decimals and fractions Graph and read numbers on number lines and coordinate grids Order and compare decimals and fractions Use the Equal-Fractions Property to rewrite fractions Add and subtract fractions and use in real-life scenarios Round up, down, and to the nearest Use estimates in real situations Order, compare and convert numbers in all forms. Know and apply the Substitution Principle Estimate, define, and use square roots Calculate probabilities involving mutually exclusive events ; Small groups ; Basic MI, L/R brain, LS, colors Use graph paper to make coordinate grids. Confirm with graphing calculators. Cut out rectangles to help with factors of a number. Paper folding for fractions development Use number line for rounding. Make a table of squares Colored tiles and probability scenarios Build-It Card Decks and Game Boards with vocabulary and Text with Lesson Masters Math Connections Glatzer; Making Math Real Life Math Mysteries Tyler 3

4 Representing Sets of Numbers and Shapes (25 days) Sets of numbers and types of geometric figures are carefully defined, organized and categorized. This organization leads to the ability to recognize whether statements about numbers and figures are true or false. Three little words: Always, Sometimes, Never Properties of numbers If-Then statements Union and intersection of sets Basic figures in geometry Good definitions Classifying shapes and numbers Identify statements as always, sometimes but not always, or never true. Apply hierarchies and Venn diagrams to real-world situations. Apply: additive identity property of zero, property of opposites, and opposite of opposites. Write if-then statements and their converse. Determine the union and intersection of sets. Draw and identify basic figures of geometry and polygons. Apply the properties of a good definition. Identify numbers by their characteristics. Fill-in-the-blank sheet Math bingo Use hierarchies to develop definitions Venn diagrams Look for patterns in right triangles with graph paper; draw number lines Shape Capture: Polygon picture and property cards Technology source book Activity Kit Visual aids Internet Math Connections Glatzer Making Math Real Life Math Mysteries Tyler 4

5 Patterns Leading to Addition and Subtraction (20 days) Addition and subtraction are related to one another in many ways. Addition is used in situations of putting together and sliding. Subtraction can arise from take-away, slide, or comparison situations. Models for addition and subtraction Rules for adding positive and negative numbers Connecting addition and subtraction Solving x + a = b Solving inequalities Understanding x + y = k Adding and probabilities Add and subtract positive and negative numbers. Apply properties to simplify expressions. Use Putting-Together and Slide Models for addition and subtraction to describe situations leading to addition. Calculate absolute value. Use fact triangles to depict relationships between numbers. Solve equations and inequalities. Graph equations. Calculate probabilities using mutually exclusive events or events with overlap. Construct triangles using a compass and straightedge. Tic-Tac-Toe Reading Aid Model the commutative and associative properties Magic squares Graphing calculator Variety of triangle constructions Basic MI, L/R brain, LS, colors Math Connections Glatzer; Making Math Real Life Math Mysteries Tyler 5

6 Some Important Geometry Ideas (20 days) Tessellations use basic transformations like translations, rotations and reflections. Parallel lines and the figures and angles they create. Distance on the coordinate axes. Translations Reflections and reflection symmetry Rotations and rotation symmetry Tessellations Angles and lines Angles and parallel lines Properties of parallelograms The Triangle-Sum property Calculate the distance between points Translate and reflect figures on a coordinate graph. Reflect figures over a line. Determine reflection and rotation symmetries of a figure. Draw the rotation image of a point or a figure. Create tessellations of polygons. Use properties of lines and angles to determine angle measure. Understand and use properties of parallelograms. Calculate the distance between two points on the coordinate plane. Children s literature Overhead transparencies showing process Patty paper to fold and show symmetry Examples of tessellations White board checking of parallel vocabulary Map of the city activity Group power Open-ended tasks Problem-solving book 6

7 Multiplication in Geometry (20 days) Area and size change are connected by multiplication and geometry. The area model for multiplication Multiplication of fractions The distributive property The area of a triangle Circles The size-change model for multiplication Find the area of a triangle, trapezoid, and rectangle given the appropriate dimensions. Recognize the Distributive Property and the Communicative and Associative Properties of Multiplication. Recognize and be able to determine perimeters and areas. Picture multiplication using arrays. Multiply fractions. Find the area and circumference of a circle. Find the perimeter, area, and circumference in real-life situations. Perform expansion or contractions on a coordinate graph. Tic-Tac-Toe Break down areas to smaller areas Confirmation of calculations with calculators Visual representations of the Distributive Property Partner work Mobiles Internet Utah Visual Aids - internet 7

8 Multiplication in Algebra (25 days) The rate-factor multiplication model sets up problems using labels. Scaling up or down is made possible using the size-change model. Multiplication as shortcut addition The rate-factor model for multiplication Multiplication with negative numbers Multiplying probabilities Combining percents Solving ax = b Graphing and solving y = ax + b Graphing inequalities on the coordinate axes Recognize and use the Repeated Addition Property of Multiplication and the Multiplication Models of -1, 0, 1 and positive and negative numbers. Apply the Rate Factor Model for Multiplication. Perform expansions and contractions with negative magnitudes on a coordinate graph. Answer wquestions involving percents and conbined percents. Solve, check, and graph equations of the form ax = b and ax + b = y. Find unknowns in real situations involving multiplication. Solve and check inequalities. in their own words with examples Grocery example Reading and translating problems Use left/right, line em up, and blow em up problems Sales tax worksheet Graphing calculator confirmation Inequality situations Number cards Special project survey to display Internet Math Connections Glatzer; Making Math Real Life Math Mysteries Tyler Math Connections Martin; Extreme Math - Tyler 8