7 th Grade Math Scope and Sequence Student Outcomes (Objectives Skills/Verbs)

Transcription

1 own discovery of the Big BIG IDEA: How are different types of numbers used to represent real life situations? Why is it necessary to have different types of numbers for different situations? Pg (no negatives) Negatives Pg Identify and use place value in mathematical and practical situations. * Comparing and Ordering Decimals Write, identify, and use powers of 10 from 10-3 through Does a number s place change its value? Why is it useful to take a large number and put it in a compacted form? How do powers of 10 change place value when multiplied by another number? What are different ways to express equivalent values? How do mathematicians use powers of 10? Can this be helpful for you? Identify Use Write Place Value Mathematical Situations Practical Situations Powers Base Exponent *Powers of Ten Translate among What are different ways to express numbers of the same value? Translate Fractions Decimals Percents fractions, decimals, Fractional Percents Douglas County School District Page 1 March 2010

2 own discovery of the Big 6-2 and percents, including fractional percents. Why and how can you calculate your grade/grade point average? Integers *Fractions, Decimals and Percents Pg Compare and order a combination of rational numbers, including fractions, decimals, percents, and integers in mathematical and practical situations What is the importance to having order to numbers? Why do we express equivalent values in different ways? If equivalent values can be expressed differently, why don t we just use one way and not have to learn the rest? Compare Order Simplify Rational Numbers Fractions Decimals Integers Percents Ratios *Comparing and Ordering Decimals *Simplifying Fractions Douglas County School District Page 2 March 2010

3 own discovery of the Big and Ratios *Ratios and Percent *Fractions, Decimals and Percents *Comparing and Ordering Fractions *Comparing and Ordering Integers Identify absolute values of integers. *Integers Generate a reasonable estimate for a computation using a Is the opposite always positive? How can numbers represent opposite situations? Can numbers represent opposite situations? When do you use estimation in daily life? How do you cluster numbers to get a fast calculation? Identify Define Simplify Generate Estimate Select Round Determine Absolute Value Integers Estimate Computation Significant digits Douglas County School District Page 3 March 2010

4 own discovery of the Big 6-3 Pg 763 variety of methods. *Estimating with Decimals *Estimating with Fractions *Percent and Estimation Since you can always use a calculator, why bother to do an estimate? When have you rounded numbers and may not even know you are doing it? Select and round to the appropriate significant digit. *Rounding Decimals *Determine the number of significant digits in a given number (must contain a decimal point) Douglas County School District Page 4 March 2010

5 own discovery of the Big Calculate with integers and other rational numbers to solve mathematical and practical situations. *Multiplying Decimals *Dividing Decimals *Adding Integers *Subtracting Integers *Multiplying Integers *Dividing Integers *Adding and Subtracting Fractions *Adding and Are two negatives always positive? Do calculations with decimals, percents, and fractions give you the same results? How has the order of operation change the value of the expression? Why must there be an agreed order for finding the value of an expression? What is the difference between and expression and an equation? Can a trip be planned (Vacation) without solving any math problems? How do you take known relationships with numbers to solve for unknown values? What does a math expression represent? Calculate Solve Use Compute Evaluate Simplify Integers Rational Numbers Order of Operations Expressions One-step Equations Decimals Mixed Numbers Fractions Percents Proportions Douglas County School District Page 5 March 2010

6 own discovery of the Big Subtracting Mixed Numbers What does a math equation represent? *Multiplying Fractions and Mixed Numbers *Dividing Fractions and Mixed Numbers *Percents and Fractions *Percents and Decimals *Percents Greater Than 100% and Percents Less Than 1% Douglas County School District Page 6 March 2010

7 own discovery of the Big *Percent of a Number *The Percent Proportion Use order of operations to evaluate expressions and solve one-step equations (containing rational numbers). *Order of Operations (4-step problems) *Variables and Expressions, Evaluating Douglas County School District Page 7 March 2010

8 own discovery of the Big Expressions *Solving Equations Identify and apply the distributive, commutative, and associative properties of rational numbers to solve problems. How does regrouping get you the same answer? How do math properties allow us to solve problems using mental math? Identify Apply Simplify Distributive Property Commutative Property Associative Property Rational Numbers *Properties 1-6 BIG IDEA: How do you represent everyday experiences using algebraic expressions, patterns, and functions? Use and create tables, charts, and graphs to extend a pattern in order to describe a What are some mathematical techniques to predict data in real life? Use Create Extend Describe Predict Tables Charts Graphs Pattern Linear rule Integer Values Functions Douglas County School District Page 8 March 2010

9 own discovery of the Big 4-5 linear rule, including integer values. Equations Linear function 4-6 *Making Predictions *Functions and Equations Evaluate formulas and algebraic expressions for given integer values. *Variables and Expressions Evaluating Expressions What are the goals of solving equations? How can expressions have different values? Does the inverse always equal 1? Is there an output (result) for every input? Evaluate Solve Graphically represent Formulas Algebraic Expressions Integer values Equations Inequalities Variable Integer solutions Two-step equations *Solving Equations Solve and graphically represent equations and Douglas County School District Page 9 March 2010

10 own discovery of the Big inequalities in one variable with integer solutions *Solving Equations *Solving Addition and Subtraction Equations *Solving Multiplication Equations *Solving 2-Step Equations *Inequalities Simplify algebraic expressions by combining like terms. What makes things alike? Simplify Combine like terms Algebraic expressions Like term Variable expressions Douglas County School District Page 10 March 2010

11 own discovery of the Big *Simplifying Variable Expressions Generate and graph a set of ordered pairs to represent a linear equation. Why is there an output (result) for every input? Generate Graph Represent Ordered pairs Linear equations Functions Equations *Functions and Equations Identify linear equations and inequalities. *Writing Expressions and Equations How do signs affect results? Identify Model Solve Writing expressions and equations Linear equations Inequalities Expression Equation Function *Inequalities Douglas County School District Page 11 March 2010

12 own discovery of the Big Model and solve equations using concrete and visual representations. *Functions and Equations BIG IDEA: How do you measure the physical world and communicate the results? Estimate and compare corresponding units of measure for area and volume between customary and metric systems. What are the differences and similarities between the customary and metric systems? Estimate Compare Corresponding units of measure Area Volume Customary systems Metric systems Douglas County School District Page 12 March 2010

13 own discovery of the Big Given a measurement, identify the greatest possible error. What is the cause and effect to an error? Identify Calculate Measurement Greatest possible error Select, model, and apply formulas to find the volume and surface area of solid figures. What are the differences of wrapping and filling 3- dimensional objects? Select Model Apply Formulas Volume Surface Area Solid Figures *Volume of Rectangular Prisms *Volume of Cylinders *Surface Area of Rectangular Prisms Why is calculating interest on money an important Calculate Simple interest Monetary Douglas County School District Page 13 March 2010

14 own discovery of the Big 6-7 Calculate simple interest in monetary problems skill? problems Write and apply proportions to solve mathematical and practical problems involving measurement and monetary conversions. How do you use proportions to shrink and stretch values? Write Apply Solve Proportions Measurement Monetary conversions Scale drawings 5-9 *Solving Proportions (for example: 4 quarters = $1) *Scale Drawings??? Use elapsed time to solve practical problems. How does time affect you in real life events? Solve Elapsed time Douglas County School District Page 14 March 2010

15 own discovery of the Big BIG IDEA: How is geometry used to represent the physical world? Identify, classify, compare, and draw regular and irregular polygons. *Polygons Why do we have specific names for geometric shapes? How did the names of geometric shapes come to be? How many different, closed figures with straight lines can be made and put in groups? Identify Classify Compare Draw Find Verify Regular polygons Measures of interior angles of polygons Triangles Quadrilaterals 8-8 Find and verify the sum of the measures of interior angles of triangles and quadrilaterals. *Angles of a Polygon Make scale drawings using ratios and How are models similar to real things? What makes a small picture of a car look like a Make Scale drawings Ratios Proportions Douglas County School District Page 15 March 2010

16 own discovery of the Big Extension proportions. *Scale Drawings Demonstrate translation, reflection, and rotation using coordinate geometry and models. Describe the location of the original figure and its transformation on a coordinate plane. real car? What do you do to draw something like a large car on a small piece of paper? How can you change the location and orientation on objects and show the change on a grid? Demonstrate Describe Transform Translation Reflection Rotation Coordinate geometry and models Coordinate plane Transformation Original and transformed figures *Graphing Transformations *Translations *Reflections Douglas County School District Page 16 March 2010

17 own discovery of the Big Hands on Lab Make a model of a 3-D figure from a 2-D drawing. How do you make a drawing look 3-D? Make a model 3-D Figure 2-D Drawing Nets Surface Area *Drawing Three- Dimensional figures Make a 2-D drawing of a 3-D figure. *Nets and Surface Area Determine slope of a line, midpoint of a segment, and the horizontal and vertical distance between two points using coordinate geometry. What is steepness? What is the opposite of steepness? How do you describe halfway? Determine Slope of a line Midpoint of a segment Horizontal distance Vertical distance Points Coordinate Geometry Douglas County School District Page 17 March 2010

18 own discovery of the Big Hands on Lab Describe the geometric relationships of parallel lines, perpendicular lines, triangles, quadrilaterals, and bisectors. *Angles *Perpendicular Parallel Lines In what ways can a tree provide examples of the geometric concepts of parallel lines, perpendicular lines, and triangles? How does and arrow represent a bisector? Describe Geometric relationships Parallel lines Perpendicular lines Triangles Quadrilaterals Bisectors Polygons *Polygons Hands on Lab Model the Pythagorean Theorem and solve for the hypotenuse. *Pythagorean Theorem *The Pythagorean Theorem Who and why are people using and being affected by the Pythagorean Theorem, whether they know it or not? What Greek philosopher/mathematicia n is famous for working with right triangles? Model Solve Pythagorean Theorem Hypotenuse Douglas County School District Page 18 March 2010

19 own discovery of the Big Hands on Lab Construct and identify congruent angles, parallel lines, and perpendicular lines. What are examples around the school/neighborhood that can be named with math terms and put in groups? Construct Identify Measure Congruent angles Parallel lines Perpendicular lines *Measuring Angles *Perpendicular and Parallel Lines Ch Make and test conjectures to explain observed mathematical relationships and to develop logical arguments to justify conclusions. Can you make statements about a person s health who only eats junk food, watches TV, plays video games, and never goes to bed before midnight? How do you use facts to create a logical argument and come to a reasonable conclusion? Make Test Explain Develop logical arguments Justify Conjectures Mathematical relationships Logical arguments Conclusions Douglas County School District Page 19 March 2010

20 own discovery of the Big BIG IDEA: How does data represent real life situations? Formulate questions that guide the collection of data. Organize, display, and read data using the appropriate graphical representations (with and w/o technology). What questions would you ask if you want to know the different activities of your classmate and then organize the data? Formulate Organize Display Read Data Graphical representations Technology Frequency table Line Plots Stem and Leaf Plot Misleading statistics *Frequency Tables *Making Predictions *Line Plots *Stem-and-Leaf Plots *Misleading Statistics Douglas County School District Page 20 March 2010

21 own discovery of the Big Interpret graphical representations of data to describe patterns, trends and data distribution *Making Predictions How can you look at a variety of graph types and make predictions/ Interpret Describe patterns and trends Predict Graphical representations Patterns Trends Data distribution Mean Median Mode *Mean, Median and Mode Analyze the effect of change of scale will have on statistical charts and graphs. *Misleading Statistics Will using different scales on graphs representing the same data lend to different conclusions? Analyze Describe Change of scale Statistical charts Statistical graphs Misleading statistics Find the number of How many ways can the students in this class line up? Find Permutations Event Douglas County School District Page 21 March 2010

22 own discovery of the Big 11-7 permutations possible for an event in mathematical and practical situations. *Permutations Find the theoretical probability of an event using different counting methods including sample spaces and compare that probability with experimental results. Do you want to know the chance of success before you do something? How can chance be determined? If everyone in your class tossed a coin 100 times, will everyone have the same number of heads as tails? Find Compare Represent Theoretical probability Event Counting methods Sample spaces Experimental results Tree diagrams Counting principle Represent the probability of an event as a number between 0 Douglas County School District Page 22 March 2010

23 own discovery of the Big and 1. *Theoretical and Experimental Probability *Tree Diagrams *The Counting Principle Interpolate and extrapolate from data to make predictions for a given set of data. *Misleading Statistics What are reasons to collect data? What can be done with data when you have it? What ways can data be used or organized? How can data be used to give the wrong idea? Interpolate Extrapolate Make predictions Data Prediction Set of data Misleading statistics Douglas County School District Page 23 March 2010