7th Grade Math Essential Units of Study Year at a Glance

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1 7th Grade Math Essential Units of Study Year at a Glance 1st Grading Period 2nd Grading Period 3rd Grading Period 4th Grading Period 5th Grading Period 6th Grading Period Essential Unit of Study Week of 8/22/11 8/29/11 9/5/11 9/12/11 9/19/11 9/26/11 10/3/11 10/10/11 10/17/11 10/24/11 10/31/11 11/7/11 11/14/11 11/28/11 12/5/11 12/12/11 1/2/12 1/9/12 1/16/12 1/23/12 1/30/12 2/6/12 2/13/12 2/20/12 2/27/12 3/5/12 3/19/12 3/26/12 4/2/12 4/9/12 4/16/12 4/23/12 4/30/12 5/7/12 5/14/12 5/21/12 5/28/12 Integers Decimal Operations Fraction Operations Convert, Compare, Order Rational Numbers Algebraic Reasoning Proportionality 2-D Geometry and Measurement FC 3-D Geometry and Measurement Statistics Probability STAAR Prep Week STAAR Testing Gear Up for 8th Grade Testing Windows Administration Scanning Due FC = February Conference Assessment I November 7-18 November 18 = Break Units 1-5 = Assessment Window Assessment II February 27 - March 9 March 9 Units 1-7 STAAR March 26 (8th Grade Math) April 24 (6th & 7th Grade Math) Legend

2 7th Grade TEKS Tracking Chart by Assessment Directions: Using your student report, circle the question numbers you got correct, and put an X through the question numbers you missed. Complete the ratio and percent correct at the bottom. Look for trends in your data. Use your test booklet to look back at the problems you missed and find any errors. Reporting Category 1 Reporting Category 2 Reporting Category 3 Reporting Category 4 Reporting Category 5 TEKS Description 1 2 STAAR 7.1A Compare and order integers & positive rational numbers S B Convert between fractions, decimals, whole numbers, & percents R 2, 8, 15 29, C Represent squares & square roots using geometric models S A Represent multiplication & division situations involving fracs & dec with models S B Use addition, subtraction, multiplication, and division to solve problems involving fractions & decimals R 12, 18, 19, C Use models to add, sub, mult, div integers/connect actions to algorithms S 7, D Use division to find unit rates/ratios in proportional relationships S E Simplify expressions involving order of operations & exponents S , 30, 35, F Select and use appropriate operations to solve problems & justify R 9, 14 33, G Determine the reasonableness of a solution S A Estimate & find solutions to application problems involving percent R 4, 8, B Estimate/find solutions to application probs with proportional relationships R 6, 13, A Generate formulas involv. conversions-perimeter,area,circ,vol,scale S 5 7.4B Graph data to demonstrate relationships-conv, per, area, circ, vol S 9 7.4C Describe relationships between term and position in sequence S A Use models & symbols to solve equations S B Formulate problem situations from simple equations & vice versa R 6, 11, 17 31, A Use measurements to classify angles-complementary/supplementary S B Use properties to classify triangles & quadrilaterals S C Use properties to classify 3-D figures S 7.6D Use critical attributes to define similarity R 2, 10, A Locate & name points on a coordinate plane. S B Graph reflections & translations on a coordinate plane R 1, 7,16 7.8A Sketch 3-D figures given top/side/front views S 7.8B Make net of the surface area of 3-D figure S 7.8C Solve problems in fields of art & architecture S A Estimate & solve application problems involving length & area R 3, 12, B Connect models for volume of prisms and cylinders to formulas S 7.9C Estimate measurements & solve application probs involving volume R 7.10A Construct sample spaces for simple or composite experiments S 7.10B Find the probability of independent events S 7.11A Select/use an appropriate representation for collected data S 7.11B Make inferences & arguments from analysis of data R 7.12A Describe data using mean/median/mode/range. S 7.12B Choose mean, median, mode, or range to describe data & justify R Percent of Items Correct Assessment /22 /40 /64 Blank Boxes Indicate TEKS Not Assessed

3 7 th Grade Math EUS 1: Integers What do you already know about this topic? In 8 th grade, you continue the use of integers with positive and negative fractions and decimals, including graphing their coordinates. The use of exponents will be extended with scientific notation and Pythagorean Theorem. In this unit, we will study integers by: exploring squares and square roots, comparing and ordering integers and absolute value, modeling and developing all operations with integers, and applying integers in coordinate graphing. Reflection Essential Questions: In 6 th grade, you used integers to represent integers in real life situations, graphed numbers in quadrant 1, performed the order of operations, and explored exponents with prime factorization. Why do we have negative numbers? How is working with negative numbers alike and/or different from working with positive numbers? Why do we need an order of operations? How do squares and square root relate to applying geometry in the real world?

4 7th Grade Math EUS 1: Integers Vocabulary: absolute value base coordinate (x,y) cubed exponent integer origin Squares & Square Roots Skill# I can: demonstrate an understanding of the vocabulary related V to Integers A-1 A-2 perfect square quadrants squared square root x-axis y-axis zero pair identify and create geometric models that represent perfect squares and square roots make connections between the area and side length of a square and squares/square roots Alignment Evidence TEKS Text Compass Unit Test Mastered? Yes/Not Yet 1, 2, 3, 4, 5 7.1C 1-3 6, C Compare & Order B-1 label, plot, and read integers on a number line 7.1A , AL003 8 B-2 compare and order integers, with and without models 7.1A , 24 C-1 model integer addition with number lines and counters 7.2C , AL C-2 solve integer addition problems 7.2C , MA , 11 C-3 model integer subtraction with number lines and counters 7.2C 2-5 Exp. AL Integer Operations Coordinate Graphing C-4 solve integer subtraction problems 7.2C , 67203, MA6534 C-5 model integer multiplication with number lines and counters 7.2C C-6 solve integer multiplication problems 7.2C , MA6541, MA6542 C-7 model integer division with number lines and counters 7.2C C-8 solve integer division problems 7.2C , 17 C-9 use order of operations (with and without absolute value and integers) to solve problems with multiple operations 7.2E 7.2F , 13 14, 15 M7105-M , 19, 29 D-1 number and label a four quadrant coordinate plane 7.7A 2-3 M7231, M D-2 write an ordered pair for a given location 7.7A D-3 plot a point on a coordinate plane given its ordered pair 7.7A , 22

5 7 th Grade Math EUS 2: Rational Numbers: Decimals What do you already know about this topic? In 8 th grade, you will continue the use of rational numbers by applying them in a variety of contexts and evaluating solutions for reasonableness. Reflection In this unit, we will study decimals by: modeling and developing all operations with decimals, and applying decimals in a variety of ways. Essential Questions: In 6 th grade, you used and applied decimal addition and subtraction, as well as whole number operations. How are models helpful when performing operations with decimals? Where are decimals used in real life?

6 7th Grade Math EUS 2: Rational Numbers - Decimals Alignment Evidence Vocabulary: compatible numbers Skill# I can: TEKS Text Compass Unit Test Mastered? Yes/Not Yet V Demonstrate an understanding of the vocabulary related to decimals A-1 Add decimals to solve problems 7.2B p A-2 Subtract decimals to solve problems 7.2B p Decimal Application Decimal Operations A-3 Model multiplication of decimals 7.2A A-4 Multiply decimals to solve problems 7.2B 3-2 A-5 Model division of decimals 7.2A A-6 Divide decimals by whole numbers to solve problems A-7 Divide decimals by decimals to solve problems 7.2B 3-4 B-1 B-2 B-3 Estimate solutions to application problems involving decimals Solve multi-step application problems involving decimals Justify selection of appropriate operations in a problem involving decimals Exp 3-2 Exp , MA6352, B , MA6362, 76246, B 3-1 M7033, M7034 9, F 3-5 M7097-M F 3-5 MA6291, MA6292 B-4 Determine reasonableness of a solution 7.2G , , 5, , 8, 17 10, 13, 19 11, 14

7 7 th Grade Math EUS 3: Rational Numbers: Fractions What do you already know about this topic? In 8 th grade, you will continue the use of rational numbers, applying in a variety of contexts and evaluating solutions for reasonableness. Reflection In this unit, we will study fractions by: modeling and developing all operations with fractions, and applying fractions in a variety of ways. Essential Questions: In 6 th grade, you modeled and applied fraction addition and subtraction, as well as whole number operations. How are models helpful when performing operations with fractions? What are some real world applications for fractional operations?

8 7th Grade Math EUS 3: Rational Numbers - Fractions Alignment Evidence Vocabulary: reciprocal Skill# I can: TEKS Text Compass Unit Test Mastered? Yes/Not Yet V demonstrate an understanding of the vocabulary related to fractions 1, 2 A-1 Add fractions to solve problems 7.2B Fraction Operations Fraction Application A-2 Subtract fractions to solve problems 7.2B A-3 Model multiplication of fractions 7.2A Expl 6-5 A-4 Multiply fractions to solve problems 7.2B , 14 MA64151, MA64152, 8067, 8109 A-5 Model division of fractions 7.2A A-6 Divide fractions by fractions to solve problems 7.2B 6-7 B-1 B-2 B-3 Estimate solutions to application problems involving fractions Solve multi-step application problems involving fractions Justify selection of appropriate operations in a problem involving fractions 7.2B , , 8110 M7033, M , 7, 15 8, 9, 17 10, F M7097-M , F MA6291, MA6292 B-4 Determine reasonableness of a solution 7.2G , 20

9 7 th Grade Math EUS 4: Rational Numbers: Convert, Compare, and Order What do you already know about this topic? In 8 th grade, you will expand the number sets that you convert, compare, and order to include positive and negative rational numbers, irrational numbers, and real numbers. In this unit, we will study rational number manipulations by: converting between various forms of rational numbers, comparing and ordering sets of integers and rational numbers. Reflection Essential Questions: In 6 th grade, you compared and ordered positive rational numbers, as well as fractions, decimals, and percents with compatible numbers. Why are there so many different forms of numbers to represent the same value? Why is it important to be able to convert between fractions, decimals, and percents? Are there times when one form of rational numbers is better than another? When and why?

10 7th Grade Math EUS 4: Convert, Compare, and Order Rational Numbers Vocabulary: greater than or equal to less than or equal to percent rational number Skill# I can: TEKS Alignment Text Compass Evidence Unit Test Mastered? Yes/Not Yet V Students will demonstrate an understanding of the vocabulary related to Convert, Compare, and Order Rational Numbers 9, 10 A-1 convert decimals to fractions 7.1B 5-5 M7027- M , 24 A-2 convert fractions to decimals 7.1B 5-5 M7027- M , 25 A-3 convert fractions to percents 7.1B 5-6 M7027- M , 26 Convert Between Forms of Rational Numbers A-4 convert decimals to percents 7.1B 5-7 A-5 convert percents to decimals 7.1B 5-7 A-6 convert percents to fractions 7.1B 5-6 M7027- M7032 M7027- M7032 M7027- M , 21 15, 22 16, 23 A-7 memorize benchmark equivalencies (halves, thirds, fourths, fifths, eighths, tenths) 7.1B M7027- M7032 1, 2, 3, 4, 5, 6, 7, 8 A-8 A-9 convert percents greater than 100% or less than 1% into fractions convert percents greater than 100% or less than 1% into decimals 7.1B B Compare & Order B-1 compare integers and positive rational numbers 7.1A 5-9 MA6521, MA6522 B-2 order integers and positive rational numbers 7.1A

11 7 th Grade Math EUS 5: Algebraic Reasoning What do you already know about this topic? In 8 th grade, you will generate multiple representations of data such as tables, graphs, equations and verbal descriptions, and evaluate expressions for any term in an arithmetic sequence. Reflection In this unit, we will study algebraic reasoning by: exploring arithmetic sequences writing algebraic equations and word problems, and modeling and solving algebraic equations. In 6 th grade, you used tables and symbols to represent proportional situations and measurement relationships, and wrote equations for problem situations. Essential Questions: What are patterns that exist in the real and natural world? Why are models useful in understanding solutions to equations? How can real world problems be solved with equations?

12 7 th Grade Math EUS 5: Algebraic Reasoning Alignment Evidence Vocabulary: arithmetic sequence coefficient constant inverse operation Skill# I can: nth term position variable TEKS Text Compass Unit Test Mastered? Yes/Not Yet Demonstrate an understanding of the vocabulary related to Algebraic Reasoning 1, 2, 3, 4, 5 Sequences A-1 Determine the rule for the sequence. 7.4C 1-9 6, A-2 Generate a sequence from a given rule 7.4C ext 7, 20 Equations and Word Problems B-1 Formulate a problem situation when given an equation 7.5B B-2 Define a variable in relationship to a given problem 7.5B B-3 Formulate an equation when given a problem situation 7.5B MA , 21, 22 9, 11 10, 12, 23, 24 Modeling and Solving Equations C-1 Write an equation from a model. 7.5A C-2 C-3 Draw and use models to solve single- and multi-step equations Solve one-step equations using inverse operations & check the solution using substitution 7.5A 4-2 expl 7.5A , 25 M7302-M7307, MA6261-MA6264 MA6551, MA6552, M7121, M , 16, 17, 18

13 7 th Grade Math EUS 6: Proportionality What do you already know about this topic? In 8 th grade, you will continue the application of proportionality and percents in real world situations and in relationship to geometry and measurement. Reflection In this unit, we will study proportionality by: computing and applying unit rates, learning multiple proportion strategies, applying proportions, and applying percents. Essential Questions: In 6 th grade, you used ratios to describe proportional situations and to make predictions, and modeled percents. How is proportionality useful in the real world? What are some examples of proportional situations that involve percents? Are fractions and ratios more alike or more different? Why?

14 7 th Grade Math EUS 6: Proportionality Alignment Evidence Vocabulary: commission discount percent of change proportion sales price Skill# I can: tax tip unit rate TEKS Text Compass Unit Test Mastered? Yes/Not Yet V demonstrate an understanding of the vocabulary related to Proportionality 1, 2, 3, 4, 5 unit rates proportion strategies A-1 divide to convert rates into unit rates 7.2D 7-2 6, 7 A-2 apply unit rates to real life situations (mph, wages, etc.) 7.2D B-1 B-2 use cross-products, unit rates, and mental math to solve proportions use models to solve problems involving proportions (including percents) 7-2, 7-2 ext MA B 7-4 M7059, M B 10, 13 8, 21 proportion application C-1 write a proportion from a problem situation 7.3 B C-2 solve a proportion from a problem situation 7.3 B , , 22 M7073-M , 23 percent applications D-1 write a percent proportion from a problem situation 7.3A 8-2 D-2 D-3 D-4 solve a percent proportion (or equation) from a problem situation estimate and apply percents to tax, tip, and commission situations estimate and apply percents to discount and sales price situations MA6871, MA , A , MA , A A D-5 estimate and apply percents to percent of change situations 7.3A , , 18, , , , MA , 27

15 7 th Grade Math EUS 7: 2-D Geometry and Measurement What do you already know about this topic? In 8 th grade, you will extend your use of formulas, generate similar figures using dilations, and apply the Pythagorean Theorem. In this unit, we will study two-dimensional geometry and measurement by: generating formulas and graphs, comparing and classifying figures, applying the coordinate plane to transformations, and estimating measures and solving application problems. Reflection Essential Questions: Where do you see similarity in the real world? In 6 th grade, you used formulas for perimeter and area, measured and classified angles. What are real world applications of reflections and translations? Why do we measure? Why are formulas important?

16 7 th Grade Math EUS 7: 2-D Geometry and Measurement Vocabulary: complementary angles congruent equilateral triangle isosceles triangle parallelogram transformation Generate formulas & graphs Compare and classify figures Coordinate System Estimate measurements and solve Skill# I can: V demonstrate an understanding of vocabulary related to 2-D 1, 2, 3, 4, Geometry & Measurement 5, 6, 7, 8 A-1 manipulate an area/perimeter(including circumference) formula to isolate a particular variable 7.4A 9, 24 A-2 choose and/or create an appropriate formula given a problem situation or a graph 7.4A 10 A-3 B-1 graph relationships in concepts such as conversions, perimeter, area, circumference, and scaling 7.4B Ext classify angle pairs as supplementary and complementary and determine the complement and/or supplement of a given angle 7.6A , MA69210, M7163, M7164 B-2 use properties to classify triangles & quadrilaterals 7.6B 11-3 B-3 identify whether two figures are similar. 7.6D 11-6 C-1 C-2 translation reflection rhombus scalene triangle similar supplementary angles trapezoid translate figures on a coordinate plane, and determine the coordinates of the transformed figure reflect figures on a coordinate plane, and determine the coordinates of the transformed figure D-1 apply formulas to calculate perimeter of two-dimensional figures D-2 apply formulas to calculate circumference of circles D-3 apply formulas to calculate area of two-dimensional figures D-4 apply formulas to calculate area of composite figures and shaded regions D-5 create and solve a proportion to find missing measurements in similar figures D-6 apply similarity to real life situations, such as indirect measurement, scale models, etc. TEKS MA6941, MA6942, M7123-M , MA5768, 67249, MA69102, M7165-M , 25 12, 26 13, 14 15, B , B , C 7.9A 7.8C 7.9A 7.8C 7.9A 7.8C 7.9A Expl , 12-2, 12-4 MA6271, MA MA69123, MA , , B , M7165-M , B 11-6 Alignment Text Compass 67128, MA6714, M8127-M8132 Evidence Unit Test 30 23, 33 Mastered? Yes/Not Yet

17 7 th Grade Math EUS 8: 3-D Geometry and Measurement What do you already know about this topic? In 8 th grade, you will find volume and surface area of many common 3-D figures, apply proportionality to describe the effects on changing dimensions, and find missing measures of similar 3-D figures. In this unit, we will study three-dimensional geometry and measurement by: representing volume with formulas and graphs, exploring the properties and nets of 3-D figures, and applying volume formulas. Reflection Essential Questions: In 6 th grade, you used formulas to determine area of 2-D figures and began exploring volume of rectangular prisms. Compare and contrast prisms and pyramids, prisms and cylinders, pyramids and cones, etc Why do we need formulas? How are area and volume related?

18 7 th Grade Math EUS 8: 3-D Geometry and Measurement Alignment Evidence Vocabulary: base cone cylinder net Skill# I can: prism pyramid TEKS Text Compass Unit Test Mastered? Yes/Not Yet V demonstrate an understanding the vocabulary related to 3-D Geometry and Measurement Represent Volume Properties and Nets A-1 connect models to formulas for finding volume. 7.9B 12-9, A-2 generate the formula for volume of a solid figure from a table. A-3 graph data to demonstrate relationships in volume. 7.4B 7.4A 10 Ext B-1 classify 3-dimensional figures. 7.6 C 12-7 B-2 sketch 3-dimensional figures when given the top, side, and front views. 7.8A B-3 draw the net of a 3-dimensional figures. 7.8B Expl 12-8, 12-8 Ext 12-6 MA6971, MA6972, M7171, M7172 MA6973, MA6974, 56303, MA , MA , 2 9 Volume Application C-1 estimate the volume of prisms and cylinders C-2 use formulas to solve for the volume of prisms and cylinders C-3 solve application problems involving prisms and cylinders 7.8C 7.9C 7.8C 7.9C 7.8C 7.9C 12-9, , , , MA69162, M7173-M7178, , 12 6, 7, 13 8, 14, 15

19 7 th Grade Math EUS 9: Statistics What do you already know about this topic? In 8 th grade, you will continue to expand your use of graphs and measures of central tendency, as well as explore bias and sampling methods. Reflection In this unit, we will study statistics by: creating and choosing graphs appropriate for given situations, applying measures of central tendency, and reading and applying graphs. Essential Questions: In 6 th grade, you created graphs, calculated mean, median, mode and range, and solved problems using graphs and collected data. Are the mean and median of a set of data more alike or different? Why? Why can t you use mean, median, and mode interchangeably? Why are there so many ways to represent data? How can data be used to influence decisions?

20 7 th Grade Math EUS 9: Statistics Vocabulary: Alignment Evidence interval measure of central tendancy outlier scale statstics Create and Choose Appropriate Graphs Skill# I can: V demonstrate an understanding of the vocabulary related to Statistics A-1 create a circle graph 7.11A 9-4 Ext, 11-2 MA6861- MA6862, A-2 create a Venn diagram 7.11A , MA A-3 choose the most appropriate graph for a set of data and justify the choice TEKS Text 7.11A 9-8 Compass MA6611, MA6612 Unit Test 1, 2, 3 4 6, 15 Mastered? Yes/Not Yet Apply Measures of Central Tendency B-1 calculate mean, median, mode, and range 7.12A 9-2 B-2 B-3 describe how changes in data affect measures of central tendency choose most appropriate measure of central tendency to describe the data and justify choice B 9-2 M7271-M7276, 67229, MA6682 M7510, MA6683- MA6684 M7277-M7278, M8255-M8260 7, 8, 9, 10, , 17 Read & Apply Graphs C-1 interpret and use data presented in a graph 7.11B 9-6 M7235-M7236, M7265-M7270 C-2 make inferences and predictions using data 7.11B , 19, 20 13, 18

21 7 th Grade Math EUS 10: Probability What do you already know about this topic? In 8 th grade, you will continue the use of probability to explore dependent and independent events and make predictions. In this unit, we will study probability by: determining sample spaces using a variety of methods, calculating probabilities of independent events, and comparing and contrasting theoretical and experimental probabilities. Reflection Essential Questions: In 6 th grade, you used tree diagrams and list for sample spaces and found probability of simple events. Is probability always accurate? How are experimental and theoretical probabilities alike and different? What is the best way to model a sample space? Why?

22 7 th Grade Math EUS 10: Probability Alignment Evidence Vocabulary: complementary events composite events experimental probability independent event Skill# I can: sample space theoretical probability TEKS Text Compass Unit Test Mastered? Yes/Not Yet V demonstrate an understanding of the vocabulary related to probability 1, 2, 3 Sample Spaces Calculate Probabilities A-1 create tree diagrams for composite events 7.10A , A-2 create lists of sample spaces for simple or composite events 7.10A MA61042 A-3 determine the number of outcomes using the counting principle B-1 calculate the probability of independent events 7.10B 10-8 B-2 find the complement of an event 7.10B A , , 76287, MA61061, MA , MA61052 B-3 find the probability of events involving geometry 7.10B 8, 14 B-4 convert probability into different rational number forms 7.10B 15 6, 13 7 Theoretical vs. Experimental C-1 calculate experimental probability , 16 C-2 compare and contrast theoretical versus experimental probabilities M7507, M , 17