* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download LPS Advanced Algebra Objectives
List of important publications in mathematics wikipedia , lookup
Analytical mechanics wikipedia , lookup
Line (geometry) wikipedia , lookup
Elementary algebra wikipedia , lookup
Mathematics of radio engineering wikipedia , lookup
System of polynomial equations wikipedia , lookup
System of linear equations wikipedia , lookup
Partial differential equation wikipedia , lookup
LPS Algebra Ext 1 Syllabus Semester One Best Practices: Read “Essential Components of Effective Math Lessons” State learning objectives for each lesson every day Use specific vocabulary as a part of the daily lesson To help make instructional decisions: a) Study Prerequisite Skills Review b) Review Strategies for Reading Mathematics (Chapter Resource Books) Preview problems before making an assignment Use Guided Practice as part of the daily lesson The Skills Review Handbook provides extra examples and practice (p. 759) Use Mixed Review and Maintaining Skills throughout the course Use Extra Practice (p. 783) when needed Focus on problem solving each day (helpful for CRT) * Indicates objectives that are tested on the CRT Pretest and Posttest are available for Chapters 1 and 2 and a vocabulary worksheet. CHAPTER 1: Connections to Algebra Section 1.1 159* Is able to use order of operations to simplify and evaluate variable and numeric expressions. 155* Is able to evaluate a formula. 17 Will know and use the formulas for the area of rectangles, squares, triangles, parallelograms, trapezoids, circles, and composite shapes. Focus: Understanding and evaluating variable expressions. Evaluate simple formulas. Problems to pull from: p.6-8 # 17-45, 50-51 Extra Practice: Practice Worksheet 1.1A Section 1.2 6* Is able to use radicals, exponents, absolute value, fractions, decimals, order of operations, and properties of real numbers to solve problems. Focus: Writing powers in exponential & expanded form; Evaluating powers Evaluating exponential expressions; Area of squares; Volume of cubes Problems to pull from: pp.12-13 # 13-33, 40-54, 61-63 Extra Practice: Practice Worksheet 1.2A #1-27 06/22/17 Section 1.3 159* Is able to use order of operations to simplify and evaluate variable and numeric expressions 6* Is able to use radicals, exponents, absolute value, fractions, decimals, order of operations, and properties of real numbers to solve problems. Focus: D1: Order of operations – left to right, without grouping symbols; Stress: “Left – to – Right Rule” D2: Order of operations with grouping symbols D3: Extra Practice Problems to pull from: (D1) Practice worksheet 1.3A # 1-26 (D2) p.18-19 # 17-41, 54-57 (D3) PEMDAS Story Activity (supplemental) Practice Worksheet 1.3B #1-25 Extra Practice: p.21 # 20-22, p.29 # 74-82 Section 1.4 115* Is able to solve linear equations using addition, subtraction, multiplication and division. 8 Is able to perform estimations and computations of real numbers mentally. 116* Is able to solve inequalities. Focus: D1: Identify equations, expressions, and inequalities; Checking solutions; Solving mental math D2: Identifying inequalities; Checking solutions Problems to pull from: (D1) p. # 27., 1-6, 26-50, 59 (D2) Supplementary Worksheet 1.4 Day 2 Extra Practice: Practice worksheet 1.4A # 1-36, p 28-29 57-58,61-62 Section 1.5 127* Is able to translate verbal sentences into algebraic equations or inequalities. 128* Is able to translate verbal phrases into algebraic expressions. Focus: D1: Translate expressions. Supplemental Notes Sheet and Chart for operations Stress: “less than”, grouping( ) D2: Translate equations and inequalities. Supplemental Notes Sheet Stress: difference between “less than” and “is less than” Problems to pull from: (D1) p. 33 # 10-19, Practice worksheet 1.5 A # 1-12 (D2) pp. 33-34 # 20-35, 40-41, Practice worksheet 1.5 A # 13-24 Extra Practice – Supplementary Worksheets 1.5 Day 1 and 1.5 Day 2 CHAPTER 2: Properties of Real Numbers Section 2.1 1 Is able to identify and order whole numbers, integers, rational, or irrational (real numbers). Focus: D1: Graph and compare integers (both horizontal and vertical) D2: Graph and compare real numbers Note*** Graphing is for ordering and comparing real numbers, not for accuracy Problems to pull from: (D1) p. 68 # 14-30, p. 69 # 50-54, 60 (D2) p. 68 # 31-49, p. 69 # 55-59, p. 70 # 61,62 Extra Practice – Practice Worksheet 2.1A 06/22/17 Section 2.2 5* Is able to evaluate absolute value expressions. Focus: D1: Find the opposite of a number and evaluate absolute value expressions D2: Solve simple absolute value expressions; Find velocity and speed Omit*** Example 5 (Counterexample) Problems to pull from: (D1) p. 74 # 17-32, p. 76 # 56,57, Practice Worksheet A # 1-12 (D2) p. 74-75 # 33-50, 58, 59, Practice Worksheet A # 13-22 Section 2.3 8 Is able to perform estimations and computations of real numbers. Focus: D1: Add real numbers using a number line and rules of addition; Emphasize rules and properties of addition (Supplementary Notes Sheet for properties) D2: Introduce and use properties of addition Problems to pull from: (D1) p. 81 # 15-35, Practice Worksheet A # 1-15 (D2) p. 82 # 36-49, 54, 57, 58, Practice Worksheet A # 16-32, 34 Section 2.4 8 Is able to perform estimations and computations of real numbers. Focus: D1: Introduce and use subtraction rules for real numbers D2: Extra Practice Problems to pull from: (D1) p. 89-90 # 14-41, 54-55, 60-61, 63 (D2) Practice Worksheet A # 1-24, 34, 36-37 Section 2.5 8 Is able to perform estimations and computations of real numbers. Focus: D1: Multiply real Numbers; Emphasize rules for multiplying pairs of real numbers; Simplify Variable expressions D2: Evaluate variable expressions; Introduce properties of multiplication Problems to pull from: (D1) pp. 96-98 # 17-18, 23-28, 32-40, 59, Practice Worksheet A # 1-21 (D2) Supplementary Worksheet 2.5 Day 2 Before 2.6 (Direct instruction with guided practice) 157* Is able to combine like terms. Focus: Combine like terms; Find terms of an expression Examples 1 & 2 from section 2.7; Example 4 Section 2.4 p. 784 # 46-51, p 110 # 15-29, p 90-91 #48-53, 62 06/22/17 Section 2.6 128* Is able to translate verbal phrases into algebraic expressions. 158* Is able to use the distributive property to simplify expressions. Focus: Distributive Property D1: Positive multiplier only D2: Negative multiplier; Fraction/decimal multipliers D3: Practice with all multipliers Problems to pull from: (D1) p. 104 # 17-38, 71, 73-76 (D2) p. 104 # 41-50, Practice Worksheet A # 1-19 (D3) p. 784 #38-45, Supplementary Worksheet 2.6 Day 3 Section 2.7 157* Is able to combine like terms. 158* Is able to use the distributive property to simplify expressions. Focus: Combining like terms and simplify expressions D1: Supplementary Collaborative Lesson Problems to pull from: (D1) Supplementary Worksheet 2.7 Day 1 (D2) p. 110 # 1-14, 30-38, 41-44, 55-58 Section 2.8 128* Is able to translate verbal phrases into algebraic expressions. 157* Is able to combine like terms. 158* Is able to use the distributive property to simplify expressions. Focus: Divide to simplify expressions D1: Example 1 ONLY D2: Complex fractions D3: Extra Practice Problems to pull from: (D1) Supplementary Worksheet 2.8 Day 1 (D2) Supplementary Worksheet 2.8 Day 2 (D3) Supplementary Worksheet 2.8 Day 3 CHAPTER 3: Solving Linear Equations Section 3.1 115* Is able to solve linear equations using addition, subtraction, multiplication and division. Focus: Solve one step equations using addition and subtraction Problems to pull from: (D1) pp.135-136 # 19-59, 63 (D2) Practice Worksheet 3.1B Extra Practice: Practice Worksheet 3.1A Section 3.2 115* Is able to solve linear equations using addition, subtraction, multiplication and division. Focus: Solve one step equations using multiplication and division D1: Solve using multiplication and division D2: Solve by multiplying by the reciprocal Problems to pull from: (D1) p.141-142 # 16-36, 48, 50-53 (D2) Supplementary worksheet 3.2 Day 2 Extra Practice: Practice Worksheet 3.2B 06/22/17 Section 3.3 129* Is able to solve multi-step equations. Focus: D1: Solve equations of the type 8x + 3 = 19 (simple 2 step equation) D2: Solve 2 step equations with fractions D3: Solve 2 step equations after combining like terms D4: Solve equations using the distributive property and collecting like terms Problems to pull from: (D1) Supplementary Worksheet 3.3 Day 1 (D2) Supplementary Worksheet 3.3 Day 2 (D3) Supplementary Worksheet 3.3 Day 3 (D4) Supplementary Worksheet 3.3 Day 4 Supplementary materials – worksheet chapter 3 lesson 3 review Section 1.6 Is able to model and solve real-life problems Problem Solving Techniques Supplementary Material Focus: D1: Translate equations and solve D2: Solve real-life problems D3: More Practice – Do not introduce anything new Problems to pull from: (D1) Supplementary Material 1.6 Day 1 (D2) Supplementary Material 1.6 Day 2 (D3) Find your own supplemental material Section 3.4 130* Is able to solve equations with variables on both sides. Focus: Solve equations with variables on both sides D1: Solve without combining like terms D2: Solve with combining like terms D3: Identify the number of solutions Problems to pull from: (D1) p 154 # 17-27; Practice 3.4A #10-21; Solve completely (D2) Supplementary Worksheet 3.4 Day 2 (D3) p 154-156 #9-14, 37-46, 56 Supplementary materials – Review worksheet 3.3-3.4 Extra Practice: Practice Worksheet 3.4B Section 3.5 129* Is able to solve multi-step equations. 130* Is able to solve equations with variables on both sides. Focus: Solve multi-step equations with variables on both sides D1: Solve multi-step equations with variables on both sides without fractions D2: Solve multi-step equations with variables on both sides with fractions D3: Solve multi-step equations with variables on both sides Problems to pull from: (D1) p.160 #19-30 (D2) p.160 #11-18, 31-36, 40-43 (D3) Practice 3.5A #1-10, p. 161 #44-49 Extra Practice: Practice Worksheet 3.5B 06/22/17 Section 3.6 129* Is able to solve multi-step equations. 130* Is able to solve equations with variables on both sides. Focus: Solve equations that contain decimals D1: Solving equations and rounding the answers (decimals on one side only) D2: Solving equations with decimal coefficients and constants Problems to pull from: (D1) p.166 #20-29; Practice worksheet 3.6A #1-15 (D2) p.166 #19, 30-35, 39-45, 47-49; p. 169 15, 22 Extra Practice: Practice worksheet 3.6A #16-27 Section 3.9 123*Is able to write and solve percent equations. Focus: Solve percent problems Ignore presentations in examples and the summary where the emphasis is placed upon “base” etc. Emphasize translation of word sentences to algebraic equations. Note: some students will be familiar with the proportion method but emphasis should be placed upon algebraic equations to solve these problems. Problems to pull from: (D1) p. 186 #13-33, Supplemental Worksheet Lesson 9 worksheet 1 (D2) Notes for Lesson 9 Discount & Sales Tax Lesson 9 worksheet 2 Section 3.7 131* Is able to solve a formula or equation for one of its variables (y). Focus: To solve an equation for y D1: solving for y with 1 or –1 as its coefficient D2: Solving equations for y with coefficients other than 1 or -1 D3: Solve formulas for a single variable D4: Extra Practice Problems to pull from: (D1) Supplementary Worksheet 3.7 Day 1 (D2) Supplementary Worksheet 3.7 Day 2 (D3) Supplementary Worksheet 3.7 Day 3 (D4) Supplementary Worksheet 3.7 Day 4 Extra Practice: Supplementary Worksheet 3.1-3.7 Review DATA ANALYSIS: Supplementary Unit Project ideas included Section 1.7 72 Is able to use tables to organize data. Focus: D1: Organize data in a table; Interpret table, bar and line graphs D2: Make bar and line graphs Problems to pull from: (D1) Supplementary Worksheet 1.7 Day 1 (D2) Supplementary Worksheet 1.7 Day 2 Extra Practice: Supplementary Worksheet 1.7 Day 3 06/22/17 Section 4.1 73 Is able to represent data using a scatter plot. 74 Is able to interpret information on a coordinate graph. 81 Is able to approximate the best fitting line for data. 82* Is able to use a scatter plot to identify the correlation shown by a set of data. Focus: D1: Plotting points on a coordinate plane (vocabulary) Supplemental Notes Sheet D2: Scatter plots; line of best fit; correlation Problems to pull from: (D1) Supplementary Worksheet 4.1 Day 1 (D2) Supplementary Worksheet 4.1 Day 2 Extra Practice: p. 206 #10-26 Probability , 83 Is able to find the probability of an event and use the results to make decisions. 87* Is able to calculate probabilities of dependent and independent events. Focus: D1: Find simple probability D2: More practice D3: Calculate mean, median, and mode D4: Frequency distributions Problems to pull from: (D1) Supplementary Worksheet Probability #1 (D2) Supplementary Worksheet Probability #2 Mean, Median, and Mode, Frequency Distributions 71* Is able to calculate mean, median, and mode of a set of data. 85* Is able to use relative frequency to determine information about surveys. Focus: D1: Calculate mean, median, and mode D2: Frequency distributions Problems to pull from: (D1) Supplementary Worksheet Mean, Median, and Mode #1 (D2) Supplementary Worksheet Frequency Tables #1 Unit Extra Practice: p. 777-780 06/22/17 LPS Algebra Ext 1 Syllabus Semester Two CHAPTER 4: Graphing Linear Equations and Functions Section 4.2 89* Is able to graph a line given a linear equation. Focus: D1: Solve for y D2: Checking solutions and writing a table of values D3: Graph Problems to pull from: (D1) Supplementary Worksheet 4.2 #1 (D2) Supplementary Worksheet 4.2 #2 (D3) p. 214 # 40-46, 48-55, 57-58 Section 4.3 132* Is able to classify lines by slope (horizontal, vertical, parallel, perpendicular, rising or falling). Focus: Graph horizontal and vertical lines Omit Example #4 Problems to pull from: (D1) p. 219 # 14-32, 35-36 (D2) Practice Worksheet 4.3A # 1-25 and 4.3B #1-10 Section 4.4 173* Is able to find the x- and y-intercept of a line given its equation. Focus: D1: Find x and y intercepts D2: Graph using x and y intercepts D3: Graphing Problems to pull from: (D1) p. 225 # 15-32 (D2) p. 225 # 33-47 (D3) Supplementary Worksheet 4.4 #3 Section 4.5 132* Is able to classify lines by slope (horizontal, vertical, parallel, perpendicular, rising or falling). 109* Is able to determine and use rate of change (slope). Focus: D1: Find slope by counting rise over run (either from a graph or from two points to plot); Discuss positive and negative slope ***Recommended 4.5 Lesson Opener (Chapter 4 Resource Book) D2: Use formula to find slope D3: Find slope of horizontal and vertical lines from graphs and by using the formula Problems to pull from: (D1) p. 233 # 5, 7-8, 10, 12, 13-18, 19, 21 (D2) Supplementary Worksheet 4.5 #2, p. 234-235: 35-38, 41-43 (D3) Supplementary Worksheet 4.5 #3, p. 235: 44 06/22/17 Section 4.7 132* Is able to classify lines by slope (horizontal, vertical, parallel, perpendicular, rising or falling). 172* Is able to find the slope and/or y-intercept of a line its given its equation. *** Supplementary Lesson (District Collaborative Group) ***Note: Parallel lines will be taught in section 5.6 Focus: D1: Write equations in slope-intercept form: Find slope and y-intercept D2: Write equations in slope-intercept form; Graph using slope and y-intercept D3: Practice with emphasis on graphing D4: Identify parallel lines ***Supplementary Collaborative Lesson/ and worksheets Emphasize: slope = m, y-intercept = b Problems to pull from: (D1) (D2) (D3) (D4) p. 246 # 11-25 and p. 249 # 67-68 p. 246-248 # 26-37, 55-60 Supplementary Worksheet 4.7 #3 p. 247-249 # 38-40, 43-48 for more practice find your own supplementary material. Section 4.8/1.8 147* Is able to determine whether or not a given relation is a function. Focus: D1: Make input-output table; Determine functions, domain, and range. Determine if a relation is a function by looking at an input/output table, a mapping, and a graph (Vertical Line Test) D2: Evaluate a function; Use function notation D3: Graph a function D4: Find the domain of a function. Problems to pull from: (D1) (D2) (D3) (D4) Supplementary Worksheet 1.8 Day 1 and 4.8 Day 1 Supplementary Worksheet 4.8 Day 2 Supplementary Worksheet 4.8 Day 3 Supplementary Worksheet 4.8 Day 4 CHAPTER 5: Writing Linear Equations Method 1- Teach straight through sections 5.1-5.3, 5.5 in order Section 5.1 132* Is able to classify lines by slope (horizontal, vertical, parallel, perpendicular, rising or falling) 168* Is able to write a linear equation given a point and slope. 171* Is able to write a linear equation given its graph. 172* Is able to find the slope and/or y-intercept of a line its given its equation. 175 Is able to convert linear equations to standard form or slope-intercept form. Focus: D1: Students will be able to write a linear equation in slope intercept form given the slope and the y intercept.. (Given information can be determined from graphs as well as numerically.) D2: More practice. Problems to pull from: (D1) p 272 13-39, 54-55 (D2) Practice 5.1A 1-24, Practice 5.1B 1-18 06/22/17 Section 5.2 168* Is able to write a linear equation given a point and slope. ***Note: Omit point slope form of a line ***Note: Parallel lines will be taught in section 5.6 Focus: D1: Students will be able to write a linear equation in slope intercept given the slope and a point on the line. All slopes are integers. (Given information can be determined from graphs as well as numerically.) D2: Same as above only slopes are in fraction form. D3: More practice as needed. ***On all book assignments and worksheets from the resource book, change directions to: “ Write linear equations in slope intercept.” Problems to pull from: (D1) Supplementary Worksheet 5.2 #1, p. 281 # 7-8, 10-12, 19-31, 35, 38-39, 41, 43 (D2) p. 281 # 14-34, 44-45, 51 (D3) Practice 5.2A # 1-12, Practice 5.2B #1-12 Section 5.3 169* Is able to write a linear equation given two points. 175 Is able to convert linear equations to standard form or slope-intercept form. Focus: D1: Students will be able to write a linear equation in slope intercept given 2 points Slopes are integers. (Given information can be determined from graphs as well as numerically.) D2: Same as above only slopes are in fraction form. D3: More practice as needed. Problems to pull from: (D1) Supplementary Worksheet 5.3 # 1, p. 288 # 8, 13, 15, 17, 18, 20, 21, 23, 24, 28-31, 33 (D2) Supplementary Worksheet 5.3 # 2, p. 288 # 3-7, 9-12, 14, 16, 19, 22, 25-27, 32, 34-39, 41-42 (D3) Practice 5.3A # 1-15. 19 Section 5.5 127*Is able to translate verbal sentences into algebraic equations or inequalities. Focus: D1: Students will be able to identify the slope and what it represents and the y intercept, and what it represents from a verbal model (equation is given). D2: Given the slope and y intercept, write the equation in slope intercept from and interpret its meaning. D3: Given a point and the slope, write the equation in slope intercept form and interpret its meaning. D4: Extra Practice Problems to pull from: (D1) Supplementary Lesson 5.5, example 1 and worksheet 1. (D2) Supplementary Lesson 5.5, example 2 and worksheet 2. (D3) Supplementary Lesson 5.5, example 3 and worksheet 3. (D4) p. 301-302 #7-23, omit 15, 22, 44-49 Practice Wksh 1.5B #1-11 06/22/17 Method 2: 5.5 included in 5.1-5.2 (rather than separate) Supplemental Material 5.3 Same as Method 1 5.1: 5.1 Day 1 Worksheet 5.1 Day 2 Student Notes and Worksheet 5.1 Day 3 Student Notes and Worksheet 5.1 Day 4 Student Notes and Worksheet 5.2: 5.2 Day 1 Worksheet 5.2 Day 2 Student Notes and Worksheet 5.2 Day 3 Student Notes and Worksheet Section 5.6/4.7 132* Is able to classify lines by slope (horizontal, vertical, parallel, perpendicular, rising or falling). 169* Is able to write a linear equation given two points. Investigation activity: Pg 274 44-46 for day 1. Focus: D1: Identify parallel lines & write equation of a line parallel to a given line through a given point. D2: Write equations of perpendicular lines. D3: Extra Practice Problems to pull from: (D1) p 247-249 #49-54, 63, 64, 69; Supplementary Worksheet 5.6 #1 (D2) p. 309-311 # 11-16, 32-39, 44-45, 48; Practice 5.6A # 1-18 (D3) Supplementary Worksheet Extra Practice: 4.7A Practice Worksheet 22-25 CHAPTER 6: Solving and Graphing Linear Inequalities Section 6.1 104*Is able to graph an inequality on a number line. 116*Is able to solve inequalities. Focus: D1: Write an inequality in symbolic form, verbal form and graph D2: Solve one-step inequalities using addition or subtraction Problems to pull from: (D1) Supplementary Worksheet 6.1 Day 1 (D2) Supplementary Worksheet 6.1 Day 2 and p 327, 57-58, 60 Section 6.2 104*Is able to graph an inequality on a number line. 116*Is able to solve inequalities. Focus: D1: Solve one-step inequalities using multiplication or division with a positive number D2: Solve one-step inequalities using multiplication or division with a negative number D3: More practice Problems to pull from: (D1) Supplementary Worksheet (D2) Supplementary Worksheet (D3) Practice worksheet 6.2A or 6.2B 06/22/17 Section 6.3 104*Is able to graph an inequality on a number line. 116*Is able to solve inequalities. Focus: D1: Solve multi-step inequalities with a variable on one side D2: Solve multi-step inequalities with ( ) and variables on both sides D3: More practice Problems to pull from: (D1) Supplementary Worksheet 6.3 #1 (D2) Supplementary Worksheet 6.3 #2 (D3) Practice Worksheet 6.3 A Extra Practice: Practice Worksheet 6.3B and Supplementary Worksheet 6.3 #3 Section 6.4 104*Is able to graph an inequality on a number line. 116*Is able to solve inequalities. Focus: D1: Write in words, symbols, and graph compound inequalities with “and” D2: Solve compound “and” inequalities (no reversal of signs) D3: Solve more complicated compound “and” inequalities (reversal of signs) Problems to pull from: (D1) Supplementary Worksheet 6.4#1 (D2) p. 346-347 # 29-38, 48 (D3) p. 346 # 22-28, 39-46 Section 6.5 104* Is able to graph an inequality on a number line. 116* Is able to solve inequalities. Focus: D1: Write in words, symbols, and graph compound inequalities with “or” D2: Solve compound “or “ inequalities D3: Extra Practice Problems to pull from: (D1) Supplementary Worksheet 6.5 #1 (D2) p. 352 # 21-40, 43-45 (D3) Practice Worksheet 6.5B Section 6.6 121*Is able to solve absolute value equations and inequalities. ***Omit Examples 4 and 5 Focus: D1: Review absolute-value; Solve one-step absolute value equations D2: Solve multi-step absolute-value equations D3: Solve multi-step absolute value equations where the absolute-value must be isolated Problems to pull from: (D1) p. 358 # 10-27 (D2) Practice Worksheet 6.6B 1-30 (D3) pp. 359-360 # 32-40, 50, 51 p. 788 # 33-35 06/22/17 Section 6.7 121*Is able to solve absolute value equations and inequalities. . Focus: D1: Solve one-step absolute-value inequalities D2: Solve multi-step absolute-value inequalities D3: Solve multi-step absolute-value inequalities where the absolute-value must be isolated Problems to pull from: (D1) p. 364 # 14-25 (D2) Practice Worksheet 6.7B 1-7, 10, 13-18, 20-27 (D3) p. 365 # 30-41, 44-45, 48-49 Section 6.8 92* Is able to graph linear inequalities. 116*Is able to solve inequalities. Focus: D1: Review slope-intercept and how to graph using the slope and y-intercept D2: Discuss dotted/solid lines; Check Solutions (suggested Practice 6.8A 1-6), Graph linear inequalities in slope-intercept form. D3: Graph linear inequalities using y = mx + b Graph vertical and horizontal lines D4: More practice 32-35 suggested Warmup Problems to pull from: (D1) Supplementary Worksheet 6.8 Day 1 (D2) Supplementary Worksheet 6.8 Day 2 (D3) Supplementary Worksheet 6.8 Day 3 (D4) p. 371 # 32-50, 55-56 Chapter 4-6 Reviews included in Supplemental Materials 06/22/17