2009 Mathematics Standards of Learning – Implementation Supported by Professional Development

1. 2009 Mathematics Standards of Learning – Implementation Supported by Professional Development 4th – 5th Grade Math Presentation Session #1 February 2011 Parts taken from Michael Bolling’s (Mathematics Coordinator) – VSUP Presentation

2. The point U(-6, -3) is translated 3 units right. What are the coordinates of the resulting point, U′? The 2009 SOL and the new SOL Assessments • Increased rigor • Higher-level questions • Technology enhanced items

3. Gr 5- New Content Changes What’s new/ in focus? Identify and describe prime and composite numbers Measure and draw angles and triangles. New EmphasizedVocab. 5.4 – Create and solve single step and multistep practical problems for addition, subtractions, multiplication and. INCLUDE DIVISION with and without remainders. Equilateral Scalene Isosceles Volume Line graphs Stem and Leaf plots Identify and describe the characteristics of even and odd numbers 5.5b – Create and solve single step and multistep practical problems involving decimals. COMPARE and ORDER fractions and decimals Division with decimals – computation only 5.7 – Evaluate whole number expressions using order of operations limited to parentheses, +, -, X and / 5.8a – Find perimeter, areas and VOLUME in standard units Model one-step linear equations in one variable using addition and subtraction. Estimate and measure length, weight/mass, area, and liquid volume 5.16 – Describe mean as Fair Share (M, M, & M as measures of center Measure and classify angles (added straight angles) Classify triangles - add - Equilateral, Scalene, and Isosceles Triangle 5.19 – Investigate and recognize distributive property of addition over multiplication 3

4. 5.2 a) Recognize equivalent fractions/decimals. B) compare and order fractions & decimals 7.1 c) Compare and order fractions, decimals, percents, and scientific notation 6.2 a) compare/order fractions, decimals, and % 6.4 model multiplication and division of fractions New content New content A sample of the progression of fractions. K.5 Identify halves and fourths 2.3 Identify/ write/compare halves, thirds, fourths, sixths, eighths, tenths 3.3 c) compare fractions with like/unlike denominators 4.2 a) compare and order fractions /mixed numbers 1.3 Identify/ write halves, thirds, fourths

5. 2.a,b - Identify parts of sets and/or regions that represent halves, thirds, fourths, sixths, eighths, and tenths. Write the fractions ( and not just unit fractions) Which model represents 2/3 of a set?

6. Third grade adds 1/12ths (previously students will learn ½, ¼, 1/3, 1/8, 1/10) FAIR SHARE 2 2 2 2 2 2 2 2

7. Third grade adds 1/12ths (previously students will learn ½, ¼, 1/3, 1/8, 1/10) FAIR SHARE 2 2 2 2 2 2 2 2

8. Grades 1 & 2 – Unit Fractions (1/2, 1/3, ¼, 1/6, 1/8, 1/10) 0 Help them understand the size relationship between ¼, 1/3, and ½ of a given whole. Talk about: Which is greater? Which is less? 1 4 1 3 1 2 1

9. 3.3c – Compare Fractions using >, <, or = signs)(1/2, 1/3, ¼, 1/8, 1/10, 1/12) 4.2 Compare and order fractions/mixed numbers (Number line will be important!) 0 1 1 10 1 8 1 4 1 2 1 3 1 12

10. 4th Grade - Comparing fractions to benchmarks Gr. 3 will add and subtract fractions with denominators of 12 or less. They will also learn X facts through 12’s (was 9’s)

11. Assessing Higher-level Thinking Skills 3.7 The student will add and subtract proper fractions having denominators of 12 or less.

12. Assessing Higher-level Thinking Skills 4.3 d) The student will, given a model, write the decimal and fraction equivalents. 0.2 or 4.2 equivalent fractions

13. Assessing Higher-level Thinking Skills 4.13 b) The student will represent probability as a number between 0 and 1, inclusive. Where on the number line would you place an arrow to show the probability of choosing a green marble? Jennifer has 12 marbles. 8/12 2/3

14. The Number line!

16. Assessing Higher-level Thinking Skills 6.20 The student will graph inequalities on a number line. Students will need a solid conceptual understanding of inequalities before going to Middle School based upon the NUMBER LINE! 4 4

17. Assessing Higher-level Thinking Skills 8.5 b) The student will find the two consecutive whole numbers between which a square root lies. How you can help. Necessary Background: Students will need a thorough understanding and mastery of the number line and perfect squares. (also numbers, fractions, and decimals) Between which two whole numbers does lie? Between which two square roots does 5 lie? Between 5 and 6 Between SQR(16) and SQR (36) SQR (16) (25) (36) (49) SQR (16) (25) (36) (49) 4 5 6 7 4 5 6 7

18. Equality and Properties – preparation for justifications 7.16 a-e) applyproperties with real numbers, comm/associative property of +/X, distributive, +/X identity, +/X inverse, X property of 0 New from grade 7 Newfrom grade 7 6.19 a-c) investigate and identify property of +/X, multiplicative property of zero, inverse property for multiplication New content New from grade 3 1.18 demonstrate equality using equal signs 3.20 a) identity/ commutative properties for add/mult 4.16 b) associative property for add/mult 5.19 distributive property of multiplication over addition Leading into students giving justifications to steps when solving equations and inequalities in MS and HS 2.22 demonstrate an understanding of equality using = and ≠

19. Equations and Inequalities What does the equal sign mean?

20. Equality Where are we headed? • Connected to N&NS SOL 2.1c • 1.18 The student will demonstrate an understanding of equality through the use of the equal sign. • 2.22 The student will demonstrate an understanding of equality by recognizing that the symbol = in an equation indicates equivalent quantities and the symbol ≠ indicates that quantities are not equivalent. • 5 + 3 = • AND THE ANSWER IS…….? • Now students should think about options to balance the equation on the right side. List 5 options that would make the sentence balance? • 8,10-2, 1+7, • 5 + 3 2+5+1, 3+10-5

21. Equalities -2009 SOL 4.16a recognize/demonstrate meaning (thinking) of equality in an equation. What will the students say? 8 = 1 + 7 True or False? 2 + 3 = 2 x 3 3 + 5 = 5 + 3 7 x 4 = 4 + 4 + 4 + 4 How many different ways can you show 9 = 9?

22. SOL 2.22 demonstrate understanding of equality and not equal signs SOL 1.18 demonstrate equality using an equal sign Equal Sign = Not Equal Sign = http://illuminations.nctm.org/ActivityDetail.aspx?id=33

23. Inequalities 2009 SOL 3.20(C.F. - Essential Understanding ) 4 4 3 2

24. Equalities 2009 SOL 3.20(C.F. - Essential Understanding ) Commutative Property of addition The order with which you add the numbers doesn’t change anything. Both sides are still equal. Grade 1 4 4 3 3

26. Equalities - 2009 2 X ( 3 + 1 ) ( 2 X 3 ) + (2 X 1) 4 4 3 3 Gr5 – Distributive Property of Multiplication over Addition 26

27. Equalities (use to prove properties) http://illuminations.nctm.org/ActivityDetail.aspx?id=26

28. Equalities/Properties2009 SOL Gr. 4 – Associative property of addition and multiplication Gr. 5 Distributive Property of multiplication over addition Identity Property of Addition/Multiplication 8 + 0 = 8 8 x 1 = 8 Commutative Property of Addition/Multiplication 4 + 3 = 3 + 4 2 x 5 = 5 x 2

29. Modeling One-step Linear Equations2009 SOL 5.18c Using a cup and candy corn, construct a model for J = 6

30. Modeling One-step Linear Equations2009 SOL 5.18c How many pieces are represented by the jack-o-lantern?

31. Modeling One-step Linear Equations2009 SOL 5.18c Using your cups and candy corn, construct a model for J + 4 = 7

32. Modeling One-step Linear Equations2009 SOL 5.18c J = 3 pieces of candy

33. What equation is modeled below? B + 2 = 9

34. Assessing Higher-level Thinking Skills 5.8 c) The student will model one-step linear equations in one variable, using addition and subtraction. = x = 1

35. We can all continue concept of variable (Previous Grades) ?

36. Expressions and Operations 5.7 Order of Operations 7.3 operations with integers 7.13 evaluate algebraic expressions 6.8 Order of Operations no { }, | | Only ( ) 8.1 simplify numerical expressions involving positive exponents, using rational numbers, order of operations, and properties to justify Alg1.1 represent verbal quantitative situations algebraically/evaluate expressions for given replacement values of variables New from grade 7 New from grade 7 New content including (modeling)

37. Assessing Higher-level Thinking Skills 3rd Order of Operations 5.7 2nd 1st 6.8 , given x = -2 7.13b evaluate

38. Statistics Alg1.9 – Standard deviation, mean absolute deviation, variance, dispersion, z-scores New content 5.16 Mean as Fair Share Alg2.11 Normal Distributions Alg1.9 Standard Deviation 6.15 Mean as Balance Point New content New content New content

39. Mean as Fair Share Average: (10 + 8 + 3) / 3 items = 7 10 8 3

40. Mean as Fair Share Average: (10 + 8 + 3) / 3 items = 7 7 7 7

41. Mean as Balance Point 3 8 10 It’s all about the total distance away from the “mean/average” Helps to create a foundation to understand “absolute value” 7 41

42. SOL 4.14 – Collect, organize, display, interpret data from a variety of graphs • collect and organize data • Recollect and compare data • observe, measure, surveys, experiments • Construct line plots, bar graphs and picture graphs to represent the data • Read and Interpret the data in these graphs

43. Statistics in Algebra One How can you help? Help students become comfortable in collecting, displaying, and analyzing data. They should also be able to make logical predictions from the data. http://www.mathwire.com/ Collect data, display and analyze data, understand the behavior of data sets, understand how data is spread about the mean, how is this used to inform decisions 43

44. Ask extended questions: • Define the days where the number of students ordering lunch is increasing. • Which days is the number of students ordering lunch decreasing? • Where is the data not increasing? • Where is the data not decreasing? • Talk about : • how data is sometimes grouped in clusters • how sometimes there are data points that lie far from the group of data. • Discuss what conclusions can be made? Number of students ordering lunch M T W T F Sat Sun Ages of parents and grandparents

45. Assessing Higher-level Thinking Skills 3.6 The student will represent multiplication and division, using area, set, and number line models…

46. Assessing Higher-level Thinking Skills 3.9dThe student will estimate…area and perimeter. The curriculum framework says the student will also measure to determine area and perimeter.

47. Higher Order Thinking Skills Connected to N&NS SOL 3.2 1.6 The student will create and solve one-step story and picture problems using basic addition facts with sums 10 18 or less and the corresponding subtraction facts. 2.8 The student will create and solve one- and two-step addition and subtraction problems, using data from simple tables, picture graphs, and bar graphs 3.4 The student will estimate solutions to and solve single-step and multistep problems involving the sum and difference of two whole numbers, each 9,999 or less, with or without regrouping. the use of two or more operations; and operations can be different. 47

48. 4.4b & 4.5d – Solve single and multi-step practical problems involving add/sub/multi. of whole number and add/sub of fractions, and decimals K – 1 - Modeling to solve word problems Tamara had 3 pennies. She got 5 pennies for cleaning her room. Then she lost 2 pennies. How many pennies does she now have? Grade 3 Zach had 64 ounces of soda. He poured 8 ounces into each of 5 glasses. How much soda was left over? 48 Emily is reading the latest Magic Maggie book. She reads 12 pages each day. After 7 days, Emily still has 20 pages left to read. How many pages are in Emily's book?

49. Students need opportunities to solve various problem types through modeling, reasoning, and reflection to strengthen their mathematics understandings and use of concepts and skills. Let the students struggle, take a risk at getting it wrong, explain why, re-think, re-do! Check out this site: http://www.mathwire.com/problemsolving/probsk12.html#k12number

50. Assessing Higher-level Thinking Skills • 5.4 The student will create and solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division with and without remainders of whole numbers. • 5.5 The student will • a) find the sum, difference, product, and quotient of two numbers expressed as decimals through thousandths (divisors with only one nonzero digit); and • b) create and solve single-step and multistep practical problems involving decimals. • 5.6 The student will solve single-step and multistep practical problems involving addition and subtraction with fractions and mixed numbers and express answers in simplest form. 5.5 b) Michael jogged 3.4 miles each day for 3 days. Jennifer jogged 4.2 miles each day for the same 3 days. What is the difference between the number of miles Jennifer jogged and the number of miles Michael jogged on these 3 days?