1 / 61

2009 Mathematics Standards of Learning – Implementation Supported by Professional Development

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

peta
Download Presentation

2009 Mathematics Standards of Learning – Implementation Supported by Professional Development

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 2009 Mathematics Standards of Learning – Implementation Supported by Professional Development Third 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 3- New Content Changes Compare fractions using WORDS and SYMBOLS (greater than, less than, equal to) Add/sub proper fractions with like denominators of 12 or less (was 10 or less) New Vocab. Tell time to nearest minute Angles Vertices Points Lines rays MODEL fractions including mixed and WRITE NUMBERS (was divide regions and sets – moved down) Moved to grade 4 Reading, writing, adding, subtracting decimals ESTIMATE and solve up to multistep problems Estimate and measure area and perimeter Moved to grade 1 & 2 Demonstrate understanding of equality sign Estimate and measure length to the nearest ½ inch (was inch) Count square to determine area Id examples of the identity and commutative properties for addition and multiplication Determine elapsed time in one-hr. increments over 12 hour period Represent multi. and div. using area, set, and NUMBER LINE MODELS Recall multiplication facts through 12’s (was 9’s) 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. K.5 Identify the parts of a set and/or a region that represents halves and fourths. Recognize that fractions represent parts of equal size of a whole Grade 1: start taking about fair share. Write the fraction

  6. How many equal parts do you see? Why is this not cut into equal parts? Which is cut into fourths?

  7. New: 1st - Write the fraction ( K – halves and fourths1stgrade - Thirds ) 4 out of 12 1 3 1 3 4 4 Model one-third with 12 triangles? 4 1 3

  8. 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?

  9. 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

  10. 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

  11. 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

  12. 3.3c – Compare Fractions using >, <, or = signs)(1/2, 1/3, ¼, 1/8, 1/10, 1/12) 4th grade will order the unit fractions (Number line) 0 1 1 10 1 8 1 4 1 2 1 3 1 12

  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. 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 ≠

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

  16. 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

  17. 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

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

  19. 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

  20. Identity and Commutative Property of addition/multiplication • How would you show this with a balance scale? 2X3 = 3X2 • Add 2 groups of three on one side. • Add three groups of two on the other side. • Both sides will be equal

  21. EqualitiesSOL 2.22 and SOL 3.20 (use to prove properties) http://illuminations.nctm.org/ActivityDetail.aspx?id=26

  22. Equalities/Properties2009 SOL 3.20 Identity Property of Addition 8 + 0 = 8 Commutative Property of Addition 4 + 3 = 3 + 4 Identity Property of Multiplication 8 x 1 = 8 Commutative Property of Multiplication 2 x 5 = 5 x 2

  23. 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?

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

  25. Modeling One-step Linear Equations2009 SOL 5.18c How many to balance?

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

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

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

  29. 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

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

  31. How many apples would you need to replace the barrel ?Remember you must keep the equation equal. 3 Apples

  32. 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)

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

  34. 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 4 4

  35. 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

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

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

  38. 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 38

  39. SOL 3.17 – Analyze and interpret information with up to 30 data points and up to 8 categories, by writing one sentence. • 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

  40. 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 40

  41. 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? Ages of parents and grandparents

  42. Assessing Higher-level Thinking Skills 3.9dThe student will estimate…area and perimeter. Count the number of squares. Build and name geometric shapes using 24 squares.

  43. 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. 43

  44. Build skills to solve multi-step problems 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? Zach had 64 ounces of soda. He poured 8 ounces into each of 5 glasses. How much soda was left over? 44 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?

  45. 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

  46. 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?

  47. Assessing Higher-level Thinking Skills How you can help. Necessary Background: Give the students word problems to solve. Then ask them what would happen if one variable changed. Example: If you ran 3 minutes each day at recess for a total of 5 days. How many minutes would you have run for the week? Next: Ask how many total minutes would you have run if on Tuesday you ran more than usual and ran 8 minutes. 7.5 c) The student will describe how changing one measured attribute of a rectangular prism affects its volume and surface area. 5 in. Describe how the volume of the rectangular prism shown (height = 8 in.) would be affected if the height was increased by a scale factor of ½ or 2. V = h X 3 X 5 8 in. V = (8)(15) - original V = (4)(15) – height is half V = (16)(15) – height is double 3 in. The volume would be cut in half or doubled accordingly. SA = 2(l*w)+ 2(w*h) + 2(l*h)

  48. Note: Blueprints Changes • Some Reporting Categories Combined • Watch the growing emphasis on the Statistics, Patterns, Functions, and Algebra Reporting Category shown on the next slides

More Related