![Eighth Grade Test questions---1895 Arithmetic [Time, 1.25
hours]
1. Name and define the Fundamental Rules of Arithmetic.
2. A wagon box is 2 ft. deep, 10 feet long, and 3 ft. wide. How
many bushels of wheat will it hold?
3. If a load of wheat weighs 3942 lbs., what is it worth at
50cts/bushel, deducting 1050 lbs. for tare?
4. District No. 33 has a valuation of $35,000. What is the
necessary levy to carry on a school seven months at $50 per
month, and have $104 for incidentals?
5. Find the cost of 6720 lbs. coal at $6.00 per ton.
Parent Session EARJ 2013](https://image.slidesharecdn.com/ismmsparent-131112002759-phpapp02/85/Erma-Anderson-MS-Parent-Coffee-2013-60-320.jpg)
Erma Anderson MS Parent Coffee 2013
- 1. At The Crossroads Meeting the Challenges of a Changing World Parent Session SAS 2013
- 2. What Are Our Challenges? Of the 20 fastest growing occupations, 15 need extensive math and science preparation Parent Session SAS 2013
- 3. Parent Session SAS 2013
- 4. Mathematical thinking . . . A gateway to higher mathematics? OR A wall blocking path for students? Parent Session SAS 2013
- 5. The Future 75 % of jobs will be in STEM Not just STEM careers, it is STEM in every job Technology as a global knowledge economy is the future, and it requires different skills. future Business and industry want employees with these skills! 5
- 6. 21st Century Learning We are responsible for preparing students to address problems we cannot foresee with knowledge that has not yet been developed using technology not yet invented. Ralph Wolf Parent Session EARJ 2013
- 7. Jobs of the Future The TOP 10 jobs in 2015 are not yet invented. Parent Session EARJ 2013
- 8. 21st Century Skills Framework Thinking and Learning Skills Critical Thinking & Problem Solving Skills Creativity & Innovation Skills Communication & Information Skills Collaboration Skills Parent Session EARJ 2013
- 10. What Does It Mean to Understand Mathematics? Knowing Understanding Understanding is the measure of quality and quantity of connections between new ideas and existing ideas ASB MCI2 Problem Solving
- 11. Understanding is the key to remembering what is learned and being able to use it flexibly. - Hiebert, in Lester & Charles, Teaching Mathematics through Problem Solving, 2004.
- 12. A Thought People who do not understand mathematics today are like those who could not read or write in the industrial age. Robert Moses ASB MCI2 Problem Solving
- 13. The Bridge To Understanding Representation SEEING Stage Concrete DOING Stage Abstract SYMBOLIC Stage Parent Session EARJ 2013
- 14. Building Mathematical Concepts Concrete Manipulatives Pictorial Representation Abstract Symbols IIII 4+4=8 IIII 2x4=8 *Significant time must be spent working with concrete materials and constructing pictorial representations in order for abstract symbol and PARENT 2013
- 15. Value Multiple Representations concrete or pictorial symbolic graphical tabular verbal Parent Session EARJ 2013
- 16. Conceptual vs. Procedural Knowledge Conceptual (connected networks) Knowledge and understanding of logical relationships and representations with an ability to talk, write and give examples of these relationships. Procedural (sequence of actions) Knowledge of rules and procedures used in carrying out routine mathematical tasks and the symbols used to represent mathematics. -- David Allen The question of which kind of knowledge is most important is the wrong question to ask. Both kinds of knowledge are required for mathematical expertise... Instead, we should focus on designing teaching environments that help students build internal representations of procedures that become part of larger conceptual networks. James Heibert and Tom Carpenter, Learning and Teaching with Understanding, 1992
- 17. Phil Daro
- 18. Priorities in Mathematics Grade Priorities in Support of Rich Instruction and Expectations of Fluency and Conceptual Understanding K2 Addition and subtraction, measurement using whole number quantities 35 Multiplication and division of whole numbers and fractions 6 7 8 Ratios and proportional reasoning; early expressions and equations Ratios and proportional reasoning; arithmetic of rational numbers Linear algebra 5/29/12
- 19. Key Fluencies Grade Required Fluency K Add/subtract within 5 1 Add/subtract within 10 Add/subtract within 20 2 3 Add/subtract within 100 (pencil and paper) Multiply/divide within 100 Add/subtract within 1000 4 Add/subtract within 1,000,000 5 Multi-digit multiplication 6 Multi-digit division Multi-digit decimal operations 7 Solve px + q = r, p(x + q) = r 8 Solve simple 22 systems by inspection 19
- 20. Number Sense Howden (1989) described it as good intuition about numbers and their relationships. It develops gradually as a result of exploring numbers, visualizing them in a variety of contexts, and relating them in ways that are not limited by traditional algorithms. .
- 21. Prior Understandings 2.G.2. Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. www.JennyRay.net 21
- 22. Distributive Property & Area Models 3 x 7 =__ 3 5 + 2 15 + 6 3x7= 3 x (5 + 2) = (3 x 5) + (3 x 2)= 15 + 6 = 21 www.JennyRay.net 22
- 23. Area Models 25 x 38= 950 20 + 5 30 + 8 150 40 600 160 750 + 200 = 950 www.JennyRay.net 23
- 24. 27 x 4 Partitioning Strategies for Multiplication 27 x 4 4 x 20 = 80 4 x 7 = 28 27 + 27 + 27 + 27 108 54 54 108 ----------------------------------267 x 7 7 x 200 = 1400 7 x 60 = 420 1820 1876 www.JennyRay.net 24
- 25. 14 x 25: An Area Model 20 80 200 + 5 20 50 www.JennyRay.net 25
- 27. Partial Products 38 x 19 30 x 10 78 x 54 300 70 x 50 30 x 9 270 70 x 4 280 8 x 10 3500 8 x 50 400 8x9 80 + 72 8x4 722 + 32 4212
- 28. Partial Products (Area Model) 62 x 18 60 2 600 480 10 600 20 20 16 8 480 16 1116
- 29. 54 x 37 1500+350+120+28 =1998 50 4 30 1500 120 7 350 28
- 30. Decimals 3 x 0.24 0.3 x 0.6 0.12 + 0.60 = 0.72
- 31. Draw a picture that shows 2 3 3 4
- 32. Array 2 of 3 rows 3 of 4 in each row shaded area 2 rows of 3 6 1 = = = total area 3 rows of 4 12 2
- 33. Mixed Numbers, too! 8x3他 8 x 3 = 24 3 24 8x = =6 4 4 24 + 6 = 30
- 34. Wheres the Math? Models help students explore concepts and build understanding Models provide a context for students to solve problems and explain reasoning Models provide opportunities for students to generalize conceptual understanding
- 36. Multiplication (rational numbers) What does 4 x 3 mean? 4 x 2/3 = 4 groups of 2/3 each = 4X2/3 =2/3+2/3 +2/3+2/3+2/3 = 8/3 Why is it not 8/12?
- 37. Multiplication number line model Aoife earns 12 per hour. What would she earn in 2, 3, 4, 3/4 hours? Notice of becoming multiplication 3/4 x12 = 12 x 他 =9
- 38. Multiplication Area Model Cara had 2/5 of her birthday cake left from her party. She ate 他 of the leftover cake. How much of the original cake did she eat? 2/5 cake Divide into quarters 他 of 2/5 3 2 6 3 = = 4 5 20 10 Multiplication making smaller http://www.learner.org/courses/learningmath/number/session9/part_a/try.html Area of 3x2 out of area of 4x5
- 39. A muffin recipe requires 2/3 of a cup of milk. Each recipe makes 12 muffins. How many muffins can be made using 6 cups of milk? Adapted from Multiplicative Thinking. Workshop 1. Properties of Multiplication and Division. http.nzmaths.com, 2010.
- 40. The Additive Thinker A muffin recipe requires 2/3 of a cup of milk. Each recipe makes 12 muffins. How many muffins can be made using 6 cups of milk?
- 41. 2 1 3 4 2 Each rectangle represents a third of a cup of milk.
- 42. A muffin recipe requires 2/3 of a cup of milk. Each recipe makes 12 muffins. How many muffins can be made using 6 cups of milk?
- 43. Content + Practices The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important processes and proficiencies with longstanding importance in mathematics education. (CCSS, 2010) Parent Session EARJ 2013
- 44. Learning happens within students, not to them. Learning is a process of making meaning that happens one student at a time. Carol Ann Tomlinson and Jay McTighe and Integrating Differentiated Instruction Understanding by Design 息 2006
- 45. 1 Make sense of problems and persevere in solving them 2 Reason abstractly and quantitatively 5 4 Model with mathematics Standards for Mathematical Practice 6 Look for and make use of structure Construct 3 viable arguments and critique the reasoning of others 7 Attend to precision Use appropriate tools strategically. 8 Look for and express regularity in repeated reasoning
- 46. Grouping the Standards of Mathematical Practice 1. Make sense of problems and persevere in solving them. 6. Attend to precision. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. Overarching habits of mind of a productive mathematical thinker. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. William McCallum University of Arizona- April 1, 2011 Reasoning and explaining Modeling and using tools. Seeing structure and generalizing.
- 47. 1. Make sense of problems and persevere in solving Do students: EXPLAIN? ANALYZE? Make CONJECTURES? PLAN a solution pathway? MULTIPLE representations? Use DIFFERENT METHODS to check? Check that it all makes sense? Understand other approaches? See connections among different approaches?
- 48. 2. Reason abstractly and quantitatively Do students: Make sense of quantities & their relationships? Decontextualize? Contextualize? Create a coherent representation? Consider units involved? Deal with the meaning of the quantities?
- 49. 3. Construct viable arguments and critique the reasoning of others. Do students: Understand & use stated assumptions, definitions, and previous results? Analyze situations, recognize & use counterexamples? Justify conclusions, communicate to others & respond to arguments? Compare the effectiveness of 2 plausible arguments? Distinguish correct logical reasoning from flawed & articulate the flaw? Look at an argument, decide if it makes sense,& ask useful questions to clarify or improve it? Make conjectures& build a logical progression?
- 50. 4. Model with mathematics Do students: Apply the mathematics they know everyday? Analyze relationships mathematically to draw conclusions? Initially use what they know to simplify the problem? Identify important qualities in a practical situation? Interpret results In the context of the situation? Reflect on whether the results make sense?
- 51. 5. Use appropriate tools strategically. Do students: Consider available tools? Know the tools appropriate for their grade or course? Make sound decisions about when tools are helpful? Identify & use relevant external math Sources? Use technology tools to explore & deepen understanding of concepts?
- 52. 6. Attend to precision. Do students: Communicate precisely with others? Use clear definitions? Use the equal sign consistently & appropriately? Calculate accurately & efficiently?
- 53. 7. Look for and make use of structure. Do students: Look closely to determine a pattern or structure? Use properties? Decompose & recombine numbers & expressions? Have the facility to shift perspectives?
- 54. 8. Look for and express regularity in repeated reasoning. Do students: Notice if calculations are repeated? a% of b =b Look for general methods & shortcuts? Maintain process while attending to details? Evaluate the reasonableness of intermediate results? %o fa
- 55. Shift in Mathematics #1 Deeper Learning Fewer Concepts How Parents Can Help Students at Home Students must Parents can Spend more time on fewer concepts Know what the priority work is for the grade level Represent math in multiple ways Ask, Can you show me that in another way? Apply strategies, not just get answers Focus on how the child is tackling the problem over what the answer is
- 56. Shift in Mathematics #2 Focus on Strong Number Sense and Problem Solving How Parents Can Help Students at Home Students must Parents can Be able to apply strategies and use core math facts quickly Ask the childs teacher what core math facts should be practiced at home Ask students which strategies they are using Compose and decompose numbers Help children break apart and put together numbers to make problem solving easier
- 57. Shift in Mathematics #3 Focus on Communication of Thinking and Language Rich Classrooms How Parents Can Help Students at Home Students must Parents can Understand why the math works explain and justify Ask questions to find out whether the child really knows why the answer is correct Talk about why the math works explain and justify Ask children to explain how they solved the problem and why they chose the strategies they used Prove that they know why and how the math worksexplain and justify Ask children to show how they know they have the correct solution Talk about alternative strategies Use academic vocabulary to explain their reasoning and critique that of others Expect children to use the language of math Talk about math
- 58. Shift in Mathematics #4 Perseverance and Grappling with Mathematics How Parents Can Help Students at Home Students must Parents can See mistakes as learning opportunities Help their children use their mistakes as windows into their thinking Understand that there is usually more than one way to solve a problem Celebrate and value alternative responses Ask, Is there another way to solve this? Spend more time solving a single problem in a deep way Expect fewer problems but more writing and explaining in homework
- 59. Making Sense of Mathematics? ?:?? Which is more rigorous ? 1895? 1931? 2012? PARENT 2013
- 60. Eighth Grade Test questions---1895 Arithmetic [Time, 1.25 hours] 1. Name and define the Fundamental Rules of Arithmetic. 2. A wagon box is 2 ft. deep, 10 feet long, and 3 ft. wide. How many bushels of wheat will it hold? 3. If a load of wheat weighs 3942 lbs., what is it worth at 50cts/bushel, deducting 1050 lbs. for tare? 4. District No. 33 has a valuation of $35,000. What is the necessary levy to carry on a school seven months at $50 per month, and have $104 for incidentals? 5. Find the cost of 6720 lbs. coal at $6.00 per ton. Parent Session EARJ 2013
- 61. Eighth Grade Test 6. Find the interest of $512.60 for 8 months and 18 days at 7 percent. 7. What is the cost of 40 boards 12 inches wide and 16 ft. long at $20 per metre? 8. Find bank discount on $300 for 90 days (no grace) at 10 percent. 9. What is the cost of a square farm at $15 per acre, the distance of which is 640 rods? 10. Write a Bank Check, a Promissory Note, and a Receipt Parent Session EARJ 2013
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- 63. Parent Session EARJ 2013
- 64. Parent Session EARJ 2013
- 66. A thought We can best close the achievement gap by eliminating the opportunity gap. If we, as mathematics teachers K-12, each make it our personal goal for every student to have the opportunity to learn mathematics in ways that promote the habits of mind espoused in the standards for mathematical practice, we will be successful in helping all students to be successful in learning and doing mathematics. Parent Session EARJ 2013
- 67. Together we make a difference! PARENT 2013
Editor's Notes
- #28: The first alternative to the standard algorithm is multiplying using partial products. This strategy is about using decomposition and place value, two critical aspects of all mathematics. What challenges could you see for a student using this method? (Allow time for discussion)
- #29: Here is the same partial products strategy used within an area model. Students draw a rectangle and divide given the number of digits in each number. For example 62 is divided into 60 (six tens) and 2. Once the student has each number decomposed, he then multiplies each column by each row. For example, 10 times 2 is equal to 20, while 10 times 60 is equal to 600. The answer is represented by the area of a rectangle with sides 62 and 18.
- #30: Lets try one. Here is the problem 54 x 37. Given the number of digits in 54 and 37, what will be the dimension's of my rectangle? ( 2 by 2) What is the next move? Decompose each number and note on the rectangle. Click Next we multiply each column and row. Click to show product of each. Finally we add all of the products together to find the answer to our initial problem. Click
- #48: Handout #2: Susies SMPs Follow along, underline or highlight words. The paragraphs are dense, I had to separate them and make an outline so that I could understand them (show my outline)
- #50: .