1 Building Content Knowledge Education Transformation Office Math Fourth GradeBuilding Content KnowledgeEducation Transformation Office
2 Common Board Configuration (CBC) DATE: August 2013Introductions:3 – ActivityVocabulary: Pacing guide, Skills Sheets,, Journal Entries , NGSSS, Item SpecsExit Slip:Revisit Essential QuestionBELL RINGER:BENCHMARK: Math and Resources and Content.AGENDA:I Do:Review focus group materialsWe Do:Teach One/Learn One ActivityThey Do:Map out how you’re going to teach the beginning of the year concepts.You Do:Processing Time: Answer the essential questionHomework InstructionObjective: Today we will explore the math review resources and best practices to teach the content effectively.ESSENTIAL QUESTION: How can exploring the math content and resources help me to be an effective teacher?
3 Write 2 actions that will assist you in meeting your goals 3-2-1Set 3 Goals for this school yearWrite 2 actions that will assist you in meeting your goalsWrite 1challenge that mayEncounter
4 Essential Question:How can exploring the math content help me to be a more effective teacher?
9 What is NEW???? GO MATH will now consist of all COMMON CORE Newly created Bellringers by benchmark including basic skill practiceTeacher Led Center (TLC) packets by benchmarksNew Dashboard for ThinkCentral
11 GO MATH Go Math textbooks are all correlated to Common Core. Schools will receive updated Common Core Teacher’s EditionsYou will continue to have access to the “Old GO MATH” with the NGSSS through thinkcentral.com
17 Digging Deeper Into the Math Content- 4th Grade TOPIC I: Place Value, Addition and Subtraction to One MillionNew Edition Common Core TextbookMACC.4NBT. 1.1; MACC.4NBT.1.2 ; MACC.4.NBT.1.3; MACC.4NBT. 2.4Infusing the NGSSS MA.4.A.6.1-Reading, Writing and Comparing Whole Numbers
18 OELCS 2005 Math Module 3 Speaker Notes Standards for Mathematical Practices“The Standards for Mathematical Practice are unique in that they describe how teachers need to teach to ensure their students become mathematically proficient. We were purposeful in calling them standards because then they won’t be ignored.”Mathematically literate students are able to analyze, reason, and communicate ideas effectively as they pose, formulate, solve and interpret mathematical problems in a variety of situations.~ Bill McCallum
19 OELCS 2005 Math Module 3 Speaker Notes Mathematical PracticesMake sense of problems and persevere in solving themReason abstractly and quantitativelyConstruct viable arguments and critique the reasoning of othersModel with mathematicsUse appropriate tools strategicallyAttend to precisionLook for and make use of structureLook for and express regularity in repeated reasoningMake Sense, Persevere, Reason abstractly and quantitatively, construct viable arguments, critique others reasoning, Model with mathematics , use tools strategically while attending to precision, structure and repeated reasoning
20 Topic I Mathematical Practices MP 2: Reason abstractly and quantitativelyMathematically proficient students can…have the ability to contextualize and decontextualize (navigate between the concrete and the abstract).manipulatives pictures symbolsunderstand and explain the computation methods they use.
21 Topic I Mathematical Practices MP 6: Attend to precisionMathematically proficient students can…use clear definitions and mathematical vocabulary to communicate their own reasoningcareful about specifying units of measure and labels to clarify the correspondence with quantities in a problem
22 Essential Content 1. Rounding A. Reading and Writing Numbers 1. Standard Form2. Expanded Form3. Written FormB. Place Value, Value of Digit and Face ValueOnesTensHundredThousandTen ThousandHundred ThousandMillionC. Estimate1. Roundingonestenshundredthousandten thousandhundred thousandmillion2. Compatible NumbersD. Problem Solving1. Adding numbers through millions2. Subtracting numbers through millions
23 Professional Development Podcasts * Found on Thinkcentral.com Under Resources
24 (Take two minutes to discuss with your group) MP 2 and MP 6 PD PodcastHow did you see the practice being implemented?What are some benefits by viewing the Podcasts?(Take two minutes to discuss with your group)
25 Benchmark Clarifications What Must Students Be Able to Do? Students will identify, compare and/or order numbers through the millions place in real-world contexts.Students will find the answers to real-world problems that involve adding and subtracting numbers through the millions.Students will make estimations of numbers through the millions in real-world situations.
26 What Are the Content Limits? Items may include the inequality symbols (>, <, , , ).Items will not include decimals or fractions.Items involving units of measure may not involve converting from one unit to another.Front-end estimation will NOT be an acceptable estimation strategy.
27 Always Know Your Benchmarks Found in Your Test Item Specifications These are theCommon CoreStandardsreplacing theNGSSS
29 What is FRONT END Estimation When using front-end estimation, use the first number without worrying about what it is closest to.
30 What Are Good Strategies ? Order from least to greatest256, 162, 2241. MAKE A PLACE VALUE CHART.2. Line numbers up ( Stackthem on top of each other).3. Compare from left to rightonce they are lined up correctly.4. Since the directions areleast to greatest, circlethe smallest number on theleft would be listedfirst.
31 Make a Place Value Chart 5. Put a line through the number already listed.6. The other numbers have the same digit. Circle both 2’s then compare the numbers directly behind. The number that is smallest will be listed next.7. Have the students compare the underlined numbers to see which one is smaller.8. Since 2 is the smaller number, 224 would be listed next and 256 is last.9. The order would be:162, 224, 256
32 Additional StrategyHave students place the numbers in the place value chart starting in the ones place.If there are a different amount of digits in the number, have the students place zeros in the front.4876823
33 The alligator always eats the larger number. Comparing StrategiesThe alligator always eats the larger number.* Read it like a sentence from left to right.6 is less than 1010 is greater than 6
34 Rounding Strategies 5 or more…raise the a score 1. Use rounding chant-4 or less…let it rest5 or more…raise the a score2. When estimating, round first and then complete problem.Example+ 296
35 Expanded Form12,5021. Start with the digit in the place value all the way to the left.2. Turn all of the numbers behind to zeros.3. Place a ( + ) sign between the numbers4. Repeat with each number moving from the left to the right.12,502= 10, ,OR10, x 10,000 = 10,0002, x 1,000 = 2,000x =x == 10, ,
36 The Bar Model to Subtract This visual bar model allows the students to see the pictorial representation. It will help them understand what DIFFERENCE means.
37 Suggested Activities 1. Make a flip chart 3. Mystery picture – Match the standard form with the word form2. Give students number from a chart to ORDER or COMPARE4. Place Value GameOn long strips of paper make place value charts, making sure the commas are in place and writing the words (ones, tens, hundreds, etc.) under the blank line where a number will be placed. With a partner and a deck of cards the children shuffle the deck and then pass out the predetermined number of cards according to how far you want them to learn place value. Hundred thousands would be 6 cards, millions 7 cards, 10 millions 8 cards, etc. Cards are face down in a pile. Face cards equal 1, aces are 0, and everything else what they say. They are trying to make the largest number possible to win (or smallest). Both players turn over a card at the same time and decide where to place it. Once placed, it must stay there. You must be able to say the number you made to win the pile of cards. They learn place value and soon move on to the strategy of where to place the cards to their best advantage. They continue until all the cards are used. The winner has the largest number.
38 End of the Topic Group Activity Collaborative Strategy- Numbered Heads1. Each individual will receive a popsicle stick with a number.2. Everyone with the same number will group as a pair to work on an a computation problem and a word problem.3. At this time choose who will be the:A. TeacherB. Student4. Teachers please explicitly teach the concept and incorporate the following in your lesson:A. Problem Solving StrategyB. Address Common Errors
39 Your Turn to Give It a Try (Think-Pair-Share) # 1 Estimate. Then find the difference.# 2
40 Your Turn to Give It a Try (Think-Pair-Share) # 1 Estimate. Then find the difference.# 2
41 How Do These Problems Relate to Mathematical Practices 2 & 6 Discuss with your partners and give at least three examples for Topic II(Take 5 minutes to record your responses)
42 Digging Deeper Into the Math Content- 4th Grade TOPIC Il: MultiplicationNew Edition Common Core TextbookMACC.4.NBT.2.5; MACC.4.OA.1.1; MACC.4.OA.1.2; MACC.4.OA.1.3;Infusing the NGSSS MA.4.A.1.1; MA.4.A.6.2; MA.4.A.6.4
43 Topic II Mathematical Practices MP 1: Make sense of problems and persevere in solving them.Mathematically proficient students can…explain the meaning of the problemmonitor and evaluate their progress “Does this make sense?”use a variety of strategies to solve problems
44 Topic II Mathematical Practices MP 4: Model with Mathematics.Mathematically proficient students can…apply mathematics to solve problems that arise in everyday lifereflect on their attempt to solve problems and make revisions to improve their model as necessary
45 Essential ContentA. Multiple Representations of Multiplication and Division of Whole Numbers1. Manipulatives2. Drawings3. Algorithms4. ComparisonsB. Recall Multiplication Facts 2-9 (Daily Routine)C. Multiplication Strategies1. Partial Product2. Distributive Property3. RegroupingD. Relate Repeated Addition to Multiplication.E. Relate Repeated Subtraction to DivisionF. Problem Solving1.Drawings2.Write number sentences3.Inverse operation
46 These are theCommon CoreStandardsreplacingthe NGSSS
48 Benchmark Clarifications What Must Students Be Able to Do? Students will solve real-world problems using basic multiplication and the related division facts.Students will solve multi-digit whole-number multiplication problems or supply partial products in real-world multiplication problems.
49 What are the Content Limits? Items may include whole-number multiplication facts from 0 X 0 through 12 X 12 and the related division facts.For items that require solving multi-digit multiplication problems, the two factors may not exceed three digits by three digits or four digits by two digits.When both factors have three digits, at least one digit must be a zero.1.(when the 0 is on the top,x switch it to the bottom) x 2502.x xThree digit byThree digitsFour digit byTwo digits
50 What Are Good Strategies? Teachers don’t need to stress the memorization of the property names as much as the application of what the property does.When teaching distributive property use the grid paper to model the break apart method.Emphasize place value when multiplyingMultiplication Ladder---track students learning their factsMultiplication with base ten blocks
51 Multiplication Comparisons (New with Common Core) This strategy will assist your students to better understand algebraic expressions.The [bracket] = the total of 15(as 5)is5) ina single box onTop or bottom(3 times) draw 3 boxes of 5
57 Using Partial Products for Solving Multi-product Multiplication ExpandX Expand40 x 70 = x 8 = x 5 = x = ,510
58 Multiplication with Base-10 Blocks With Regrouping
59 Have the students use grid paper OR Tiles Factors Using ArraysHave the students use grid paper OR TilesFind the factors of 20:Always list the factors in order from greatest to least or least to great.NOT IN RANDOMORDER!2 x 104 x 5
61 Multiples Strategy Make a List Example: Find the first 5 multiples of 41. Skip Count4- 4,8,12,16, OR2. Multiply counting consecutively starting with 14 x 1= 4, 4 x 2 = 8, 4 x 3= 12, 4 x 4= 16, 4 x 5=20
67 Your Turn to Give It a Try (Think-Pair-Share) # 3Use the distributive property to solve.#4 Use base-ten pictorials to show your work.
68 Your Turn to Give It a Try (Think-Pair-Share) Use the distributive property to solve.51 X 560 + 8X
69 How Do These Problems Relate to Mathematical Practices 1 & 4 Discuss with your partners and give at least three examples for Topic II(Take 5 minutes to record your responses)
70 Digging Deeper Into the Math Content- 4th Grade TOPIC IlI: Multiplying Multi-Digit NumbersNew Edition Common Core TextbookMACC.4.NBT.2.5; MACC.4.OA.1.3No CC for MA.4.A.6.6Infusing the NGSSS MA.4.A.1.2; MA.4.A.6.6
71 Topic III Mathematical Practices MP 4: Model with Mathematics.Mathematically proficient students can…apply mathematics to solve problems that arise in everyday lifereflect on their attempt to solve problems and make revisions to improve their model as necessary
72 Topic III Mathematical Practices MP 8: Look for and express regularity in repeated reasoningMathematically proficient students can…notice repeating calculations and look for efficient methods/ representations to solve a problemevaluate the reasonableness of their results throughout the problem solving process.
73 Essential ContentA. Multiplication 1. Real world problem solving 2. Two, Three, Four digits by one digit 3. Two digits by two digits 4. Area Models B. Real World Problem Solving 1. Two Step Problems 2. Number Sentences 3. Estimation 4. Rounding a. nearest 10 b. nearest 100C. Properties of Multiplication 1. Distributive Property 2. Associative Property
74 These are theCommon CoreStandardsreplacingthe NGSSS
76 Benchmark Clarifications What Must Students Be Able to Do? Students will solve real-world problems using basic multiplication and the related division facts.Students will solve multi-digit whole-number multiplication problems or supply partial products in real-world multiplication problems.
77 What Are the Content Limits? Items may include whole-number multiplication facts from0 X 0 through 12 X 12 and the related division facts.For items that require solving multi-digit multiplication problems, the two factors may not exceed three digits by three digits or four digits by two digits.When both factors have three digits, at least one digit must be a zero.Items may include finding partial products of a multi-digit multiplication problem or finding errors in multiplication problems.Items may include checking for reasonableness of products.Items may use properties (e.g., commutative, associative, inverse, identity, distributive, zero) to solve problems but will not include asking students to name the specific properties.
80 Partial Products with 2-Digit Numbers( Break Apart) Model 13 x 18Draw an array that shows 13 by 18.Break apart 13 and 18 into smaller addends so you can multiply easier.13 = and =3.1008030244. Add all the products= 23410 x x 83 x x 8
81 Distributive Property of Multiplication With Larger Numbers When multiplying large number you can break apart the factors in order to make multiplying easier.X = 40 ( )= ( 40 x 5000) + ( 40 x 20 )= ,= ,800
90 Your Turn to Give It a Try (Think-Pair-Share) #1 Use the standard algorithm.# 2Use the strategy, partial product or break apart to solve. Show your work.
91 Your Turn to Give It a Try (Think-Pair-Share) #1Use the standard algorithm.# 244 6 84, 3 6 8X40050+ 25,275805
92 How Do These Problems Relate to Mathematical Practices 4 & 8 Discuss with your partners and give at least three examples for Topic II(Take 5 minutes to record your responses)
93 Digging Deeper Into the Math Content- 4th Grade TOPIC IV: Algebraic RulesNew Edition Common Core TextbookNONENGSSS –MA.4.A.4.2; MA.4.A.4.3
94 Essential ContentA. Variables 1. Solving for an unknown B. Algebraic Expressions 1. Determine a rule 2. Write an expressionC. Expressions with Two Operations 1. Write expressions with more than 1 operation 2. Evaluate expressions with 1 variable and two operations D. Repeating Patterns 1. Recognize patterns 2. Describe algebraic rule
97 Benchmark Clarifications What Must Students Be Able to Do? Students will translate a written description or a graphic to an expression or equation or translate an expression or equation to a written or graphic description to solve a real-world problem.Students will identify a missing number or element in a numeric or graphic relationship.Students will describe or generalize the rule of a visual relationship using an expression, equation, or description of the graphic.
98 What Are the Content Limits? Items must use rules or relationships that involve only one operation or a one-step function.A relationship must be defined in words, or at least three examples of the relationship must be provided.Relationships involving multiplication or division are limited to the multiplication facts of 0 X 0 through 12 X 12 and the related division facts.Items may include only one variable