Vacaville USD September 4, 2014 FOURTH GRADE Session 1 Vacaville USD September 4, 2014

AGENDA Problem Solving and Patterns Math Practice Standards and Effective Questions Word Problems Place Value, Rounding, Reading and Writing Numbers Addition/Subtraction Strategies – Mental Math Multiplication

Expectations We are each responsible for our own learning and for the learning of the group. We respect each others learning styles and work together to make this time successful for everyone. We value the opinions and knowledge of all participants.

Regina’s Logo How many tiles are needed to make a Size 5? What about a Size 10? a Size 20? A Size 100?

Regina’s Logo What is a strategy that will let you quickly and easily figure out how many tiles you will need for any given size?

Regina’s Logo Recursive Add 3 each time SIZE # OF TILES 1 5 2 8 3 11 4 14 17

Regina’s Logo 3n + 2

Regina’s Logo 3n + 2

Regina’s Logo 2(n + 1) + n

Regina’s Logo 2n + (n + 2)

4. OA. 5. Generate a number or shape pattern that follows a given rule 4.OA.5. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.

The Use of Effective Questions

Questioning plays a critical role in the way teachers Guide the class Engage students in the content Encourage participation Foster understanding

CCSS Mathematical Practices REASONING AND EXPLAINING Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Make sense of problems and persevere in solving them OVERARCHING HABITS OF MIND Attend to precision MODELING AND USING TOOLS Model with mathematics Use appropriate tools strategically SEEING STRUCTURE AND GENERALIZING Look for and make use of structure Look for and express regularity in repeated reasoning

SMP’s So how does the use of effective questioning relate to the Standards for Mathematical Practice?

SMP’s and Questions Your group will receive 16 cards 8 lists of questions related to the SMP’s Your job is to match each SMP with the questions designed to support that SMP.

Asking Effective Questions Pick 2 colors... Use one color to highlight questions that you are already asking. Use the 2nd color to highlight questions that you would like to ask this year.

Additional Resources Effective Questions – PBS

Solving Word Problems

Read the entire problem, “visualizing” the problem conceptually Determine who and/or what the problem is about Rewrite the question in sentence form leaving a space for the answer.

Draw the unit bars that you’ll eventually adjust as you construct the visual image of the problem Chunk the problem, adjust the unit bars to reflect the information in the problem, and fill in the question mark.

Correctly compute and solve the problem (show all work!) Write the answer in the sentence and make sure the answer makes sense.

At the flower shop, there are 5 times as many roses as sunflowers At the flower shop, there are 5 times as many roses as sunflowers. If there are 60 sunflowers, how many roses are there?

At the flower shop, there are 5 times as many roses as sunflowers At the flower shop, there are 5 times as many roses as sunflowers. If there are 60 roses, how many sunflowers are there?

At the flower shop, there are 5 times as many roses as sunflowers At the flower shop, there are 5 times as many roses as sunflowers. If there are 60 roses and sunflowers altogether, how many roses are there? How many sunflowers are there?

Standards 4.OA.2 Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.

4.OA.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

Place Value Rounding Reading and Writing Numbers

Standards What are the place value standards for 4th grade? What are students supposed to know and understand from 3rd grade?

Standards 4.NBT.1. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.

Standards 4.NBT.1. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.

Standards 4.NBT.2. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multidigit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

Standards 4.NBT.3. Use place value understanding to round multi-digit whole numbers to any place.

Standards What are the place value standards for 4th grade? What are students supposed to know and understand from 3rd grade?

Tens Times As Many Put 1 one on your place value mat What would it mean to have 10 times as many? 10 ones = ten So 1 ten is ten times as much as 1 one

Tens Times As Many Put 3 ones on your place value mat What would it mean to have 10 times as many? 30 ones = 3 tens So 3 tens is ten times as much as 3 ones

Tens Times As Many Look at the 1 ten on your place value mat What would it mean to have 10 times as many? 10 tens = 1 hundred So 1 hundred is ten times as much as 10 tens

Tens Times As Many Put 4 tens on your place value mat What would it mean to have 10 times as many? 40 tens = 4 hundreds So 4 hundreds is ten times as much as 40 tens

Tens Times As Many Put 2 hundreds on your place value mat 2 hundreds is 10 times as much as what number? 2 hundreds = 20 tens So 2 hundreds is ten times as much as 2 tens

Tens Times As Many Put 1 hundred on your place value mat What would it mean to have 10 times as many? 10 hundreds = 1 thousand So 1 thousand is ten times as much as 1 hundred

Patterns in Place Value Base 10 blocks Take out a 1’s piece What does it look like? Why does it have a value of 1?

Patterns in Place Value Take out a 10’s piece What does it look like? How is it similar or different from a 1’s piece? Why does it have a value of 10?

Patterns in Place Value Take out a 100’s piece What does it look like? How is it similar or different from a 10’s piece? Why does it have a value of 100?

Patterns in Place Value Look at the block that I just gave you. What do we call this block? How many 100’s would it take to fill this block? So 1,000 is ___ times as much as 100 What does it look like? Is it similar to any of the pieces we have examined so far? ten

Patterns in Place Value Our number system has some very important structures and patterns Place Value Digits 0 1 2 3 4 5 6 7 8 9 Each place is 10 times as much (or 10 times as large) as the place immediately to its right

Patterns in Place Value Watch and see if you notice any additional patterns or structures as we continue to look at place value So a 1,000’s piece looks a lot like a 1’s piece. What do you think it will look like if I put 10 thousand’s pieces together? What piece is it similar to? What do you think we might name this place?

Patterns in Place Value What do you think it will look like if I put 10 ten-thousand’s pieces together? What piece is it similar to? What do you think we might name this place? Extend our place value mat. Ones family or units family Thousands family

10 times as many Work at your tables (number off) 1 and 2 are partners; 3 and 4 are partners; etc. Odd numbers start with the chart; trade off with your partner Person 2 – Starts with the calculator; passes around the table after each problem

10 times as many I’m going to give you a number Odd numbers record the number on the chart Person 2 – calculate 10 times that number Odd numbers record the new number

476 10 times as many I’m going to give you a number Odds: record that number on your chart Person 2: calculate 10 times that number Odds: record the new number

4 7 6 4 7 6 0

10 times as many Let’s try again Evens: record that number on your chart Person 3: calculate 10 times that number Evens: record the new number 5,920

10 times as many Keep trading and recording 607 3,600 1,234 71,900

What do you notice? What happens to the digits in each number when we multiply by 10? WHY?

100 times as many What do you think would happen to the digits in each number if we multiplied by 100? Let’s check and see if our prediction is correct.

Metric Conversions Find the equivalent measures. 1 m = __________ cm That means that a meter is ______ times as large as a centimeter. 100 100

Metric Conversions Find the equivalent measures. 1 m = __________ cm 100 300 8,000 12

Metric Conversions Find the equivalent measures. 1 km = __________ m 1,000 4,000 7,000 18

Other Place Value Concepts Expanded Form Reading Writing Comparing Rounding

Expanded Form 45,793 40,000 + 5,000 + 700 + 90 + 3 4 x 10,000 + 51,000 + 7100 + 910 + 31

Reading Read: 452,807 First group the number into families thousand, ones Now read the numbers in each family Remember they are all 3 digits or less Four hundred fifty two thousand Eight hundred seven 452 807

Two hundred three thousand five hundred forty Writing Numbers Write in number form: Two hundred three thousand five hundred forty Break the number into families and write it one part at a time 203 , 540

Two hundred three thousand five hundred forty Writing Numbers Write in number form: Two hundred three thousand five hundred forty Break the number into families and write it one part at a time 203 , 540

Comparing Go back to your place value recording mats Odds: Record the number 72,498 Evens: Underneath that number, record the number 72,600

Comparing Which is larger? Write the relationship using ____ > ____

Comparing Which is larger? 145,299 or 95,387 How do you know? Complete using >, <, or = 89,432  157,308

Rounding What does it mean to round a number to the nearest thousand? If I were to count by thousands, which number would be the closest to my number.

Rounding Count by 1,000 starting at 0

Round 2,784 to the nearest thousand How many 1,000’s? Count by 1,000. What’s next? What’s in the middle of 2,000 and 3,000? Is 2,784 closer to 2,000 or 3,000? 3,000 = 30 hundreds 2,500 = 25 hundreds 2,000 = 20 hundreds

Round 372,584 to the nearest hundred thousand How many 100,000’s? Count by 100,000. What’s next? What’s the midpoint of 300,000 and 400,000? Is 372,584 closer to 300,000 or 400,000? 400,000 350,000 300,000

Rounding Round 372,584to the nearest hundred thousand 400,000

Round 372,584 to the nearest ten thousand How many 10,000’s? Count by10,000. What’s next? What’s the midpoint? Is 372,584 closer to 370,000 or 380,000? 380,000 375,000 370,000

Rounding Round 372,584to the nearest hundred thousand 400,000 ten thousand 370,000

Try a couple! Round 347,523 to the nearest ten-thousand Round 347,523 to the nearest thousand

Addition and Subtraction

Standards What are the addition and subtraction standards for 4th grade? What are students supposed to know and understand from 3rd grade?

Standards 4.NBT.4. Fluently add and subtract multi-digit whole numbers using the standard algorithm.

Standards What are the addition and subtraction standards for 4th grade? What are students supposed to know and understand from 3rd grade?

Progression Concrete Pictorial or Representational Abstract Invented and Alternative Algorithms Traditional Algorithms

Mental Math 135 + 48 400 – 165

Multiplication

Standards 4.OA.1 Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.

4. OA. 2 and OA. 3 Word Problems 4. OA 4.OA.2 and OA.3 Word Problems 4.OA.4 Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite.

4.NBT.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Standards So, what are students supposed to know and understand about multiplication from 3rd grade?

Multiplication Solve 23 x 4 at your tables. Use at least 4 different methods! Concrete Representational Abstract

Using Groups to Multiply 23 x 4

Using Arrays to Multiply 23 x 4 12 4 rows of 3 = 12 80 4 rows of 20 = 80 92

Area Model

Area Representation 20 + 3 23 x 4 4 4  20 80 3  4 12

Abstract 23 + 23 92 20 + 3 + 20 + 3 80 + 12

Partial Products 23 x 4 80 4 x 20 12 4 x 3 92

Using Arrays to Multiply Use Base 10 blocks and an area model to solve the following: 21 x 13

31 x 14 =

Pictorial Representation 30 + 1 10 + 4 31 x 14 10  30 300 10  1 10 4  30 120 4  1 4

Partial Products x 1 4 300 10 120 4 434 31 (10  30) (10  1) (4  30) (4  1) 434

Partial Products x 1 4 4 120 10 300 434 3 1 (4  1) (4  30) (10  1) (10  30) 434

Pictorial Representation 80 + 4 84 x 57 50 + 7 50  80 50  4 4,000 200 7  80 7  4 560 28