PS166 4 th and 5th Grade Math Parent Workshop

Transcription

1 PS166 4 th and 5th Grade Math Parent Workshop October 30 th, 2014 Math Consultant: Nicola Godwin K-5 Math Teaching Resources LLC

2 In 4 th Grade, instructional time focuses on three critical areas: (1) developing understanding and fluency with multi-digit multiplication, and developing understanding of dividing to find quotients involving multi-digit dividends; (2) Developing an understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers, (3) Understanding that geometric figures can be analyzed and classified based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and symmetry.

3 In 5 th Grade, instructional time focuses on three critical areas: (1) developing fluency with addition and subtraction of fractions, and developing understanding of the multiplication of fractions and of division of fractions in limited cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions) (2) extending division to 2-digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations; (3) developing understanding of volume

4 Module 1: Place Value, Rounding and Algorithms for Addition and Subtraction (25 days) Module 2 Multi-Digit Multiplication and Division (43 days) Module 3 Unit Conversions (7 days) Module 4 Angle Measures and Plane Figures (20 days) Module 5 Fraction Equivalence, Ordering and Operations (45 days) Module 6 Decimal Fractions (20 days) Module 7 Exploring Measurement with Multiplication (20 days) Module 1 Place Value and Decimal Fractions (20 days) Module 2 Multi-Digit Whole Number and Decimal Fractions Operations (35 days) Module 3 Addition and Subtraction of Fractions (22 days) Module 4 Multiplication and Division of Fractions and Decimal Fractions (38 days) Module 5 Addition and Multiplication with Volume and Area (25 days) Module 6 Problem Solving with the Coordinate Plane (40 days)

5 4 th Grade New York State Common Core Mathematics Test April 22nd April 24 th 2015

6 4 th Grade: 2014 Testing Times

7 5 th Grade New York State Common Core Mathematics Test April 22nd April 24 th 2015

8 5 th Grade: 2014 Testing Times

9 4.NBT5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two 2-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 Left to right showing partial products: 425 x 3 (3 x 1 digit) Area model: 425 x 3 thinking: (3 x 400) (3 x 20) = 1, (3 x 5) 1,275

10 4 x 1 Digit 1421 x 4 thinking: 4000 (4 x 1000) 1600 (4 x 400) 80 (4 x 20) (4 x 1) = 5,684 5,684 2 x 2 Digit 24 X 12 thinking: 200 (20 X10) 40 (20 X 2) 40 (4 X 10) 8 (4 X 2) Rectangular Array:

11 5.NBT5 Fluently multiply multi-digit whole numbers using the standard algorithm Digits that represent newly composed tens and hundreds are written below the line instead of above 94. The 1 from 30x4=120 is placed correctly in the hundreds place and the digit 2 from 30x90=2700 is placed correctly in the thousands place. If these digits had been placed above 94, they would be in incorrect places. The 0 in the ones place of the second line is there because the whole line of digits is produced by multiplying by 30 (not 3).

12 4.NBT6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division Partial Quotients: = 2,725 6 =

13 4.OA3 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. How would you interpret the remainder? (use a whole number, fraction, decimal, or round up to the next whole number?) a) CDs are on sale for $4.00. Peter has $30.00 in his wallet. How many CDs can he buy? b) Dad shared 30 large cookies equally onto 4 plates. How many cookies were on each plate? c) Mr. Smith gave his four children $30.00 to share equally. How much money did each child get? d) There are 30 children in a 4 th grade class. Each table seats 4 children. How many tables will be needed?

14 5.NBT6 Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. 3, =? Area model: , 680 3, = 230 R3

15 5.NBT7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction, relate the strategy to a written method and explain the reasoning used. 5 x 2.5 = hundredths are shaded purple so 0.2 x 1.5 = 0.30

16 5.NBT7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction, relate the strategy to a written method and explain the reasoning used. Estimate: 5 x 3 = 15 5 x 2.5 =? X 5 Think: 2. 5 (5 x 5 tenths=25 tenths) 10.0 (5 x 2 ones) = 12.5 or 25 (write the decimal as a whole number and multiply) x Use my estimate to place the decimal point in the product 2.5 x 5 = 12.5

17 5.NBT7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction, relate the strategy to a written method and explain the reasoning used x 46 =? Estimate: 10 x 46 = X 46 Think: (40 x 9) 32.0 (40 x 0.8) 54.0 (6 x 9) 4.8 (6 x 0.8) or write the decimal as a whole number and multiply. Use my estimate to place the decimal point in the product. 98 x 46= My estimate was 460 so the product is

18 Standards for Mathematical Practice

19 4 th Grade 2014 Released Question (1 point) A school has 17 tables in the cafeteria. Each table seats 12 students. What is the greatest number of students that can be seated at these tables? A 114 B 184 C 194 D 204 Key: D Measured CCLS 4.NBT. 5 Commentary: This question measures 4.NBT.5 by asking the student to multiply two 2-digit numbers using strategies based on place value and the properties of operations. In this case, two-digit multiplication is used to solve a real-world problem.

20 4 th Grade 2014 Released Question (2 points) Andres is a baker. He baked 3,240 cookies in one week. He placed the cookies in boxes containing 9 cookies each. What was the total number of boxes Andres used? Show your work. Commentary: This question measures 4.NBT.6 because it assesses a student s ability to find a whole number quotient with up to a four-digit dividend and a one-digit divisor.

21 4 th Grade 2014 Released Question (3 points) This question measures 4.OA.3 because it assesses the student s ability to solve a multi-step word problem posed with whole numbers and having a whole-number answer using the four operations, including problems in which remainders must be interpreted.

22 5 th Grade 2014 Released Question (1 point)

23 Commentary: This question measures 5.NBT.6 because it assesses a student s ability to find a whole number quotient of a whole number with a four-digit dividend and a two digit divisor.

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25 Short, ongoing routine that provides students with meaningful ongoing practice with mental computation to develop computational fluency. Addition Number Talk Adding up in chunks The largest addend is kept whole and the other addend is chunked or broken apart to add mentally Example: =? = = 285 Subtraction Number Talk Constant difference Adjust each number in the problem by the same amount to make numbers that are easier to work with mentally Example: =? =

26 More Sample Questions: Video Lessons: More Resources for each Standard: DO YOU HAVE ANY QUESTIONS?