4th Grade Math Instructional Focus Units - Kyrene … · Web view4th Grade Math Instructional Focus Units 2015/2016 Revised 5 /8/15 4 Standards in BOLD and UNDERLINED are found under

4th Grade Math Instructional Focus Units 2015/2016Revised 5/8/15

Instructional Focus Units Estimated TimeFocus 1 Introducing Multiples and Factors Foundations for Equivalent Fractions 3 Weeks

Focus 2 Generalizing Place Value Understanding for Multi-Digit Numbers Pt. 1 3 Weeks

Focus 3 Generalizing Place Value Understanding For Multi-Digit Numbers Pt. 2 2 Weeks

Focus 4 Applying Multiplication and Division Strategies to Solve Problems with Larger Numbers

4 Weeks

Focus 5 Extending Understanding of Fraction Equivalence, Operations, and Connections to Decimals – Part 1

3 Weeks

Focus 6 Solving Problems Using Multiplicative Comparison 2 Weeks

Focus 7 Extending Understanding of Fraction Equivalence, Operations, and Connections to Decimals – Part 2

4 Weeks

Focus 8 Solving Problems By Applying Place Value to Multiplicative Thinking 5 Weeks

Focus 9 Exploring and Analyzing the Properties of 2-Dimensional Shapes 4 Weeks

Focus 10

Applying Understanding of Fraction Equivalence and Operations 3 Weeks

Focus 11

Generating and Analyzing Patterns 2 Weeks

Focus 12

Decimal Fractions 3 Weeks

1 Standards in BOLD and UNDERLINED are found under major clusters.


***Based on the standards, not all lessons within the resource may be needed to meet the needs of your students.





Focus 1: Introducing Multiples and Factors Foundations for Equivalent FractionsIn this focus, students develop understanding of multiples and factors, applying their understanding of multiplication. This understanding will help students develop and use efficient and accurate computational strategies involving multi-digit numbers, as well as lay the foundation for equivalent fractions. These concepts and terms “prime” and “composite” are new to grade 4, so they are introduced early in the year to give students time to develop and apply this understanding.Standards4.OA.A.14.OA.A.24.OA.A.34.OA.B.4

Estimated Time3 Weeks

Principal ResourceIDS Unit 1 (Combine 1.2-1.3, 1.4-1.5, 2.3-2.4.Remove 2.2)Include 1.6A Common Core IDS Book

Additional Resource-Teaching Student Centered Mathematics by John Van de Walle - Grades 3-5: Chapter 4, 113-117-Developing Number Concepts: Place Value, Multiplication, & Division - Kathy Richardson: Chapter 2, 133-147-Investigations Differentiation & Intervention Guide pages 2-13-Engage New York, Grade 4, Module 3, Topic D, Lesson 13

Routines-IDS Unit 1 - 10 Minute Math-Fosnot Mini Lessons for Early Multiplication and Division (pp 42-53)-Number Talks for Addition and Subtraction-Word Problem Types Equal Groups-Unknown Product and Arrays/Area-Unknown Product

Notes


http://www.azed.gov/azcommoncore/files/2013/07/grade4mathfinalstd_august_2013.pdf


Focus 2: Generalizing Place Value Understanding for Multi-Digit Numbers Pt. 1In this focus, students will develop and practice efficient addition and subtraction strategies of multi-digit whole numbers while developing place value concepts. Understanding and use of standard algorithms for addition and subtraction is NOT a key component of this focus at this time. Standard algorithms will be addressed in Focus 3.Standards4.NBT.A.24.NBT.A.34.MD.A.2


Principal ResourceIDS Unit 5 Sessions 1.3, 1.4, 1.5, Common Core IDS book 1.5A, 1.6, 2.1, 2.2, 2.3, 4.1, 4.2, 2.5, 2.6/4.3 (combine), 4.4, 4.5, 4.6

Additional Resource-Teaching Student Centered Mathematics by John Van de Walle - Grades 3-5: pp 45, 2.4-2.6 and pp 72-73 (expanded lesson of 2.6)-Investigations Differentiation & Intervention Guide pages 58-60 and 62-73RoutinesIDS Unit 5- 10 Minute Math-Selected Fosnot Minilessons for Extended Addition and Subtraction (pp 34-59)-Word Problem Types: All Problem types for Common Core Table 1

NotesEmphasis of this focus is place value in whole number operations, NOT USING THE STANDARD ALGORITHM FOR OPERATIONS. Use the sessions in the order noted. Standard US algorithm will be addressed at a later date; To assess student understanding of addition or subtraction strategies, use probes 15a or 16a in Uncovering Student Thinking in Mathematics-25 Informative Assessment Probes




Focus 3: Generalizing Place Value Understanding For Multi-Digit Numbers Pt. 2In this focus, students will further develop and practice efficient addition and subtraction strategies of multi-digit whole numbers while developing place value concepts. Understanding and use of the US Standard algorithm for addition and subtraction is a key component of this focus.Standards4.NBT.A.14.NBT.A.24.NBT.A.34.NBT.B.44.MD.A.2


Principal Resource-IDS Unit 5 Sessions 3.1, 3.2, 3.3, 3.4, 3.5, Common Core IDS book 3.6A, IDS Unit 5 Session 2.4, Common Core IDS book 4.4A (in this order)-Teacher Created Materials

Additional Resource

Routines-10 Minute Math -Selected Fosnot Minilessons for Extended Addition and Subtraction (pp 34-59)-Word Problem Types: All Problem types for Common Core Table 1

NotesEmphasis of this focus is place value and standard algorithms in whole number operations. Rather than building a 10,000 chart (3.1), use the image on p. 103 to have the discussions.




Focus 4: Applying Multiplication and Division Strategies to Solve Problems with Larger NumbersIn this focus, students continue using computational and problem solving strategies. Students are building conceptual understanding of multiplication of larger numbers and division with remainders. Standards4.OA.A.14.OA.A.24.OA.A.34.OA.B.44.NBT.B.54.NBT.B.6

AZ.4.OA.A.3.1


Principal ResourceIDS Unit 3

AZ.4.OA.A.3.1 -Teacher created resources-SMART Exchange:

4 th Grade Listing Counting

Additional Resource-Teaching Student Centered Mathematics by John Van de Walle - Grades 3-5: Chapter 4, 121-123-Developing Number Concepts: Place Value, Multiplication, & Division - Kathy Richardson: Chapter 3, 181-191-Investigations Differentiation & Intervention Guide pages 26-41-Engage New York, Grade 4, Module 3, Topic G, Lessons 27-32 (4.NBT.B.6), Topic H, Lessons 34-38 (4.NBT.B.5)Routines-IDS Unit 3 - 10 Minute Math-Fosnot Minilessons for Early Multiplication and Division (pp 54-58, 64-66)-Number Talks for Multiplication and Division- Word Problem Types: Equal Groups (Unknown Product, Group Size Unknown and Number of Groups Unknown) and Arrays/Area (Unknown Product, Group Size Unknown and Number of Groups Unknown)

Notes




Focus 5: Extending Understanding of Fraction Equivalence, Operations, and Connections to Decimals – Part 1In this focus, students develop an understanding of fraction equivalence and various methods for comparing fractions. Students should understand that when comparing fractions, it is not always necessary to generate equivalent fractions. Other methods, such as comparing fractions to a benchmark, can be used to discuss relative sizes. The justification of comparing or generating equivalent fractions using visual models is an emphasis of this focus. Standards4.NF.A.14.NF.A.24.NF.B.3a4.NF.B.3b 4.NF.B.3c4.NF.B.3d4.NF.B.4a4.MD.A.24.MD.B.4


Principal ResourceIDS Unit 6 Investigations 1 and 2 ONLY, including Common Core IDS book 1.8A and 2.7A.

Additional Resource-Teaching Student Centered Mathematics by John Van de Walle - Chapters 5 and 6-Investigations Differentiation & Intervention Guide pages 74-85-Engage New York, Module 5,Topic A, Lessons 1-3-Learnzillion (4.NF.B.3b) - http://learnzillion.com/lessons/1423Routines-10 Minute Math-Continue using selected Fosnot Minilessons, Number Talks, and Word Problem Types from Common Core Tables 1 and 2

NotesTo assess student understanding of fraction concepts, use probes 9, 9b or 10 in Uncovering Student Thinking in Mathematics-25 Informative Assessment Probes

Grade 4 expectations are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.


http://learnzillion.com/lessons/1423



Focus 6: Solving Problems Using Multiplicative ComparisonIn this focus, students are introduced to multiplicative compare problems. For students to develop this concept, they must be provided rich problem situations that encourage them to make sense of the relationships among the quantities involved, model the situation, and check their solutions using a different strategy. CCSSM Table 2 is an important resource for understanding multiplicative comparison problems.Standards4.OA.A.14.OA.A.2


Principal ResourceFosnot Unit- The Big Dinner

Additional Resource

Routines-Use suggested mini-lessons in the book -Word Problem Types: All 3 types of Compare problems from Common Core Table 2

Notes




Focus 7: Extending Understanding of Fraction Equivalence, Operations, and Connections to Decimals – Part 2In this focus, students continue to develop an understanding of fraction equivalence and various methods for comparing fractions. Students should understand that when comparing fractions, it is not always necessary to generate equivalent fractions. Other methods, such as comparing fractions to a benchmark, can be used to discuss relative sizes. The justification of comparing or generating equivalent fractions using visual models is an emphasis of this focus. Students will also use their understanding of equivalent fractions to begin to use decimal notation.Standards4.NF.B.4b4.NF.B.4c4.NF.C.54.NF.C.64.NF.C.74.MD.A.24.MD.B.4


Principal ResourceIDS Unit 6 Investigations 3 ONLY, including Common Core IDS book 3A.1, 3A.2, 3A.3.

Additional Resource-Teaching Student Centered Mathematics by John Van de Walle - Chapters 5 and 6-Investigations Differentiation & Intervention Guide pages 74-85-Engage New York, Grade 4, Module 5, Topic E, Lesson 28 (4.MD.B.4)Routines-10 Minute Math-Continue using selected Fosnot Minilessons, Number Talks, and Word Problem Types from Common Core Tables 1 and 2

NotesTo assess student understanding of fraction concepts, use probes 9, 9b or 10 in Uncovering Student Thinking in Mathematics-25 Informative Assessment Probes

Grade 4 expectations are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.




Focus 8: Solving Problems By Applying Place Value to Multiplicative ThinkingThe focus is to provide students time to develop and practice efficient multiplication and division strategies of multi-digit whole numbers while applying place value concepts.Standards4.OA.A.34.OA.C.54.NBT.B.54.NBT.B.64.MD.A.2

Estimated Time5 Weeks (2 weeks Fosnot; 3 weeks IDS Unit 8)

Principal Resource(first 2 weeks)-Fosnot Unit- The Teachers' Lounge

(3 weeks)-IDS Unit 8 Investigations 1, 2, and 3, including Common Core IDS book 2.4A and 3.5A

Additional Resource-Investigations Differentiation & Intervention Guide pages 98-109

Routines-Fosnot mini-lessons from The Teacher’s Lounge

-10 Minute Math- Continue using selected Fosnot Minilessons, Number Talks, and Word Problem Types from Common Core Tables 1 and 2

Notes




Focus 9: Exploring and Analyzing the Properties of 2-Dimensional ShapesIn this focus students develop their spatial reasoning skills by using a wide variety of attributes to talk about 2-Dimensional shapes. Students analyze geometric figures based on angle measurement, parallel and perpendicular lines, and symmetry. Measurement is a topic that is featured in order to discuss geometric principles.

Standards4.MD.A.14.MD.A.24.MD.C.64.G.A.14.G.A.24.G.A.3

4.MD.C.54.MD.C.7

4.MD.A.3


Principal ResourceIDS Unit 4 including Common Core IDS book 2.3a and 3.4a Exclude sessions 4.3 and 4.4. Combine sessions 4.1 and 4.2.

Skip all LogoPaths activities and combine assessments into other lesson sessions.

4.MD.C.5, 4.MD.C.7 -Engage New York, Grade 4, Module 4, Topic C, Lessons 9-11

4.MD.A.3 – Engage New York, Grade 4, Module 3, Topic A, lessons 2 & 3

Additional Resource-Teaching Student Centered Mathematics by John Van de Walle - Chapters 8 and 9-Investigations Differentiation & Intervention Guide pages 46-57-Engage New York, Grade 4, Module 4, Topic B, Lessons 5-8

Routines-10 Minute Math-Address concepts of measurement conversions through the use of teacher created materials and problem solving in those contexts

Notes-To assess student understanding of geometric concepts, use probes 21, 21a or 21b. For area concepts use probe 22a in Uncovering Student Thinking in Mathematics-25 Informative Assessment Probes


http://www.engageny.org/resource/grade-4-mathematics-module-3








Focus 10: Applying Understanding of Fraction Equivalence and OperationsIn this focus students develop an understanding of fraction equivalence and various methods for comparing fractions. The justification of comparing or generating equivalent fractions using visual models should be emphasized. Standards4.NF.A.14.NF.A.24.NF.B.3a4.NF.B.3b4.NF.B.3d4.NF.B.4a4.NF.B.4c


Principal ResourceFosnot Unit- Field Trips and Fund Raisers

Additional Resource-Fosnot Mini Lessons -Engage New York, Grade 4, Module 5, Topic A, Lessons 4-6

Notes






Focus 11: Generating and Analyzing PatternsIn this focus, students identify arithmetic patterns in order to develop understanding of change as a mathematical concept. Students learn to use graphs and equations as models to represent change.Standards4.OA.C.54.NBT.B.5 4.NBT.B.64.MD.A.1


Principal ResourceIDS Unit 9 Investigations 2 & 3

Additional Resource- Differentiation & Intervention Guide pages 110-121

Routines-10 Minute Math-Selected Fosnot Minilessons-Word Problem Types: Make sure students are solving multi-step word problems

Notes




Focus 12: Decimal Fractions In this focus, students build on Focus Unit 7 to further explore decimal numbers via their relationship to decimal fractions, expressing a given quantity in both fraction and decimal forms. Utilizing the understanding of fractions developed throughout Focus Units 5 and 7, students apply the same reasoning to decimal numbers, building a solid foundation for Grade 5 work with decimal operations. Standards4.NBT.A.14.NF.A.14.NF.B.34.NF.C.54.NF.C.64.NF.C.74.MD.A.14.MD.A.2


Principal ResourceEngage New York, Grade 4, Module 6, Topics A, B, C, & D Lessons 1-12

Additional Resource-Teaching Student Centered Mathematics by John Van de Walle - Chapters 5 and 6-Investigations Differentiation & Intervention Guide pages 74-85Routines-10 Minute Math-Continue using selected Fosnot Minilessons, Number Talks, and Word Problem Types from Common Core Tables 1 and 2

Notes

Table 2: Common multiplication and division situations.7







Unknown Product Group Size Unknown(“How many in each group?” Division)

Number of Groups Unknown(“How many groups?” Division)

3 x 6 = ? 3 x ? = 18, and 18 ÷ 3 = ? ? x 6 = 18, and 18 ÷ 6 = ?

Equal Groups

There are 3 bags with 6 plums in each bag. How many plums are there in all?

Measurement example.

You need 3 lengths of string, each 6 inches long. How much string will you need altogether?

If 18 plums are shared equally into 3 bags, then how many plums will be in each bag?


You have 18 inches of string, which you will cut into 3 equal pieces. How long will each piece of string be?

If 18 plums are to be packed 6 to a bag, then how many bags are needed?


You have 18 inches of string, which you will cut into pieces that are 6 inches long. How many pieces of string will you have?

Arrays,4 Area5

There are 3 rows of apples with 6 apples in each row. How many apples are there?

Area example.

What is the area of a 3 cm by 6 cm rectangle?

If 18 apples are arranged into 3 equal rows, how many apples will be in each row?

Area example.

A rectangle has area 18 square centimeters. If one side is 3 cm long, how long is a side next to it?

If 18 apples are arranged into equal rows of 6 apples, how many rows will there be?

Area example.

A rectangle has area 18 square centimeters. If one side is 6 cm long, how long is a side next to it?

Compare

A blue hat costs $6. A red hat costs 3 times as much as the blue hat. How much does the red hat cost?


A rubber band is 6 cm long. How long will the rubber band be when it is stretched to be 3 times as long?

A red hat costs $18 and that is 3 times as much as a blue hat costs. How much does a blue hat cost?


A rubber band is stretched to be 18 cm long and that is 3 times as long as it was at first. How long was the rubber band at first?

A red hat costs $18 and a blue hat costs $6. How many times as much does the red hat cost as the blue hat?


A rubber band was 6 cm long at first. Now it is stretched to be 18 cm long. How many times as long is the rubber band now as it was at first?

General General a x b = ? a x ? = p, and p ÷ a = ? ? x b = p, and p ÷ b = ?

7The first examples in each cell are examples of discrete things. These are easier for students and should be given before the measurement examples.4The language in the array examples shows the easiest form of array problems. A harder form is to use the terms rows and columns: The apples in the grocery window are in 3 rows and 6 columns. How many apples are in there? Both forms are valuable.5Area involves arrays of squares that have been pushed together so that there are no gaps or overlaps, so array problems include these especially important measurement situations.


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4th Grade Math Instructional Focus Units - Kyrene … · Web view4th Grade Math Instructional Focus Units 2015/2016 Revised 5 /8/15 4 Standards in BOLD and UNDERLINED are found under