4th Grade Math Instructional Focus Units



Instructional Focus UnitsEstimated TimeFocus 1Introducing Multiples and Factors Foundations for Equivalent Fractions3 WeeksFocus 2Generalizing Place Value Understanding for Multi-Digit Numbers Pt. 13 WeeksFocus 3Generalizing Place Value Understanding For Multi-Digit Numbers Pt. 22 WeeksFocus 4Applying Multiplication and Division Strategies to Solve Problems with Larger Numbers 4 WeeksFocus 5Extending Understanding of Fraction Equivalence, Operations, and Connections to Decimals – Part 1 3 WeeksFocus 6Solving Problems Using Multiplicative Comparison2 WeeksFocus 7Extending Understanding of Fraction Equivalence, Operations, and Connections to Decimals – Part 24 WeeksFocus 8Solving Problems By Applying Place Value to Multiplicative Thinking5 WeeksFocus 9Exploring and Analyzing the Properties of 2-Dimensional Shapes4 WeeksFocus 10Applying Understanding of Fraction Equivalence and Operations3 WeeksFocus 11Generating and Analyzing Patterns2 WeeksFocus 12Decimal Fractions3 Weeks***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. HYPERLINK "" Standards4.OA.A.14.OA.A.24.OA.A.34.OA.B.4Estimated Time3 WeeksPrincipal 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 BookAdditional 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 13Routines-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 ProductNotesFocus 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.2Estimated Time3 WeeksPrincipal 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, 4.6Additional 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 1NotesEmphasis 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 ProbesFocus 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.2Estimated Time2 WeeksPrincipal 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 MaterialsAdditional ResourceRoutines-10 Minute Math -Selected Fosnot Minilessons for Extended Addition and Subtraction (pp 34-59)-Word Problem Types: All Problem types for Common Core Table 1NotesEmphasis 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 Estimated Time4 WeeksPrincipal ResourceIDS Unit 3AZ.4.OA.A.3.1 -Teacher created resources-SMART Exchange:4th Grade Listing CountingAdditional 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)***Please note- Students in Grade 4 are not expected to use the standard algorithm for multiplication and division, though these EngageNY lessons include instruction using the algorithm. 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)NotesStudents in Grade 4 are not expected to use the standard algorithm for multiplication and division. Students should be using strategies based on place value and the properties of operations, and/or the relationship between multiplication and division. Students may illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. 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.4Estimated Time3 WeeksPrincipal 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) - Minute Math-Continue using selected Fosnot Minilessons, Number Talks, and Word Problem Types from Common Core Tables 1 and 2NotesTo assess student understanding of fraction concepts, use probes 9, 9b or 10 in Uncovering Student Thinking in Mathematics-25 Informative Assessment ProbesGrade 4 expectations are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.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.2Estimated Time2 WeeksPrincipal ResourceFosnot Unit- The Big DinnerAdditional ResourceRoutines-Use suggested mini-lessons in the book -Word Problem Types: All 3 types of Compare problems from Common Core Table 2NotesFocus 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 Estimated Time4 WeeksPrincipal 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 2NotesTo assess student understanding of fraction concepts, use probes 9, 9b or 10 in Uncovering Student Thinking in Mathematics-25 Informative Assessment ProbesGrade 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.2Estimated 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 98-109Routines-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 2NotesFocus 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.34.MD.C.54.MD.C.7 4.MD.A.3 Estimated Time4 WeeksPrincipal 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 9-114.MD.A.3 – Engage New York, Grade 4, Module 3, Topic A, lessons 2 & 3Additional 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 5-8Routines-10 Minute Math-Address concepts of measurement conversions through the use of teacher created materials and problem solving in those contextsNotes-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 ProbesFocus 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.4cEstimated Time3 WeeksPrincipal ResourceFosnot Unit- Field Trips and Fund RaisersAdditional Resource-Fosnot Mini Lessons -Engage New York, Grade 4, Module 5, Topic A, Lessons 4-6NotesFocus 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.1Estimated Time2 WeeksPrincipal ResourceIDS Unit 9 Investigations 2 & 3Additional Resource- Differentiation & Intervention Guide pages 110-121Routines-10 Minute Math-Selected Fosnot Minilessons-Word Problem Types: Make sure students are solving multi-step word problemsNotesFocus 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.2Estimated Time3 WeeksPrincipal ResourceEngage New York, Grade 4, Module 6, Topics A, B, C, & D Lessons 1-12Additional 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 2NotesTable 2: Common multiplication and division situations.7Unknown ProductGroup 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 GroupsThere 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?Measurement example. 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?Measurement example. 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 Area5There 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?CompareA blue hat costs $6. A red hat costs 3 times as much as the blue hat. How much does the red hat cost?Measurement example.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?Measurement example.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?Measurement example.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? GeneralGeneral 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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