st. louis public schools mathematics - grade 5 2nd quarter pacing … · 2014-08-26 · st. louis...

St. Louis Public Schools

Mathematics - Grade 5

2nd

Quarter Pacing Guide - October 13th

– December 19th

, 2014

Grade 5 Mathematics Overview: Fifth grade mathematics is about (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 two-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; and (3) developing understanding of volume. Key Areas of Focus for 3-5: Multiplication and division of whole numbers and fractions – concepts, skills and problem solving Required Fluency: 5.NBT.5 Multi-digit multiplication 2nd Quarter Overarching Learning Goals Unit 3: Multiplying and Dividing Decimals and Relating Decimals and Fractions (Approx. 18-22 days)

Number and Operations in Base Ten

Understand the place value system. (5.NBT.1, 5.NBT.2, 5.NBT.3a)

Perform operations with multi-digit whole numbers and with decimals to hundredths. (5.NBT.7) Number and Operations - Fractions

Apply and extend previous understandings of multiplication and division to multiply and divide fractions. (5.NF.3) Unit 4: Adding and Subtracting Fractions (Approx. 22 - 25 days)

Number and Operations - Fractions

Use equivalent fractions as a strategy to add and subtract fractions. (5NF.1, 5.NF.2)

Assessments Formative assessment strategies will be used frequently in every lesson to gauge students' understanding and make adjustments to instruction accordingly. Summative assessment strategies will be used at the end of each lesson and unit to gauge students’ mastery of standards and to plan for reteaching/intervention.

Standards for Mathematical Practice 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.



2nd


– December 19th

, 2014

Adapted from A Story of Units: A Curriculum Overview for Grade P-5 from EngageNY and commoncore.org Adapted from Mathematics Common Core Scope and Sequence – Grade 5 from Long Beach Unified School District Objectives and Resources/Materials adapted from enVision Math --- Copyright 2009 Pearson Education (St. Louis Public Schools holds valid license for Pearson enVision Math resources) Additional Resources from Missouri Department of Elementary and Secondary Education @ www.dese.mo.gov (MLS crosswalks and mathematics model curriculum units.) * enVision math lessons with a capital letter behind the number i.e. 1-5A are additional lessons created for transition to Common Core – these lessons are available online (not part of the 2011 student text.) **Strikethrough indicates not addressing that part of the standard.

Unit 3: Multiplying and Dividing Decimals and Relating Decimals and Fractions (Approx. 18-22 days)

Time Frame

Missouri Learning Standards (Common Core Standards)

Content Objectives (numbers correspond with resources) Students will be able to…

Mathematical Practices

Resources/Materials (numbers correspond with objectives)

Assessment Students will be able to demonstrate mastery of the standards by…

12-15 days

5.NBT.1 Find Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. 5.NBT.2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. 5.NBT.7 **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.

(1) mentally multiply decimals by 10, 100, and 1000. (5.NBT.1. 5.NBT.2) (2) use a standard algorithm to multiply a whole number and a decimal. (5.NBT.7) (3) use rounding and compatible numbers to estimate products of whole numbers and decimals; students will identify estimates as overestimates or underestimates. (5.NBT.7) (4) use number sense and place value to multiply decimals. (5.NBT.7) (5) Students find products of whole numbers and decimals to ten thousandths. (5.NBT.7) (6) use the standard algorithm to multiply decimals by decimals. (5.NBT.7) (7) mentally divide decimals by 10, 100, or 1000. (5.NBT.2, 5.NBT.7) (8) use reasoning to correctly place the decimal point in a quotient. (5.NBT.7) (9) use the standard algorithm to divide a decimal by a whole number. (5.NBT.7) (10) use compatible numbers to estimate quotients of whole numbers. (5.NBT.7) (11) use the standard algorithm to divide decimals by decimals. (5.NBT.7)

1, 2, 3, 4, 5, 6, 7, 8

enVision Math Lesson Sequence: (1) 7-1: Multiplying Decimals by 10, 100, or 1,000 pp.170-171 (2) 7-2: Multiplying a Decimal by a Whole Number pp.172-173 (3) 7-3: Estimating the Product of a Decimal and a Whole Number pp.174-175 (4) 7-4A*: Number Sense: Decimal Multiplication (5) 7-4B*: Models for Multiplying Decimals (6) 7-4: Multiplying Two Decimals pp.176-177 (7) 7-5: Dividing Decimals by 10, 100, or 1000 pp.178-179 (8) 7-6A: * Number Sense: Decimal Division (9) 7-6: Dividing a Decimal by a Whole Number pp.180-183 (10) 7-7: Estimation: Decimals Divided by Whole Numbers pp.184-185 (11) 7-8: Dividing a Decimal by a Decimal pp.186-187 Manipulatives: Bills and Coins (or Teaching Tool 34) colored pencils, calculator Teaching Tools: Decimal Grids (Teaching Tool 45), Problem Solving Recording Sheet

enVision Formative Assessments: Quick Check 7-1 Quick Check 7-2 Quick Check 7-3 Quick Check 7-4A* Quick Check 7-4B* Quick Check 7-4 Quick Check 7-5 Quick Check 7-6A* Quick Check 7-6 Quick Check 7-7 Quick Check 7-8



2nd


– December 19th

, 2014


Unit 3: Multiplying and Dividing Decimals and Relating Decimals and Fractions (Approx. 18-22 days)

Time Frame






5 -7 days

5.NF.3 Interpret a fraction as division of the numerator by the denominator (

= a ÷ b).

Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example,

interpret

as the result of dividing 3 by 4,

noting that

multiplied by 4 equals 3, and

that when 3 wholes are shared equally among 4 people each person has a share of size

. If 9 people want to share a 50-pound

sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? http://illustrativemathematics.org/illustrations/293 5.NBT.3.a Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g.,

347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (

) + 9

x (

) + 2 x (

).

(1) learn and understand that division can be used to divide objects into equal parts that are fractions of a whole, and represent those fractions on a number line. (5.NF.3) (2) express fractions greater than 1 as mixed numbers or improper fractions. (extends 5.NF.3) (3) represent decimals (tenths and hundredths) as fractions and fractions with denominators of 10 and 100 as decimals. (5.NBT.3.a) (4) represent decimals (thousandths) as fractions, and fractions with denominators of 1,000 as decimals. (5.NBT.3.a) (5) label a point on a number line using a fraction and a decimal, and write a fraction and decimal for a point on a number line. (Reviews 4.NF.7) (6) represent decimals in expanded form, e.g., 347.392 = 3 x 100 + 4 x 10

+ 7 x 1 + 3 x (

) + 9 x (

) + 2 x

(

). (5.NBT.3.a)

1, 2, 4, 5, 6, 7, 8

enVision Math Lesson Sequence: (1) 9-2: Fractions and Division pp. 224-225 (2) 9-3: Mixed Numbers and Improper Fractions pp. 226-227 (3) 9-8: Tenths and Hundredths pp.238-241 (4) 9-9: Thousandths pp.242-243 (5) 9-10: Fractions and Decimals on the Number Line pp. 244-245 Manipulatives: Fraction Models: Strips (or Teaching Tool 27) colored pencils, scissors, 10x10x10 cube Teaching Tools: Problem Solving Recording Sheet

enVision Formative Assessments: Quick Check 9-2 Quick Check 9-3 Quick Check 9-8 Quick Check 9-9 Quick Check 9-10 Summative: Unit 3 Assessment (Use Pearson Success Net or Acuity to create a unit assessment based on the Missouri Learning Standards covered in Unit 3)

http://illustrativemathematics.org/illustrations/293

http://illustrativemathematics.org/illustrations/293



2nd


– December 19th

, 2014


Unit 4: Adding and Subtracting Fractions (Approx. 15-20 days)

Time Frame






15 - 20 days

5.NF.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For

example,

+

=

+

=

. (In general,

+

= (

.)

5.NF.2 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example,

recognize an incorrect result

+

=

, by

observing that

>

.

(1) use a number lineto estimate sums and differences of fractions. (5.NF.2) (2) identify fractions that are in simplest form and find the simplest form of a fraction. (Prepares for 5.NF.1) (3) use models and computational procedures to add and subtract fractions with like denominators. (5.NF.1, 5.NF.2) (4) determine common multiples and the least common multiple of numbers. (Prepares for NF.1) (5) use models and computational procedures to add fractions with unlike denominators. (5.NF.1, 5.NF.2) (6) use models and computational procedures to subtract fractions with unlike denominators. (5.NF.1, 5.NF.2) (7) use models to add and subtract mixed numbers. (5.NF.1, 5.NF.2) (8) use models and computational procedures to add mixed numbers. (5.NF.1, 5.NF.2) (9) use models and computational procedures to subtract mixed numbers. (5.NF.1, 5.NF.2) (10) solve more complex problems involving the addition and subtraction of mixed numbers. (5.NF.1, 5.NF.2)

1, 2, 3, 4, 5, 6, 7, 8

enVision Math Lesson Sequence: (1) 10-1A*: Estimating Sums and Differences of Fractions (2) 9-7: Fractions in Simplest Form pp. 234-237 (3) 10-1: Adding and Subtracting Fractions with Like Denominators pp. 256-259 (4) 10-2: Common Multiples and Least Common Multiples pp.260-261 (5) 10-3: Adding Fractions with Unlike Denominators pp. 262-263 (6) 10-4: Subtracting Fractions with Unlike Denominators pp.264-265 (7) 10-5A*: Modeling Addition and Subtraction of Mixed Numbers (8) 10-5: Adding Mixed Numbers pp. 266-267 (9) 10-6: Subtracting Mixed Numbers pp.268-269 (10) 10-7A*: More Adding and Subtracting Mixed Numbers Supplement this unit with the MO DESE Mathematics Model Curriculum Unit: https://k12apps.dese.mo.gov/webapps/ModelCurriculum/findunit.aspx Select: 5th Grade Math “Adding and Subtracting Fractions” Manipulatives: Fraction Models: Strips (or Teaching Tool 27) Click here for Lesson Plans

enVision Formative Assessments: Quick Check 10-1A* Quick Check 9-7 Quick Check 10-1 Quick Check 10-2 Quick Check 10-3 Quick Check 10-4 Quick Check 10-5A* Quick Check 10-6 Quick Check 10-7A* Summative: Unit 4 Assessment (Use Pearson Success Net or Acuity to create a unit assessment based on the Missouri Learning Standards covered in Unit 4)

https://k12apps.dese.mo.gov/webapps/ModelCurriculum/findunit.aspx

https://k12apps.dese.mo.gov/webapps/ModelCurriculum/findunit.aspx

http://www.slps.org/Page/24109



2nd


– December 19th

, 2014


2014-‐2015 Mathematics Scope and Sequence – Grade 5 -‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐

Sequence of Grade 5 Mathematics Units Aligned with Missouri Learning Standards 1st Quarter

Aug 11 – Oct 10 (43 days) 2nd Quarter

Oct 13 – Dec 19 (44 days) 3rd Quarter

Jan 5 – March 6 (42 days) 4th Quarter

March 9 – May 22 (47 days) Unit 1: Decimal Place Value, Arithmetic and Patterns (Approx. 18 – 22 days)

Unit 3: Multiplying and Dividing Decimals & Relating Decimals and Fractions (Approx. 18 – 20 days)

Unit 5: Multiplying and Dividing Fractions and Mixed Numbers (Approx. 10 – 15 days)

Unit 7: Problem Solving with Data and Measurement (Approx. 15 – 20 days)

Missouri Learning Standards

enVision Lessons/ Resources







5.NBT.3 5.NBT.3.a 5.NBT.3.b 5.NBT.4 5.OA.1 5.OA.2 5.OA.3

1-‐1 1-‐3 1-‐4 2-‐2 2-‐6A* 2-‐6 2-‐7 2-‐8 6-‐1 6-‐3 6-‐4A*

6-‐4 6-‐5 6-‐6A* 6-‐6B* 6-‐6C*

5.NBT.1 5.NBT.2 5.NBT.3.a 5.NBT.7 5.NF.3

7-‐1 7-‐2 7-‐3 7-‐4A* 7-‐4B* 7-‐4 7-‐5 7-‐6A* 7-‐6 7-‐7 7-‐8

9-‐2 9-‐3 9-‐8 9-‐9 9-‐10

5.NF.4 5.NF.4.a 5.NF.4.b 5.NF.5 5.NF.5.a 5.NF.5.b 5.NF.6 5.NF.7 5.NF.7.a 5.NF.7.b 5.NF.7.c

11-‐1 11-‐2A* 11-‐2 11-‐3A* 11-‐3 11-‐4A* 11-‐4 11-‐5A*

5.MD.1 5.MD.2

12-‐1 12-‐2 14-‐1 14-‐2 14-‐3 14-‐4 14-‐5 DESE**3 18-‐2A* 18-‐2B 18-‐2

Unit 2: Developing Fluency with Whole Number Multiplication and Division (Approx. 18-‐ 22 days)

Unit 4: Adding and Subtracting Fractions (Approx. 22 – 25 days)

Unit 6: Understanding Concepts of Volume (Approx. 22 – 28 days)

Unit 8: Coordinate Planes and Classifying Two-‐Dimensional Figures (Approx. 20 – 25 days)









5.NBT.5 5.NBT.6 5.OA.2

3-‐4 3-‐5 3-‐6 3-‐8 4-‐1 4-‐2 4-‐4 4-‐5 4-‐6 5-‐1

5-‐2 5-‐3A* 5-‐3 5-‐4 5-‐5 5-‐6 5-‐7 5-‐8

5.NF.1 5.NF.2

10-‐1A* 9-‐7 10-‐1 10-‐2 10-‐3 10-‐4 10-‐5A* 10-‐6 10-‐7A* DESE**1

5.MD.3 5.MD.3.a 5.MD.3.b 5.MD.4 5.MD.5 5.MD.5.a 5.MD.5.b 5.MD.5.c

13-‐4 13-‐5A* 13-‐5 13-‐6A* 13-‐6 13-‐7 DESE**2

5.G.1 5.G.2 5.G.3 5.G.4 5.OA.3

17-‐2 17-‐3 17-‐4A* 17-‐4B* 17-‐4C* DESE**4 8-‐3 8-‐4 8-‐5

8-‐6A* 8-‐6B* 8-‐6

* enVision math lessons with a capital letter behind the number i.e. 1-‐5A are additional lessons created for transition to Common Core – these lessons are available online (not part of the 2011 student text.) **Missouri Department of Elementary and Secondary Education – Model Curriculum Units https://k12apps.dese.mo.gov/webapps/ModelCurriculum/findunit.aspx (1) Select 5th Grade à math à Adding and Subtracting Fractions (2) Select 5th Grade à math à Build It Volume (3) Select 5th Grade à math à Converting Like Measurement Units within a Given Measurement System (4) Select 5th Grade à math à Graphing Points on the Coordinate Plane

st. louis public schools mathematics - grade 5 2nd quarter pacing … · 2014-08-26 · st. louis...

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