Grade 4 Unit 6 Exploring Measurement Mathematics

Unit Goals – Stage 1 Number of Days: 33 Traditional: May 1 – June 15, 2017; Track B: June 9 – July 26, 2017

Unit Description: Unit 6 ends the year with an exploratory unit on measurement. Students build a conceptual understanding of the relative sizes of units of measure within a single system of measurement. They investigate measurement through the formulas for area and perimeter. Data is used to support students’ understanding of fractional measurement quantities both smaller and larger than 1. Students combine competencies from different domains to provide a context for problem solving.

Materials: 1-inch grid paper, color pencils, rulers (centimeter and 12 inch), meter stick and yard stick, tape measures, analog clocks, balance scale with mass weights, beaker (marked for mL and L), digital scale (metric and customary units), and containers (gallon, quart, pint, and cup) and Go Math! MathBoard or whiteboard (Some of these are not provided, but suggested and can be checked out at the TRC Math & Science Resource Center) Standards for Mathematical Practice Transfer Goals Students will be able to independently use their learning to… SMP.1 Make sense of problems and • Make sense of never-before-seen problems and persevere in solving them. persevere in solving them. • Construct viable arguments and critique the reasoning of others. SMP.2 Reason abstractly and quantitatively. SMP.3 Construct viable arguments and Making Meaning critique the reasoning of others. UNDERSTANDINGS (U) ESSENTIAL QUESTIONS (Q) SMP.4 Model with mathematics. Students will understand that … Students will keep considering… SMP.5 Use appropriate tools strategically. • Measurements can be expressed in larger or • How are the units of measure within a SMP.6 Attend to precision. smaller units within a measurement system. standard system related? SMP.7 Look for and make use of structure. • Formulas can be used to find perimeter and • How can you find the perimeter and area of a SMP.8 Look for and express regularity in area for rectangles in the real world. rectangle? repeated reasoning.

Standards for Mathematical Content Acquisition Clusters Addressed KNOWLEDGE (K) SKILLS Students will know… Students will be skilled at and/or be able to… Measurement and Data • The definitions of the academic vocabulary • Convert measurements from larger to smaller 4.MD.A Solve problems involving words such as capacity, convert, customary units. measurement and conversion of units, line plot metric units, and mixed • Record equivalent measurements in a two- measurements from a larger unit to a measures (e.g. 3 m 43 cm), and square inch.. column table. smaller unit. • The relative sizes of measurement units • Use the four operations to solve measurement 4.MD.B Represent and interpret data. within a single system of measurement word problems, including problems involving including yard (yd.), foot (ft.), inch (in), pound simple fractions and decimals. (lb.), ounce (oz.), gallon (gal), quart (qt.), pint • Represent measurement quantities using (pt.), cup (c), kilometer (km), meter (m), diagrams such as number lines that feature a centimeter (cm), kilogram (kg), gram (g), measurement scale. liter(L), milliliter(mL); hour (hr.), minute (min), • Use formulas to calculate perimeter and area and second (sec). of rectangles. • The formulas for finding perimeter and area of rectangles.

LONG BEACH UNIFIED SCHOOL DISTRICT 1 Posted 6/14/16 New 2016 – 2017 Grade 4 Unit 6 Exploring Measurement Mathematics

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

Standards for Mathematical Content

Measurement and Data [s] 4.MD.A Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. 4.MD.1 Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36)…

4.MD.2 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

4.MD.3 Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.

[s] 4.MD.B Represent and interpret data. 4.MD.4 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.

Key: [m]= major clusters; [s] = supporting clusters; [a] = additional clusters

LONG BEACH UNIFIED SCHOOL DISTRICT 2 Posted 6/14/16 New 2016 – 2017 Grade 4 Unit 6 Exploring Measurement Mathematics

Evidence of Learning – Stage 2 Assessment Evidence Unit Assessment Students will complete selected response and constructed response items to indicate level of mastery/understanding of the unit standards as outlined in this guide.

Measurement and Data [s] 4.MD.A • The student converts measurements from larger units to smaller units within a single system of units. • The student records measurement equivalents in a two-column table. • The student identifies measurement quantities from diagrams, such as number line diagrams that feature a measurement scale, and uses the information to solve word problems. • The student applies the area and perimeter formulas for rectangles to solve mathematical and real-world problems.

[s] 4.MD.B • The student completes a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). • The student solves problems involving addition and subtraction of fractions with like denominators by using information presented in line plots.

For selected content, students will need to… • Solve complex problems in pure and applied mathematics, making productive use of knowledge and problem solving strategies. • Clearly and precisely construct viable arguments to support their own reasoning and critique the reasoning of others.

Other Evidence Formative Assessment Opportunities • Opening Tasks • Exit slips • Go Math! Show What You Know • Quizzes • Classroom Challenges • Extension Menus • Go Math! Performance Task • It’s All About the Facts Supplemental materials • Homework (Go Math! Standards Practice Book) • In-class projects • Go Math! Getting Ready for the Smarter Balance • Recorded Teacher Observations • Go Math! Chapter 12 & 13 Test (Assessment Guide) • Writing activities • Go Math! Chapter 12 & 13 Review / Test – Student Book • SBAC Interim Assessment Block (IAB)

Access Using Formative Assessment for Differentiation for suggestions. Located on the LBUSD website – “M” Mathematics – Curriculum Documents.

LONG BEACH UNIFIED SCHOOL DISTRICT 3 Posted 6/14/16 New 2016 – 2017 Grade 4 Unit 6 Exploring Measurement Mathematics

Daily Usaré las • Participating in daily Number Talks. • Number Talks Strategies • Multiple Marker estrategias • Communicating my reasoning. and Problem Sets, Grades matemáticas 2-5 (also found on intranet mentales para in Instructional Tools) sumar, restar, multiplicar y dividir al…

90 Preservaré en la • Developing long term problem solving ST Math Objectives ST Math Tips minutes resolución de skills. • Measurement and • Access 'early finishers’ doc at per week problemas para • Visualizing math concepts. Conversions trs.stmath.com (use search (Schools/ ayudarme a • Making connections between concepts • Advanced Shapes box). grades entender las and across grades. • Regularly update homework with ST matemáticas al… • Playing interactive games. assignments under Math) Curriculum tab. • Celebrate JiJi success.

Before the I can show what I • Completing “Show What You Know”. • Ch. 12 & 13 “Show What Unit know about You Know”, pp. 469 & 523 (as measurement **Use the Diagnostic Table if needed) by… needed for intervention options: On-level, Strategic, Intensive, and Independent.

LONG BEACH UNIFIED SCHOOL DISTRICT 4 Posted 6/14/16 New 2016 – 2017 Grade 4 Unit 6 Exploring Measurement Mathematics

Learning Plan – Stage 3 Suggested Sequence of Key Learning Events and Instruction Core Resources: Supplemental Resources: Days Metas de Success Criteria Go Math! Books, Internet and Aprendizaje http://www-k6.thinkcentral.com Curriculum Intranet (LBUSD Math (Universal Access for SPED, Struggling Intranet - Instructional Tools - Elementary - Students, ELL, GATE) 4th Grade) 1 Utilizaré las OPENING TASK – Measuring Penny • Measuring Penny Opening • See medidas en el • Completing a measurement activity Task https://www.illustrativemathem entorno del mundo based on Measuring Penny. • Measuring Penny, by atics.org/4 for tasks to be real al… Loreen Leedy used throughout the unit. • Ch. 12 & 13 “Math • Engage, Explore, Evaluate Detective”, pp. 469 & 523 Problems (to use throughout • Ch. 12 & 13 “Vocabulary the unit) Builder”, pp. 470 & 524 • Notice and Wonder Introduction and Record Sheet (to use throughout the unit, Instructional Tools – Notice and Wonder) 2 – 5 Puedo identificar, • Using diagrams and models to represent • Lesson 12.1 Measurement • Good Questions, p. 69 #1-2, comparar y measurement quantities. Benchmarks 4, 6 & 7 convertir las • Using benchmarks to understand the • Lesson 12.2 Customary • Problem Solving Grades 3-5 unidades de relative sizes of customary units (inches, Units of Length pp. 81-82; Task 5.1 medidas que feet, yards) and metric units (millimeters, • Lesson 12.6 Investigate - “Measuring Height” requieren longitud centimeters, meters, kilometers). Metric Units of Length o Measuring Height Task al… • Using two-column tables and • Metric Conversions multiplication to convert measurements • Yard Instructional Slide from larger to smaller units and record • Measure Yourself equivalent measurements. • Who is the Tallest? Task • Using powers of 10 to change a larger metric unit to a smaller metric unit.

6 – 7 Puedo identificar, • Using models, such as number lines, • Lesson 12.3 Customary • Good Questions, pp. 49 - 50 comparar y and tables to show the relationship Units of Weight # 1-2, 3-5 convertir las between customary units (ounces, • Lesson 12.7 Metric Units of • Shopping Bags Task unidades de pounds and tons) and the relationship Mass and Liquid Volume • Literature Book: If You Were medidas que between metric units (kilograms and (Focus only on mass a Pound or a Kilogram by requieren de peso grams). related examples/problems) Marcie Aboff (not provided, y masa al… • Using two-column tables and the four but suggested) operations to convert measurements from larger to smaller units and record equivalent measurements.

LONG BEACH UNIFIED SCHOOL DISTRICT 5 Posted 6/14/16 New 2016 – 2017 Grade 4 Unit 6 Exploring Measurement Mathematics

8 – 9 Puedo identificar, • Using diagrams and models, such as • Lesson 12.4 Customary • Good Questions, p. 53 – 54 comparar y bars and tables, to show the relative Units of Liquid Volume # 2, 5, 8 convertir las sizes of customary units (fluid ounces, • Lesson 12.7 Metric Units of • The Gallon Game unidades de cups, pints, quarts, gallons) and metric Mass and Liquid Volume • Gallon Instructional Slide medida que units (milliliters and liters). (Focus only on liquid requieren de • Using two-column tables and the four volume related volumen líquido operations to convert measurements examples/problems) al… from larger to smaller units and record equivalent measurements. • Using powers of 10 to change a larger metric unit to a smaller metric unit.

10 - 11 Puedo identificar, • Using diagrams and models, such as • Lesson 12.8 Units of Time • Good Questions, p. 64 #1, 4, comparar y clocks, tables, and number lines, to show 7 convertir las the relative sizes of units of time • Problem Solving Grades 3-5 unidades de (seconds, minutes, hours, days, weeks, pp. 82 – 84; Task 5.2 “Quarter medida que years). of an Hour” requieren de la • Using two-column tables and the four o Quarter of an Hour Task hora al… operations to convert measurements from larger to smaller units and record equivalent measurements.

12 - 13 Puedo resolver los • Using the four operations and diagrams, • Lesson 12.9 Problem • Good Questions, p. 65 #10 problemas con el such as number lines with a Solving – Elapsed Time tiempo measurement scale, to find either the transcurrido al… start time or end time of an event. • Answering questions throughout the day, such as: How long is it until we have recess?

LONG BEACH UNIFIED SCHOOL DISTRICT 6 Posted 6/14/16 New 2016 – 2017 Grade 4 Unit 6 Exploring Measurement Mathematics

16 – 18 Puedo resolver los • Extending the use of number lines to • Lesson 12.5 Line Plots • Problem Solving Grades 3-5 problemas con los organize problem-solving data. pp. 95 – 98; Task 5.7 puntos en una • Making and interpreting line plots with “Comparing Measurements” línea al… fractional data. • Button Diameters Task • Using information presented in line plots to order and count the frequency of data. • Using my understanding of addition and subtraction of fractions.

19 – 20 Utilizaré mi FORMATIVE ASSESSMENT LESSON • FAL, Tracking Homework • Tracking Homework – FAL, entendimiento de Classroom Challenge: (Intranet - Assessments) Differentiated Activities las fracciones para Tracking Homework resolver los • Applying and extending my previous problemas understanding of adding and subtracting representados en fractions. palabras con los • Communicating my reasoning. puntos en una • Checking to see if my answers make línea al… sense.

LONG BEACH UNIFIED SCHOOL DISTRICT 7 Posted 6/14/16 New 2016 – 2017 Grade 4 Unit 6 Exploring Measurement Mathematics

Learning Plan – Stage 3 Suggested Sequence of Key Learning Events and Instruction Core Resources: Supplemental Resources: Days Metas de Success Criteria Go Math! Books, Internet and Aprendizaje http://www-k6.thinkcentral.com Curriculum Intranet (LBUSD Math (Universal Access for SPED, Struggling Intranet - Instructional Tools - Elementary - Students, ELL, GATE) 4th Grade) 21 - 25 Puedo resolver los • Exploring perimeter and area from a • Lesson 13.1 Perimeter • Karl’s Garden Task problemas que problem-solving perspective. • Lesson 13.2 Area • Good Questions, pp. 58 - 59 requieren de • Using tools (including rulers and tape • Lesson 13.3 Area of #1 - 9 & pp. 60 #1 – 5 perímetro y área measures) to measure lengths of sides. Combined Rectangles • What’s the Perimeter? al… • Using a variety of tools (including grid • Lesson 13.4 Find Unknown • Cooperative Frame for Area & paper) and models to represent the Measures Perimeter context of the problem. • Lesson 13.5 Problem • Using the formulas to calculate Solving - Find the Area perimeter, P = 2l x 2w or P = 2(l x w), and area, A = l x w, of rectangles. Note: For area, Go Math! uses • Correctly labeling perimeters with linear the formula A = b x h. This will units and areas with square units. help with later work in middle • Communicating understanding of why school when students find areas the formulas work. of parallelograms and triangles. • Exploring area as additive: the area of a However, the California figure made up of two nonoverlapping Mathematics Framework uses A rectangles is the sum of the two smaller = l x w. For coherence, if you areas. choose to use A = b x h, teach that l x w = b x h and that these can be used interchangeably.

26 Unit Assessment 27 Ch. 12 Performance Task “Store Storage” (Assessment Guide: pp. AG184 – AG188D) At this point, all standards addressed in the Grade 4 Interim Assessment Block – “Measurement and Data” have been covered. This block may now be administered.

28 - 33 Students will get ready for Grade 5 by completing various tasks. • “Getting Ready for Grade 5,” • Critical Area Review Projects, Planning Guide, pp. PG48 – Planning Guide PG91 o “The Black-Footed Ferret,” • “Getting Ready for Grade 5,” pp. PG42 – PG43 Standards Practice Book, o “Fundraiser,” pp. PG44 – pp. P223 – P270 PG45 o “Design a Car Showroom,” pp. PG46 – PG47

LONG BEACH UNIFIED SCHOOL DISTRICT 8 Posted 6/14/16 New 2016 – 2017 Grade 4 Unit 6 Exploring Measurement Mathematics

We would appreciate feedback on the following: Unit Guide bit.ly/Grade4UnitGuide Assessment and FAL bit.ly/Grade4Assessment

LONG BEACH UNIFIED SCHOOL DISTRICT 9 Posted 6/14/16 New 2016 – 2017