grade 4 unit 6 exploring measurement mathematics · grade 4 unit 6 exploring measurement...

Grade 4 Unit 6 Exploring Measurement Mathematics

LONG BEACH UNIFIED SCHOOL DISTRICT 1 Posted 6/14/16 New 2016 – 2017

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 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 Clusters Addressed Measurement and Data 4.MD.A Solve problems involving

measurement and conversion of measurements from a larger unit to a smaller unit.

4.MD.B Represent and interpret data.

Transfer Goals Students will be able to independently use their learning to… • Make sense of never-before-seen problems and persevere in solving them. • Construct viable arguments and critique the reasoning of others.

Making Meaning

UNDERSTANDINGS (U) Students will understand that … • Measurements can be expressed in larger or

smaller units within a measurement system. • Formulas can be used to find perimeter and

area for rectangles in the real world.

ESSENTIAL QUESTIONS (Q) Students will keep considering… • How are the units of measure within a

standard system related? • How can you find the perimeter and area of a

rectangle?

Acquisition KNOWLEDGE (K) Students will know… • The definitions of the academic vocabulary

words such as capacity, convert, customary units, line plot metric units, and mixed measures (e.g. 3 m 43 cm), and square inch..

• The relative sizes of measurement units within a single system of measurement including yard (yd.), foot (ft.), inch (in), pound (lb.), ounce (oz.), gallon (gal), quart (qt.), pint (pt.), cup (c), kilometer (km), meter (m), centimeter (cm), kilogram (kg), gram (g), liter(L), milliliter(mL); hour (hr.), minute (min), and second (sec).

• The formulas for finding perimeter and area of rectangles.

SKILLS Students will be skilled at and/or be able to… • Convert measurements from larger to smaller

units. • Record equivalent measurements in a two-

column table. • Use the four operations to solve measurement

word problems, including problems involving simple fractions and decimals.

• Represent measurement quantities using diagrams such as number lines that feature a measurement scale.

• Use formulas to calculate perimeter and area of rectangles.



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



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 • Go Math! Show What You Know • Classroom Challenges • Go Math! Performance Task • Homework (Go Math! Standards Practice Book) • Go Math! Getting Ready for the Smarter Balance • Go Math! Chapter 12 & 13 Test (Assessment Guide) • Go Math! Chapter 12 & 13 Review / Test – Student Book

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

• Exit slips • Quizzes • Extension Menus • It’s All About the Facts Supplemental materials • In-class projects • Recorded Teacher Observations • Writing activities • SBAC Interim Assessment Block (IAB)

http://www.lbschools.net/Main_Offices/Curriculum/Areas/Mathematics/docs/Using%20FA%20to%20Address%20Learning%20Needs%20of%20Stu%20in%20Subgroups%20MATH.pdf



Learning Plan – Stage 3 Suggested Sequence of Key Learning Events and Instruction

Days

Metas de

Aprendizaje

Success Criteria

Core Resources: Go Math!

http://www-k6.thinkcentral.com (Universal Access for SPED, Struggling

Students, ELL, GATE)

Supplemental Resources: Books, Internet and

Curriculum Intranet (LBUSD Math Intranet - Instructional Tools - Elementary -

4th Grade) Daily Sabré las

operaciones básicas de matemáticas al…

• Saying facts orally. • Writing Fact Families. • Using them to play games.

• Maintaining Fluency Through Fact Families, pp.1-10, 13-28

• Go Math! Strategies and Practice For Skills and Facts Fluency

• Basic Facts Games: “How Many Rows? How Many in Each Row? https://www.youcubed.org/task/how-many-rows/

Daily Usaré las estrategias matemáticas mentales para sumar, restar, multiplicar y dividir al…

• Participating in daily Number Talks. • Communicating my reasoning.

• Number Talks Strategies and Problem Sets, Grades 2-5 (also found on intranet in Instructional Tools)

• Multiple Marker

90 minutes per week (Schools/ grades with ST Math)

Preservaré en la resolución de problemas para ayudarme a entender las matemáticas al…

• Developing long term problem solving skills.

• Visualizing math concepts. • Making connections between concepts

and across grades. • Playing interactive games.

ST Math Objectives • Measurement and

Conversions • Advanced Shapes

ST Math Tips • Access 'early finishers’ doc at

trs.stmath.com (use search box).

• Regularly update homework assignments under Curriculum tab.

• Celebrate JiJi success.

Before the Unit (as

needed)

I can show what I know about measurement by…

• Completing “Show What You Know”.

• Ch. 12 & 13 “Show What You Know”, pp. 469 & 523

**Use the Diagnostic Table if needed for intervention options: On-level, Strategic, Intensive, and Independent.

http://www-k6.thinkcentral.com/

https://www.youcubed.org/task/how-many-rows/

https://www.youcubed.org/task/how-many-rows/




Days

Metas de

Aprendizaje

Success Criteria






4th Grade) 1 Utilizaré las

medidas en el entorno del mundo real al…

OPENING TASK – Measuring Penny • Completing a measurement activity

based on Measuring Penny.

• Measuring Penny Opening Task

• Measuring Penny, by Loreen Leedy

• Ch. 12 & 13 “Math Detective”, pp. 469 & 523

• Ch. 12 & 13 “Vocabulary Builder”, pp. 470 & 524

• See https://www.illustrativemathematics.org/4 for tasks to be used throughout the unit.

• Engage, Explore, Evaluate Problems (to use throughout the unit)

• Notice and Wonder Introduction and Record Sheet (to use throughout the unit, Instructional Tools – Notice and Wonder)

2 – 5 Puedo identificar, comparar y convertir las unidades de medidas que requieren longitud al…

• Using diagrams and models to represent measurement quantities.

• Using benchmarks to understand the relative sizes of customary units (inches, feet, yards) and metric units (millimeters, centimeters, meters, kilometers).

• Using two-column tables and multiplication to convert measurements from larger to smaller units and record equivalent measurements.

• Using powers of 10 to change a larger metric unit to a smaller metric unit.

• Lesson 12.1 Measurement Benchmarks

• Lesson 12.2 Customary Units of Length

• Lesson 12.6 Investigate - Metric Units of Length

• Good Questions, p. 69 #1-2, 4, 6 & 7

• Problem Solving Grades 3-5 pp. 81-82; Task 5.1 “Measuring Height” o Measuring Height Task

• Metric Conversions • Yard Instructional Slide • Measure Yourself • Who is the Tallest? Task

6 – 7 Puedo identificar, comparar y convertir las unidades de medidas que requieren de peso y masa al…

• Using models, such as number lines, and tables to show the relationship between customary units (ounces, pounds and tons) and the relationship between metric units (kilograms and grams).

• Using two-column tables and the four operations to convert measurements from larger to smaller units and record equivalent measurements.

• Lesson 12.3 Customary Units of Weight

• Lesson 12.7 Metric Units of Mass and Liquid Volume (Focus only on mass related examples/problems)

• Good Questions, pp. 49 - 50 # 1-2, 3-5

• Shopping Bags Task • Literature Book: If You Were

a Pound or a Kilogram by Marcie Aboff (not provided, but suggested)


https://www.illustrativemathematics.org/4

https://www.illustrativemathematics.org/4




Days

Metas de

Aprendizaje

Success Criteria






4th Grade) • Using powers of 10 to change a larger

metric unit to a smaller metric unit.

8 – 9

Puedo identificar, comparar y convertir las unidades de medida que requieren de volumen líquido al…

• Using diagrams and models, such as bars and tables, to show the relative sizes of customary units (fluid ounces, cups, pints, quarts, gallons) and metric units (milliliters and liters).


• Using powers of 10 to change a larger metric unit to a smaller metric unit.

• Lesson 12.4 Customary Units of Liquid Volume

• Lesson 12.7 Metric Units of Mass and Liquid Volume (Focus only on liquid volume related examples/problems)

• Good Questions, p. 53 – 54 # 2, 5, 8

• The Gallon Game • Gallon Instructional Slide

10 - 11 Puedo identificar, comparar y convertir las unidades de medida que requieren de la hora al…

• Using diagrams and models, such as clocks, tables, and number lines, to show the relative sizes of units of time (seconds, minutes, hours, days, weeks, years).


• Lesson 12.8 Units of Time • Good Questions, p. 64 #1, 4, 7

• Problem Solving Grades 3-5 pp. 82 – 84; Task 5.2 “Quarter of an Hour” o Quarter of an Hour Task

12 - 13 Puedo resolver los problemas con el tiempo transcurrido al…

• Using the four operations and diagrams, such as number lines with a measurement scale, to find either the start time or end time of an event.

• Answering questions throughout the day, such as: How long is it until we have recess?

• Lesson 12.9 Problem Solving – Elapsed Time

• Good Questions, p. 65 #10





Days

Metas de

Aprendizaje

Success Criteria






4th Grade) 14 - 15 Puedo resolver los

problemas que requieren de medidas mixtas al…

• Using previous understanding of the mathematical operations and measurement units.

• Renaming and regrouping units.

• Lesson 12.10 Mixed Measures

• Customary Measurements Slide

• Measurement Flashcards • Measurement Facts • Measurement Jeopardy • Measurement Conversions

Quiz • Measurement Exit Tickets • Literature Book: Millions to

Measure by David M. Schwartz (Provided at 2013-14 Training)

16 – 18

Puedo resolver los problemas con los puntos en una línea al…

• Extending the use of number lines to organize problem-solving data.

• Making and interpreting line plots with fractional data.

• Using information presented in line plots to order and count the frequency of data.

• Using my understanding of addition and subtraction of fractions.

• Lesson 12.5 Line Plots

• Problem Solving Grades 3-5 pp. 95 – 98; Task 5.7 “Comparing Measurements”

• Button Diameters Task

19 – 20

Utilizaré mi entendimiento de las fracciones para resolver los problemas representados en palabras con los puntos en una línea al…

FORMATIVE ASSESSMENT LESSON Classroom Challenge: Tracking Homework

• Applying and extending my previous understanding of adding and subtracting fractions.

• Communicating my reasoning. • Checking to see if my answers make

sense.

• FAL, Tracking Homework (Intranet - Assessments)

• Tracking Homework – FAL, Differentiated Activities





Days

Metas de

Aprendizaje

Success Criteria






4th Grade) 21 - 25 Puedo resolver los

problemas que requieren de perímetro y área al…

• Exploring perimeter and area from a problem-solving perspective.

• Using tools (including rulers and tape measures) to measure lengths of sides.

• Using a variety of tools (including grid paper) and models to represent the context of the problem.

• Using the formulas to calculate perimeter, P = 2l x 2w or P = 2(l x w), and area, A = l x w, of rectangles.

• Correctly labeling perimeters with linear units and areas with square units.

• Communicating understanding of why the formulas work.

• Exploring area as additive: the area of a figure made up of two nonoverlapping rectangles is the sum of the two smaller areas.

• Lesson 13.1 Perimeter • Lesson 13.2 Area • Lesson 13.3 Area of

Combined Rectangles • Lesson 13.4 Find Unknown

Measures • Lesson 13.5 Problem

Solving - Find the Area Note: For area, Go Math! uses the formula A = b x h. This will help with later work in middle school when students find areas of parallelograms and triangles. However, the California Mathematics Framework uses A = l x w. For coherence, if you choose to use A = b x h, teach that l x w = b x h and that these can be used interchangeably.

• Karl’s Garden Task • Good Questions, pp. 58 - 59

#1 - 9 & pp. 60 #1 – 5 • What’s the Perimeter? • Cooperative Frame for Area &

Perimeter

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,” Planning Guide, pp. PG48 – PG91

• “Getting Ready for Grade 5,” Standards Practice Book, pp. P223 – P270

• Critical Area Review Projects, Planning Guide o “The Black-Footed Ferret,”

pp. PG42 – PG43 o “Fundraiser,” pp. PG44 –

PG45 o “Design a Car Showroom,”

pp. PG46 – PG47





Days

Metas de

Aprendizaje

Success Criteria






4th Grade) • Set Your Own Class Record • Robot Maker Performance

Task • Planting Tulips Performance

Task

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


http://bit.ly/Grade4UnitGuide

http://bit.ly/Grade4Assessment