1. Hueneme Elementary School District Staff Development Day # 3 CCSS Mathematic Unit of Study Grade 4

2. Introductions Mariana Cabrera Vincent Gomez Ana Hinojosa

3. Unit 5 Title Understanding Base Ten Fractions and Decimals Length 20 Days Key Points ●Read and write base ten fractions and decimals interchangeably. ●Represent base ten fractions and decimals visually on a number line and in an area model. ●Compare decimals to hundredths. ●Add fractions of 10ths and 100ths. ●Identifying errors

4. Enduring Understandings and Essential Questions Enduring Understandings are those concepts we want students to remember ten years from now. Relationships between parts of a whole in base ten fractions and decimals can be represented in infinite ways. Essential Questions are questions based on the Enduring Understandings that we use to guide or drive instruction and assessment. ▪What is a fraction? When do we use fractions in real life? ▪How are fractions and decimals related? ▪How can you represent fractions and decimals using an area model? ▪How can you represent fractions and decimals using a number line? ▪What are some equivalent representations for fractions, and decimals? ▪How can you represent/compare fractions that are related to different wholes?

5. Academic Vocabulary (Explicitly taught throughout the course of the unit) * express * compare * justify Tier 3 (subject specific) * tenths * hundredths * whole * fraction * denominator * numerator * >,<,= * equivalent Tier 2 (used across a variety of subjects)

6. Chapter 1 (4 days) Essential Standard 4.NF.5. Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.4 For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100. Enduring Understanding Relationships between parts of a whole in base ten fractions and decimals can be represented in infinite ways. Essential Questions ●What is a whole? ●How does a fraction represent the whole? ●What does the numerator represent? Denominator? ●What is an equivalent fraction? Learning Objective (Unpacked Standards) Students will demonstrate understanding of place value of fraction models: 10ths and 100ths using models. (4.NF.5)

7. Suggested Resources for Chapter 1 Everyday Mathematics N/A (not specific to Base Ten Fractions) Math Routines Howard County: https://grade4commoncoremath.wikispaces.hcpss.org/Routine https://grade4commoncoremath.wikispaces.hcpss.org/Routine Today’s Number Number Talks Rocket Math Mental Math Literature (Fiction/Informational Text) * My Half Day by Doris Fisher * If You Were a Fraction by Trista Speed Saskan Writing * Journal Prompts * Reflection * Opening Ended Questions * Exit Slip Online Lessons/Practice * Howard County : https://grade4commoncoremath.wikispace s.hcpss.org/ * Practice Sheets http://www.commoncoresheets.com/ Videos/Interactives/Games Everyday Math - Base-10 Exchange Homework * Practice Sheets http://www.commoncoresheets.com/ * Accelerated Math

8. EssentialStandards Guaranteed: Taught and Assessed (Re-taught if necessary) Number and Operations—Fractions 4.NF.5-7 Understand decimal notation for fractions and compare decimal fractions. 4.NF.5. Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.4 For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100. (DOK 1) 4.NF.6. Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100;locate 0.62 on a number line diagram. (DOK 1) 4.NF.7. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. (DOK 3)

9. Chapter 2 (Days:6) Essential Standard 4.NF.5. Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.4 For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100. Enduring Understanding Relationships between parts of a whole in base ten fractions and decimals can be represented in infinite ways. Essential Questions * How are 10ths and 100ths related? * Do you have common denominators? Learning Objectives Student will express fractions with denominator 10 as an equivalent fraction with denominator 100 and vice versa. (4.NF.5) Students will add fractions denominator 10 and 100.For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100. (4.NF.5)

10. Suggested Resources for Chapter 2 Everyday Mathematics N/A (not specific to Base Ten Fractions) Math Routines Howard County: https://grade4commoncoremath.wikispaces.hcpss.org/Routine https://grade4commoncoremath.wikispaces.hcpss.org/Routine Today’s Number Number Talks Rocket Math Mental Math Writing * Journal Prompts * Reflection * Opening Ended Questions * Exit Slip Online Lessons/Practice Howard County https://grade4commoncoremath.wikispaces.hcps s.org/ Learn Zillion http://learnzillion.com/lessons/336-convert- fractions-into-decimals-to-the-tenths-place http://learnzillion.com/lessons/351-add-fractions- with-tenths-and-hundredths-denominators Common Core Sheets http://www.commoncoresheets.com/ Videos/Interactives/Games * Everyday Math - Base-10 Exchange Homework *Common Core Sheets http://www.commoncoresheets.com/ *Accelerated Math

11. Chapter 3 ( Days:6) Essential Standards 4.NF.6. Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; locate 0.62 on a number line diagram. 4.NF.7. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. Enduring Understanding Relationships between parts of a whole in base ten fractions and decimals can be represented in infinite ways. Essential Questions * What is a fraction? * What is a decimal? * What is a number line? Why are tenths larger then hundredths? Learning Objectives * Students can show a decimal as a fraction and a fraction as a decimal. (4.NF.6) * Students will represent a decimal in relationship to a whole number on a number line. (4.NF.6) * Students can compare two decimals in relationship to their value.(4.NF.7)

12. Suggested Resources for Chapter 3 Everyday Mathematics *Unit 4 Lessons 1-3 Math Routines Howard County: https://grade4commoncoremath.wikispace s.hcpss.org/Routine https://grade4commoncoremath.wikispace s.hcpss.org/Routine Today’s Number Number Talks Rocket Math Mental Math Writing * Journal Prompts * Reflection * Opening Ended Questions * Exit Slip Online Lessons/Practice Howard County https://grade4commoncoremath.wikispaces.hcps s.org/ Learn Zillion http://learnzillion.com/lessons/1424-convert- decimals-to-fractions-to-the-tenths-place-using- number-lineshttp://learnzillion.com/lessons/1424-convert- decimals-to-fractions-to-the-tenths-place-using- number-lines http://learnzillion.com/lessons/3217-compare- two-decimals-to-the-hundredths-place-using- fraction-models Common Core Sheets http://www.commoncoresheets.com/ Videos/Interactives/Games *Everyday Math - Base-10 Exchange Homework * Common Core Sheets http://www.commoncoresheets.com/ * Accelerated Math

13. Assessment Formative Teacher created/selected Measured Progress: Testlets Summative Teacher created/selected Measured Progress: Benchmarks Smarter Balanced Assessment (3-8)

14. Year at a Glance ….. Unit 1 Place Value Unit 2 Addition and Subtraction of Whole Numbers Unit 3 Multiplication of Whole Numbers Unit 4 Division of Whole Numbers Unit 5 Understanding Base Ten Fractions and Decimals Unit 6 Order and Compare Fractions Unit 7 Operations with Fractions Unit 8 Angles and Figures Unit 9 Conversion of Metric and US Customary Systems