Enhanced Instructional Transition Guide

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1 Addition and Subtraction with Whole Numbers and Decimals (13 days) Possible Lesson 01 (5 days) Possible Lesson 02 (8 days) POSSIBLE LESSON 01 (5 days) This lesson is one approach to teaching the State Standards associated with this unit. Districts are encouraged to customize this lesson by supplementing with district-approved resources, materials, and activities to best meet the needs of learners. The duration for this lesson is only a recommendation, and districts may modify the time frame to meet students needs. To better understand how your district is implementing CSCOPE lessons, please contact your child s teacher. (For your convenience, please find linked the TEA Commissioner s List of State Board of Education Approved Instructional Resources and Midcycle State Adopted Instructional Materials.) Lesson Synopsis: Decimal addition and subtraction computations are modeled with base-ten blocks, grids, and number lines. TEKS: The Texas Essential Knowledge and Skills (TEKS) listed below are the standards adopted by the State Board of Education, which are required by Texas law. Any standard that has a strike-through (e.g. sample phrase) indicates that portion of the standard is taught in a previous or subsequent unit. The TEKS are available on the Texas Education Agency website at Number, operation, and quantitative reasoning.. The student adds and subtracts to solve meaningful problems involving whole numbers and decimals. The student is expected to: 4.3A Use addition and subtraction to solve problems involving whole numbers. Supporting Standard 4.3B Add and subtract decimals to the hundredths place using concrete objects and pictorial models. Supporting Standard 4.10 Geometry and spatial reasoning.. The student recognizes the connection between numbers and their properties and points on a line. The student is expected to: 4.10 Locate and name points on a number line using whole numbers, fractions such as halves and fourths, and decimals such as tenths. Readiness Standard page 1 of 22

2 Underlying Processes and Mathematical Tools TEKS: 4.14 Underlying processes and mathematical tools.. The student applies Grade 4 mathematics to solve problems connected to everyday experiences and activities in and outside of school. The student is expected to: 4.14A Identify the mathematics in everyday situations. 4.14B Solve problems that incorporate understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness. 4.14C Select or develop an appropriate problem-solving plan or strategy, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem. 4.14D Use tools such as real objects, manipulatives, and technology to solve problems Underlying processes and mathematical tools.. The student communicates about Grade 4 mathematics using informal language. The student is expected to 4.15A Explain and record observations using objects, words, pictures, numbers, and technology. 4.15B Relate informal language to mathematical language and symbols Underlying processes and mathematical tools.. The student uses logical reasoning. The student is expected to: 4.16B Justify why an answer is reasonable and explain the solution process. Performance Indicator(s): page 2 of 22

3 Grade 04 Mathematics Unit 02 PI 01 Use grids (tenths or hundredths) and/or number lines to model decimal numbers in addition/subtraction problem situations (e.g., distances, money, etc.) such as: Liza ran 1.7 miles on Monday, 0.8 miles on Tuesday, and 3.75 miles on Wednesday. How many more miles did Liza run on Wednesday than she ran on the other two days? A kitchen floor needs ten rows of tiles with ten tiles in each row. A worker installed 32 hundredths of the tiles the first day. On the second day, the worker finished the job. How many tiles were installed on the second day? Susie purchased a sports drink for $1.34, a sandwich for $2.79, and a bag of chips for 3 quarters. How much did Susie pay for the drink, sandwich, and chips? For each situation, write a description of your observations of how the model was used to identify the decimal numbers in the problem, and then justify how it was used to solve it. Standard(s): 4.3A, 4.3B, 4.10, 4.14A, 4.14B, 4.14C, 4.14D, 4.15A, 4.15B, 4.16B ELPS ELPS.c.4I, ELPS.c.5F, ELPS.c.5G Key Understanding(s): When solving addition and subtraction problems involving whole numbers and decimals, only digits with the same place value can be added or subtracted because digits in like places have the same underlying unit amount. Models, including number lines, can be used to communicate the values of whole numbers and decimals to solve real-life addition and subtraction problem situations and to justify their solutions. Problem solving with addition and subtraction of whole numbers and decimal models involves analyzing the given information, the missing information, and the question(s); developing a plan with strategies; observing and communicating the mathematical ideas through verbal/written descriptions, statements, and/or equations; and evaluating the solution for reasonableness. Misconception(s): Some students may think that 0.9 and 0.09 are equivalent. Use models to create a visual representation showing why these two values are not equivalent. Vocabulary of Instruction: page 3 of 22

4 addend decimal hundredths tenths Materials: Base-Ten Block Model Cards (optional) (1 set per student, 1 set per teacher) (previously created in Unit 01 Lesson 01 Explore 1) base-ten blocks ( cubes, flats, longs, 10 units in each set) (1 set per student, 1 set per teacher) (previously created in Unit 01 Lesson 01 Explore 1) construction paper (1 sheet per student) glue (1 per 2 students) Local Resource(s) scissors (1 per 2 students) Attachments: All attachments associated with this lesson are referenced in the body of the lesson. Due to considerations for grading or student assessment, attachments that are connected with Performance Indicators or serve as answer keys are available in the district site and are not accessible on the public website. Decimal Addition and Subtraction Grids Blank Tenths and Hundredths Grids Decimal Problem Solver KEY Decimal Problem Solver Blank Decimal Number Line Adding and Subtracting Decimals Using Number Lines and Grids KEY Adding and Subtracting Decimals Using Number Lines and Grids page 4 of 22

5 GETTING READY FOR INSTRUCTION Teachers are encouraged to supplement and substitute resources, materials, and activities to meet the needs of learners. These lessons are one approach to teaching the TEKS/Specificity as well as addressing the Performance Indicators associated with each unit. District personnel may create original lessons using the Content Creator in the Tools Tab. All originally authored lessons can be saved in the My CSCOPE Tab within the My Content area. Suggested Day Suggested Instructional Procedures Notes for Teacher 1 Topics: Introduce addition with decimal numbers using base-ten blocks Spiraling Review Engage 1 Students use base-ten blocks to model decimal number addition. MATERIALS Instructional Procedures: 1. Place students in groups of 3 4. Distribute a set of base ten blocks (no 1000 cubes) to each group and display the following problem for the class to see: 2. Instruct student groups to use their base-ten blocks to create the numbers in the problem, and to find a solution. Allow students time to construct their models. Monitor and assess groups to check for understanding. Facilitate a class discussion about the different ways groups used the base-ten blocks to create a model of the addition problem and how to find the solution. Ask: base-ten blocks ( cubes, flats, longs, 10 units in each set) (1 set per student, 1 set per teacher) (previously created in Unit 01 Lesson 01 Explore 1) Base-Ten Block Model Cards (optional) (1 set per student, 1 set per teacher) (previously created in Unit 01 Lesson 01 Explore 1) TEACHER NOTE You may distribute the 1000-cubes to the groups if you wish. Be prepared to discuss the difference in page 5 of 22

6 Suggested Day Suggested Instructional Procedures Which blocks represent the whole? (the 100-flats or 1000-cubes) Which blocks represent the tenths? (the 10-longs) Which blocks represent the hundredths? (the unit cubes) How is adding decimals like adding whole numbers? How is it different? Answers may vary. It is just like adding whole numbers, but the blocks represent different amounts; The blocks now represent parts of a whole; etc. If this problem were recorded on a grid, what would it look like? Answers may vary. The decimal amounts for tenths can be shaded on a tenths or hundredths grid and the decimal amount for hundredths can be shaded on a hundredths grid; Whole numbers would be a whole grid shaded; etc. Notes for Teacher using the 1000-cube as the whole versus using the 100- flat as a whole. Either base-ten block will model the problem accurately because the relationship between the blocks is consistent. However, since students will be working with the tenths and hundredths grids in drawing pictorial representations, it may be best to steer the class towards the use of the 100-flat rather than the 1000-cube. 2 Topics: Model addition and subtraction of decimal numbers with grids Spiraling Review Explore/Explain 1 Students use tenths and hundredths grids to model addition and subtraction of decimal numbers. ATTACHMENTS Instructional Procedures: 1. Display teacher resource: Decimal Addition and Subtraction Grids. Ask: Teacher Resource: Decimal Addition and Subtraction Grids (1 per teacher) Handout: Decimal Addition and Subtraction Grids (1 per student) How did you use the base-ten blocks to represent decimals? Answers may vary. The 100-flat represented the whole, the 10-long represented the tenths, and the unit page 6 of 22

7 Suggested Day Suggested Instructional Procedures represented the hundredths; etc. How are the base-ten blocks and decimal grids similar? Answers may vary. The grids are the same shape as the blocks and separated into tenths like the 10-longs and/or hundredths which look like the unit blocks; etc. Notes for Teacher 2. Distribute handout: Decimal Addition and Subtraction Grids to each student. Instruct students to shade 4 tenths on the first decimal tenths grid, 5 tenths on the second decimal tenths grid, and an estimate of the sum on the third decimal tenths grid. Allow time for students to complete their shading. Demonstrate the same process with the decimal tenths grids on teacher resource: Decimal Addition and Subtraction Grids. 3. Instruct students to repeat the procedure using the decimal hundredths grids with the numbers 4 hundredths and 5 hundredths, respectively. Remind students to shade an estimate of the sum in the third decimal hundredths grid. Demonstrate the same process with the decimal hundredths grids on teacher resource: Decimal Addition and Subtraction Grids. page 7 of 22

8 Suggested Day Suggested Instructional Procedures Notes for Teacher 4. Instruct several student volunteers to name the decimal number and word form for the amounts shaded in each model. Facilitate a class discussion about the decimals shaded in the tenths and hundredths grids. Ask: When you added 4 tenths to 5 tenths what was the sum? (0.9) Could you write this as a fraction? What would it look like? (Yes; ) When you added 4 hundredths to 5 hundredths what was the sum? (0.09) Could you write this as a fraction? What would it look like? (Yes; ) Are nine-tenths and nine-hundredths equivalent? How do you know? (No) Answers may vary. On a hundredths grid, nine-tenths would have 90 units shaded whereas ninehundredths would only have 9 units shaded; etc. page 8 of 22

9 Suggested Day Suggested Instructional Procedures Notes for Teacher 5. Remind students that in adding decimal numbers vertically, it is important to remember place value. Therefore, lining-up the decimal is important during decimal addition and subtraction computation. Demonstrate how to line up the decimal points. Ask: How is the role of the zero in decimals the same as the role of the zero in whole numbers? Answers may vary. It is a place holder and if there is no value, a zero is placed there; the zero represents no digit divided by 10 when moving to the right of the decimal point; the zero represents no digit multiplied by 10 when moving to the left of the hundredths place; etc. How could you model subtraction using tenths and hundredths grids? Answers may vary. Display the numbers in the problem and then cross out the number being subtracted; etc. 6. Display the problem for the class to see. Instruct student groups to discuss how they might solve this problem using a decimal grid, and then record their response using the bottom half of their handout: Decimal Addition and Subtraction Grids. Allow time for students to discuss their solution process and appropriately shade their decimal grids. Monitor and assess student groups to check for understanding. 7. Using teacher resource: Decimal Addition and Subtraction Grids, display the decimal grids below: page 9 of 22

10 Suggested Day Suggested Instructional Procedures Notes for Teacher Facilitate a class discussion about how decimal grids can be used in solving decimal subtraction problems. Model the actual removal of the three-tenths from the seven-tenths to assist students in understanding the operation of subtraction with a decimal grid. 3 Topics: Solve addition and subtraction decimal problems using grids Spiraling Review Explore/Explain 2 Students solve addition and subtraction decimal problems using tenths and hundredths grids. ATTACHMENTS Instructional Procedures: 1. Place students in pairs. Distribute handout: Blank Tenths and Hundredths Grids to each student and handout: Decimal Problem Solver to each student pair. Handout: Blank Tenths and Hundredths Grids (1 per student) Teacher Resource: Decimal Problem Solver KEY (1 per teacher) page 10 of 22

11 Suggested Day Suggested Instructional Procedures 2. Instruct student groups to complete handout: Decimal Problem Solver by shading the appropriate grids on their handout: Blank Tenths and Hundredths Grids to represent the decimal numbers in each problem. 3. Distribute a sheet of construction paper to each student pair, and instruct student pairs to use the grids to model and solve each problem from their handout: Decimal Problem Solver. Instruct student pairs to glue the models of their solutions onto their construction paper. Allow time for student pairs to complete the handout. Monitor and assess student pairs to check for understanding. Facilitate a class discussion about the decimal solution models created. 4. To facilitate student understanding of solving addition and subtraction problems using decimal grids, use Local Resource(s) to find additional addition and subtraction decimal problems in real-life situations, including money. Students should use decimal grids to solve the problems and, in writing, explain their problem-solving process and justify their solution. Notes for Teacher Handout: Decimal Problem Solver (1 per 2 students) MATERIALS construction paper (1 sheet per student) glue (1 per 2 students) scissors (1 per 2 students) Local Resource(s) Clarifications and Considerations Local Resource(s) should be used to meet the specificity and rigor of the Instructional Focus Document for this unit. 4 Topics: Solve decimal problems involving addition and subtraction using number lines and/or grids Spiraling Review Elaborate 1 page 11 of 22

12 Suggested Day Suggested Instructional Procedures Students solve addition and subtraction decimal problems using number lines and/or tenths/hundredths grids. Instructional Procedures: 1. Distribute handout: Blank Decimal Number Line and Blank Tenths and Hundredths Grids to each student. Ask: How might a number line be used to model a decimal addition or subtraction problem? Answers may vary. It could be used to show counting-up or counting-down distances in decimal numbers; etc. 2. Display teacher resource: Blank Decimal Number Line and Blank Tenths and Hundredths Grids. Model how to solve a real-world decimal problem such as the following using a number line and a grid. Carrie s plant was 0.88 units tall. She cut off the flower part that was 0.45 inches tall. How tall is her plant now? Use a number line and grid to model how to solve this problem. Number line example: Notes for Teacher ATTACHMENTS Handout: Blank Decimal Number Line (1 per student) Handout: Blank Tenths and Hundredths Grids (1 per student) Teacher Resource: Blank Decimal Number Line (1 per teacher) Teacher Resource: Blank Tenths and Hundredths Grids (1 per teacher) Teacher Resource: Adding and Subtracting Decimals Using Number Lines and Grids KEY (1 per teacher) Handout: Adding and Subtracting Decimals Using Number Lines and Grids (1 per student) Grid example: page 12 of 22

13 Suggested Day Suggested Instructional Procedures Notes for Teacher Ask: How is the number line model like the grid model? Answers may vary. They are both divided into tenths and hundredths; etc. How is the number line model different than the grid model? Answers may vary. The number line is linear (not square); etc. 3. Place students in pairs and distribute handout: Adding and Subtracting Decimals Using Number Lines and Grids to each student. Instruct student pairs to shade the appropriate grid(s) and/or move on the number line to represent the decimal numbers in each problem. Allow time for student pairs to solve the decimal problems. Monitor and assess student pairs to check for understanding. Facilitate a class discussion about the decimal model solutions. 5 Evaluate 1 Instructional Procedures: 1. Assess student understanding of related concepts and processes by using the Performance ATTACHMENTS Handout: Blank Tenths and Hundredths Grids (1 per student) Handout: Blank Decimal Number Line (1 per page 13 of 22

14 Suggested Day Indicator(s) aligned to this lesson. Suggested Instructional Procedures student) Notes for Teacher Performance Indicator(s): Grade 04 Mathematics Unit 02 PI 01 Use grids (tenths or hundredths) and/or number lines to model decimal numbers in addition/subtraction problem situations (e.g., distances, money, etc.) such as: Liza ran 1.7 miles on Monday, 0.8 miles on Tuesday, and 3.75 miles on Wednesday. How many more miles did Liza run on Wednesday than she ran on the other two days? A kitchen floor needs ten rows of tiles with ten tiles in each row. A worker installed 32 hundredths of the tiles the first day. On the second day, the worker finished the job. How many tiles were installed on the second day? Susie purchased a sports drink for $1.34, a sandwich for $2.79, and a bag of chips for 3 quarters. How much did Susie pay for the drink, sandwich, and chips? For each situation, write a description of your observations of how the model was used to identify the decimal numbers in the problem, and then justify how it was used to solve it. Standard(s): 4.3A, 4.3B, 4.10, 4.14A, 4.14B, 4.14C, 4.14D, 4.15A, 4.15B, 4.16B ELPS ELPS.c.4I, ELPS.c.5F, ELPS.c.5G 03/26/13 page 14 of 22

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16 Decimal Addition and Subtraction Grids Grade 4 Mathematics Unit: 02 Lesson: 01 + = + = ======================================================================== = = 2012, TESCCC 05/24/12 page 1 of 1

17 Blank Tenths and Hundredths Grids Grade 4 Mathematics Unit: 02 Lesson: , TESCCC 05/24/12 page 1 of 1

18 Decimal Problem Solver KEY Grade 4 Mathematics Unit: 02 Lesson: 01 Use blank tenths and hundredths grids to model the decimal numbers in each problem. Cut out and glue each problem and the decimal grids onto construction paper to show how you solved it. (1) Liza ran 1.7 miles one day and 0.8 miles the second day. How many miles did Liza run altogether? = 2.5 miles and grids shaded to show same (2) A kitchen floor needs ten rows of tiles with ten tiles in each row. A worker installed 32 hundredths of the tiles the first day. On the second day, the worker finished the job. Create a model showing the number of tiles installed on the second day = 0.68 tiles and grids shaded to show same (3) Hannah has $0.23 and Stefan has $0.45. Jeff has $0.85 and Berto has $0.91. How much more money does Jeff and Berto have than Hannah and Stefan? Hannah & Stefan: = $0.68 Jeff & Berto: = $ = $1.08 and grids shaded to show same 2012, TESCCC 05/24/12 page 1 of 1

19 Decimal Problem Solver Grade 4 Mathematics Unit: 02 Lesson: 01 Use blank tenths and hundredths grids to model the decimal numbers in each problem. Cut out and glue each problem and the decimal grids onto construction paper to show how you solved it. (1) Liza ran 1.7 miles one day and 0.8 miles the second day. How many miles did Liza run altogether? (2) A kitchen floor needs ten rows of tiles with ten tiles in each row. A worker installed 32 hundredths of the tiles the first day. On the second day, the worker finished the job. Create a model showing the number of tiles installed on the second day. (3) Hannah has $0.23 and Stefan has $0.45. Jeff has $0.85 and Berto has $0.91. How much more money does Jeff and Berto have than Hannah and Stefan? 2012, TESCCC 05/24/12 page 1 of 1

20 Blank Decimal Number Lines Grade 4 Mathematics Unit: 02 Lesson: , TESCCC 05/24/12 page 1 of 1

21 Adding and Subtracting with Decimals Using Number Lines and Grids KEY Grade 4 Mathematics Unit: 02 Lesson: 01 In science class a group of students planted sunflower seeds. The plants grew quickly. The students kept very accurate measurements noting their growth from one week to the next week. The table shows the information four students in class collected. Student Plant Growth for 4 Students in Mr. Leavitt s Science Class Height at the end of Week 1 Height at the end of Week 2 Height at the end of Week 3 Height at the end of Week 4 George 0.27 meters 0.5 meters 0.9 meters 1.45 meters Mark 0.18 meters 0.35 meters 0.72 meters 1.4 meters Cooper 0.3 meters 0.55 meters 1.03 meters 1.95 meters Lauren 0.2 meters 0.43 meters 0.86 meters 1.6 meters PROBLEM 1 How tall was George s plant at the end of week 1?0.27 meters How tall was George s plant at the end of week 2?0.5 meters How much did George s plant grow from week 1 to week 2? 0.37 meters SHOW HOW TO SOLVE THIS PROBLEM USING A NUMBER LINE Models may vary PROBLEM 3 How tall was Mark s plant at the end of week 3? 0.72 meters How tall was Cooper s plant at the end of week 3? 1.03 meters How much taller was Cooper s plant than Mark s? 0.31 meters SHOW HOW TO SOLVE THIS PROBLEM USING A NUMBER LINE Models may vary PROBLEM 2 How tall was George s plant at the end of week 4? 1.45 meters George s plant grew 0.27 meters between week 4 and week 5. How tall was George s plant at the end of week 5? 1.72 meters SHOW HOW TO SOLVE THIS PROBLEM USING A GRID Models may vary PROBLEM 4 How tall was Lauren s plant at the end of week 4? 1.6 meters Lauren s plant grew 0.09 meters between week 4 and week 5. How tall was Lauren s plant at the end of week 5? 1.69 meters SHOW HOW TO SOLVE THIS PROBLEM USING A GRID Models may vary 2012, TESCCC 04/24/13 page 1 of 1

22 Grade 4 Mathematics Unit: 02 Lesson: 01 Adding and Subtracting with Decimals Using Number Lines and Grids In science class a group of students planted sunflower seeds. The plants grew quickly. The students kept very accurate measurements noting their growth from one week to the next week. The table shows the information four students in class collected. Student Plant Growth for 4 Students in Mr. Leavitt s Science Class Height at the end of Week 1 Height at the end of Week 2 Height at the end of Week 3 Height at the end of Week 4 George 0.27 meters 0.5 meters 0.9 meters 1.45 meters Mark 0.18 meters 0.35 meters 0.72 meters 1.4 meters Cooper 0.3 meters 0.55 meters 1.03 meters 1.95 meters Lauren 0.2 meters 0.43 meters 0.86 meters 1.6 meters PROBLEM 1 How tall was George s plant at the end of week 1? How tall was George s plant at the end of week 2? How much did George s plant grow from week 1 to week 2? SHOW HOW TO SOLVE THIS PROBLEM USING A NUMBER LINE PROBLEM 3 How tall was Mark s plant at the end of week 3? How tall was Cooper s plant at the end of week 3? How much taller was Cooper s plant than Mark s? SHOW HOW TO SOLVE THIS PROBLEM USING A NUMBER LINE PROBLEM 2 How tall was George s plant at the end of week 4? George s plant grew 0.27 meters between week 4 and week 5. How tall was George s plant at the end of week 5? SHOW HOW TO SOLVE THIS PROBLEM USING A GRID PROBLEM 4 How tall was Lauren s plant at the end of week 4? Lauren s plant grew 0.09 meters between week 4 and week 5. How tall was Lauren s plant at the end of week 5? SHOW HOW TO SOLVE THIS PROBLEM USING A GRID 2012, TESCCC 10/09/12 page 1 of 1