Enhanced Instructional Transition Guide

Transcription

1 Enhanced Instructional Transition Guide Grade 3/ Unit 02: Suggested Duration: 13 days Unit 02: Addition and Subtraction Foundations (13 days) Possible Lesson 01 (13 days) POSSIBLE LESSON 01 (13 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: Students use estimation strategies such as rounding and compatible numbers to facilitate the operations of addition and subtraction. Students use base-ten blocks to model addition and subtraction with numbers through 999. These models are connected to procedures for adding and subtracting in various situations. 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. The student is expected to: 3.3A Model addition and subtraction using pictures, words, and numbers. Supporting Standard 3.3B Select addition or subtraction and use the operation to solve problems involving whole numbers through 999. Readiness Standard 3.5 Number, operation, and quantitative reasoning. The student estimates to determine reasonable results. The student is expected to: 3.5A Round whole numbers to the nearest ten or hundred to approximate reasonable results in problem situations. Supporting Standard page 1 of 132

2 Enhanced Instructional Transition Guide Grade 3/ Unit 02: Suggested Duration: 13 days 3.5B Use strategies including rounding and compatible numbers to estimate solutions to addition and subtraction problems. Supporting Standard 3.10 Geometry and spatial reasoning. The student recognizes that a line can be used to represent numbers and fractions and their properties and relationships. The student is expected to: 3.10 Locate and name points on a number line using whole numbers and fractions, including halves and fourths. Readiness Standard Underlying Processes and Mathematical Tools TEKS: 3.14 Underlying processes and mathematical tools. The student applies Grade 3 mathematics to solve problems connected to everyday experiences and activities in and outside of school. The student is expected to: 3.14D Use tools such as real objects, manipulatives, and technology to solve problems Underlying processes and mathematical tools. The student communicates about Grade 3 mathematics using informal language. The student is expected to: 3.15A Explain and record observations using objects, words, pictures, numbers, and technology. 3.15B Relate informal language to mathematical language and symbols Underlying processes and mathematical tools. The student uses logical reasoning. The student is expected to: 3.16B Justify why an answer is reasonable and explain the solution process. Performance Indicator(s): page 2 of 132

3 Enhanced Instructional Transition Guide Grade 3/ Unit 02: Suggested Duration: 13 days Grade3 Unit02 PI01 Estimate and calculate the solutions to whole number addition and/or subtraction real-life problem situations such as: Rachel had 37 sports cards in her collection. She gave away 9 of her cards, but then her father gave her some new cards. Rachel now has 58 cards in her collection. How many cards did Rachel s father give her. A tennis tournament lasted 3 days. On Tuesday, 125 people attended. On Wednesday, 74 more people attended than on Tuesday. On Thursday, 23 fewer people attended than on Wednesday. How many people attended the tournament on Thursday? Use a graphic organizer for each problem to record: (1) the estimation strategy, (2) the actual solution, (3) a sketch of the solution on a number line, (4) a pictorial of one other solution strategy, and (5) a written justification of the preferred solution process and the reasonableness of the solution. Standard(s): 3.3A, 3.3B, 3.5A, 3.5B, 3.10, 3.14D, 3.15A, 3.15B, 3.16B ELPS ELPS.c.1G, ELPS.c.1H, ELPS.c.4I, ELPS.c.5G Key Understanding(s): Estimation strategies, such as rounding or compatible numbers, can be used to approximate the solution of an addition or a subtraction problem involving whole numbers to determine if the actual solution is reasonable by focusing on the meaning of the numbers. When solving addition and subtraction problems involving whole numbers, only digits with the same place value can be added or subtracted because digits in like places have the same underlying unit amount. A number line can be used as an estimation strategy to visually locate and name whole numbers to approximate the solution of an addition or subtraction problem and to determine if the actual solution is reasonable. Models, including number lines, base-ten blocks, etc., can be used to determine the solution of a whole number addition or subtraction problem by demonstrating and communicating the meaning of the operation. Misconception(s): Some students may think when the ones digit is a 5, they do not need to round to the nearest ten. Some students may think that they should use the digit to the left of the hundreds place, instead of the digit to the right of the hundreds place, when rounding 4- digit numbers. page 3 of 132

4 Enhanced Instructional Transition Guide Grade 3/ Unit 02: Suggested Duration: 13 days Some students may think when estimating the sum and difference of a problem, they should find the exact answer first and then estimate the solution. Remind them that estimation is meant to be a quick way to solve a problem when an exact sum/difference is not needed. Some students may think that when you add, the sum is always larger than the addends. This is true when working with whole numbers but not when working with negative numbers in middle school. Underdeveloped Concept(s): Some students may regroup incorrectly or may forget to regroup. Have these students use the place value chart and/or draw a square on top of each place before they add. Students then fill in each square with the correct number of tens or hundreds obtained from regrouping. Some students may not be able keep numbers aligned by place value when recording addition and subtraction with regrouping. Using a place value chart or turning lined paper vertically should help these students keep the digits of the numbers aligned. Some students may transpose digits when rewriting a horizontal addition and/or subtraction sentence vertically. Have these students work with a partner when writing the addends in the place value chart or when writing the addends vertically. One partner should read the numbers from the chart, and the other partner should check to be sure that the digits are in the correct location. Vocabulary of Instruction: approximate compatible numbers estimate exchange regroup round sum trade Materials: base-ten blocks ( cubes, flats, longs, 10 units) (1 set per student, 1 set per teacher) (previously created in Unit 01 Lesson 01 Engage 1) cardstock (2 sheets per 2 students) construction paper (optional) (or blank paper) (2 sheets per student) dry erase marker (1 per student) math journal (1 per student) plastic zip bag (sandwich sized) (1 per 2 students) page 4 of 132

5 Enhanced Instructional Transition Guide Grade 3/ Unit 02: Suggested Duration: 13 days scissors (1 per 4 students) scissors (1 per teacher) whiteboard (student sized) (1 per student) 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. Which is Closer? KEY Which is Closer? Blank Number Lines Place Value Rounding to the Nearest Ten Rounding to the Nearest Ten Graphic A Round Collection KEY A Round Collection Place Value Rounding to the Nearest Hundred Rounding to the Nearest Hundred Graphic Rounding Building Heights KEY Rounding Building Heights Rounding to the Nearest Ten or Hundred Practice KEY page 5 of 132

6 Enhanced Instructional Transition Guide Grade 3/ Unit 02: Suggested Duration: 13 days Rounding to the Nearest Ten or Hundred Practice Number Line Cool Joe s Hamburgers & Hot Dogs Rounding Sums Notes & Practice KEY Rounding Sums Notes & Practice Compatible Number Search Compatible Number Sums KEY Compatible Number Sums Baseball Seating Rounding Differences Notes & Practice KEY Rounding Differences Notes & Practice Fastest Birds in the World Estimation Differences Practice KEY Estimation Differences Practice Estimation Dominoes Directions Estimation Dominoes Estimating Sums and/or Differences Evaluation KEY Estimating Sums and/or Differences Evaluation page 6 of 132

7 Enhanced Instructional Transition Guide Grade 3/ Unit 02: Suggested Duration: 13 days Addition Model Connecting to the Procedure Recording Sheet KEY Addition Model Connecting to the Procedure Recording Sheet Modeling 3-Digit Addition Practice KEY Modeling 3-Digit Addition Practice Addition of 3-Digit Numbers with Base-Ten Blocks Notes George s Travels KEY George s Travels Place Value Chart Addition Modeling Word Problems Three Ways Part 1 KEY Modeling Word Problems Three Ways Part 1 Adding and Subtracting Using Number Lines KEY Adding and Subtracting Using Number Lines Subtraction Model Connecting to the Procedure Recording Sheet KEY Subtraction Model Connecting to the Procedure Recording Sheet Subtraction of 3-Digit Numbers with Base-Ten Blocks Notes Modeling Subtraction with Hundreds Grids KEY Modeling Subtraction with Hundreds Grids Modeling 3-Digit Subtraction Practice KEY page 7 of 132

8 Enhanced Instructional Transition Guide Grade 3/ Unit 02: Suggested Duration: 13 days Modeling 3-Digit Subtraction Practice Pencil Factory KEY Pencil Factory Place Value Chart Subtraction Modeling Word Problems Three Ways Part 2 KEY Modeling Word Problems Three Ways Part 2 Addition/Subtraction Match-up KEY Addition/Subtraction Match-up Addition/Subtraction Match-up Teacher Example Tri-Fold Flip Book Directions Problem Situation Evaluation KEY Problem Situation Evaluation 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: page 8 of 132

9 Enhanced Instructional Transition Guide Grade 3/ Unit 02: Suggested Duration: 13 days Suggested Day Engage 1 Suggested Instructional Procedures Introduce estimation using relative position Students use their location or position in the classroom to determine how close or far away they are from classroom objects. Instructional Procedures: Notes for Teacher Spiraling Review ATTACHMENTS Teacher Resource: Which is Closer? KEY (1 per teacher) Teacher Resource: Which is Closer? (1 per teacher) 1. Instruct various students to describe their position within the classroom in relation to other objects, (e.g., Jackie, are you closer to the window or closer to the door? Donald, are you closer to the pencil sharpener or the teacher s desk? Debbie, are you closer to the door or the calendar?; etc.). 2. Instruct various students to relate the position of their classroom to different parts of the school (e.g., Is our classroom closer to the library or the lunch room? Is our classroom closer to the parking lot or the office?; etc.). Remind students that numbers, just like objects in real life, are closer to some numbers than others. Ask: When trying to determine how close or far away an object is, are you trying to find the exact distance or are you trying to find a distance close to the actual distance? (A distance close to the actual distance.) MATERIALS math journal (1 per student) TEACHER NOTE Different words that are associated when asking for an estimate are approximately, around, close to, or about. Alternate these words throughout the lesson. 3. Explain to students that they were just estimating the distance or finding an estimate of the distance. Instruct students to use their math journals to write a definition for estimate. Allow time for students to complete their journal entry. Facilitate a class discussion regarding their page 9 of 132

10 Enhanced Instructional Transition Guide Grade 3/ Unit 02: Suggested Duration: 13 days Suggested Day Suggested Instructional Procedures Notes for Teacher estimate definitions. 4. Display a mathematical definition for estimate for the class to see (e.g., estimate: to find an answer close to the actual answer). 5. Display teacher resource: Which is Closer? and instruct students to answer the questions in their math journals. Allow time for students to complete their journal entry. Facilitate a class discussion regarding student s strategies for finding which number was closer. Ask: When you were trying to determine which multiple of 10 each number was closest to, were you estimating? Explain. (yes) Answers may vary. Even though we were finding an exact number, we were still estimating the distance of one number from another; etc. Topics: ATTACHMENTS Round to the nearest ten using number lines Explore/Explain 1 Students use number lines to round whole numbers to the nearest ten. Instructional Procedures: 1. Distribute handout: Blank Number Lines to each student and display teacher resource: Blank Number Lines. 2. Instruct students to draw tick marks at the beginning, the ending, and in the middle of the Handout: Blank Number Lines (1 per student) Teacher Resource: Blank Number Lines (1 per teacher) Teacher Resource: Place Value Rounding to the Nearest Ten (1 per teacher) Handout: Place Value Rounding to the Nearest Ten (1 per student) Teacher Resource: A Round Collection KEY (1 per teacher) page 10 of 132

11 Enhanced Instructional Transition Guide Grade 3/ Unit 02: Suggested Duration: 13 days Suggested Day Suggested Instructional Procedures number line on handout: Blank Number Lines. Demonstrate this procedure using the displayed teacher resource: Blank Number Lines. 3. Display the number 33 for the class to see. Ask: Notes for Teacher Handout: A Round Collection (1 per student) Handout (optional): Rounding to the Nearest Ten Graphic (1 per student) Which two multiples of 10 are closest to 33? How do you know? (30 and 40) Answers may vary. Skip counting by 10s to determine the 2 closest multiples; etc. Which multiple is lowest? (30) highest? (40) Instruct students to record this on their number lines and model the same for the class to see. What number is halfway between the lower and higher number? How do you know? (35) Answers may vary. TEACHER NOTE Struggling students might find it helpful to use a curved number line for rounding. 4. Using the displayed teacher resource: Blank Number Lines record the numbers 30, 35, and 40. Instruct students to replicate the model on their handout: Blank Number Lines. Note that the number 33 will slide down the hill to 30 (not to 40). The students can imagine that the curved number line is a roller coaster and if the car is on 33, it will slide down the hill to 30, 5. Facilitate a class discussion about the number line. Ask: Where would the number 33 be placed on this number line? Answers may vary. Between 30 and 35; closer to 35; etc. Invite a student volunteer to demonstrate how to mark the approximate location of 33 on the number line. TEACHER NOTE Handout (optional): Rounding to the Nearest Ten Graphic may be used to help students with the concept of rounding to the tens place. page 11 of 132

12 Enhanced Instructional Transition Guide Grade 3/ Unit 02: Suggested Duration: 13 days Suggested Day Suggested Instructional Procedures Notes for Teacher Ask: Which two numbers does 33 lie between? (30 and 35) Is 33 closer to the lower number, 30, or the higher number, 40, on the number line? (30, the lower number on the number line.) If 33 is rounded to the nearest 10, what number would 33 be rounded to? How do you know? (30, because it is closer to the lower number on the number line.) Which digit in the number 33 helps you find the nearest 10? (The 3 in the ones place.) 6. Display the number 233 for the class to see. Ask: If 233 is rounded to the nearest 10, which digit should be considered to determine the value of the tens place? (the 3 in the ones place) What would the number line look like to show the multiples of 10 that are closest to this number? (The lower number would be 230 and the higher number would be 240.) What number is halfway between the lower and higher number? How do you know? (235) Answers may vary. Five is halfway between 10; 35 is halfway between 30 and 40; 235 is halfway between 230 and 240; etc. 7. Using the displayed teacher resource: Blank Number Lines, record the numbers 230, 235, and 240. Instruct students to replicate the model on their handout: Blank Number Lines. 8. Facilitate a class discussion about the number line. Ask: page 12 of 132

13 Enhanced Instructional Transition Guide Grade 3/ Unit 02: Suggested Duration: 13 days Suggested Day Suggested Instructional Procedures Notes for Teacher Where on this number line should you place the number 233? Answers may vary. Between 230 and 235; closer to 235; etc. Invite a student volunteer to demonstrate how to mark the approximate location of 233 on the number line. Which two numbers does 233 lie between? (230 and 235) Is 233 closer to the lower number, 230, or the higher number, 240, on the number line? (It is closest to 230, the lower end of the number line.) If 233 is rounded to the nearest 10, what number would 233 be rounded to? How do you know? (230, because it is closer to the lower number on the number line.) Which digit in the number 233 helps you find the nearest 10? (The 3 in the ones place.) 9. Instruct students to discuss, with a neighbor, how to round 235 to the nearest 10. Facilitate a class discussion about rounding to the nearest 10. Ask: If the number 235 is rounded to the nearest 10, then 235 rounds to what number? How do you know? (240) Answers may vary. Since 235 is right in the middle of the number line, it rounds to the larger tens place; since 5 is not in the lower end of the number line or the higher end of the number line, it rounds to the higher end; etc. Remind the students that since 235 is being rounded to the nearest 10 and is in the middle of 230 and 240, then 235 is rounded to the larger place value, which is Place students in pairs. Instruct student pairs to generalize a rule for rounding whole numbers to page 13 of 132

14 Enhanced Instructional Transition Guide Grade 3/ Unit 02: Suggested Duration: 13 days Suggested Day Suggested Instructional Procedures the nearest 10. Allow time for students to discuss and write their generalization. Monitor and assess students to check for understanding. Facilitate a class discussion regarding their generalizations. 11. Display teacher resource: Place Value Rounding to the Nearest Ten and distribute handout: Place Value Rounding to the Nearest Ten to each student. Facilitate a class discussion about the similarities and differences shown in the handout and the students generalizations. 12. Distribute handout: A Round Collection to each student to complete as independent practice. Notes for Teacher 2 Topics: Round to the nearest hundred using number lines Explore/Explain 2 Students use number lines to round whole numbers to the nearest hundred. Instructional Procedures: 1. Facilitate a class discussion to debrief handout: A Round Collection. 2. Distribute handout: Blank Number Lines to each student and display teacher resource: Blank Number Lines. 3. Instruct students to draw tick marks at the beginning, the ending, and in the middle of the number line on handout: Blank Number Lines. Demonstrate this procedure using the displayed teacher resource: Blank Number Lines. 4. Display the number 672 for the class to see. Spiraling Review ATTACHMENTS Handout: Blank Number Lines (1 per student) Teacher Resource: Blank Number Lines (1 per teacher) Teacher Resource: Place Value Rounding to the Nearest Hundred (1 per teacher) Handout: Place Value Rounding to the Nearest Hundred (1 per student) Teacher Resource: Rounding Building Heights KEY (1 per teacher) Handout: Rounding Building Heights (1 per student) page 14 of 132

15 Enhanced Instructional Transition Guide Grade 3/ Unit 02: Suggested Duration: 13 days Suggested Day Suggested Instructional Procedures Ask: Which two multiples of 100 are closest to 672? How do you know? (600 and 700) Answers may vary. Skip counting by 100s to determine the 2 closest multiples; etc. Which multiple is lowest? (600) highest? (700) Instruct students to record this on their number lines and model the same for the class to see. What number is halfway between the lower and higher number? How do you know? (650) Answers may vary. Because 50 is half of 100, = 650 and = 650; etc. 5. Using the displayed teacher resource: Blank Number Lines record the numbers 600, 650, and 700. Instruct students to replicate the model on their handout: Blank Number Lines. 6. Facilitate a class discussion about the number line. Ask: Where would the number 672 be placed on the number line? Answers may vary. Between 650 and 700; closer to 700; etc. Invite a student volunteer to demonstrate how to mark the approximate location of 672 on the number line. Ask: Which two numbers does 672 lie between? (650 and 700) Notes for Teacher Teacher Resource (optional): Rounding to the Nearest Ten or Hundred Practice KEY (1 per teacher) Handout (optional): Rounding to the Nearest Ten or Hundred Practice: (1 per student) Handout: (optional): Rounding to the Nearest Hundred Graphic (1 per student) TEACHER NOTE The handout (optional): Rounding to the Nearest Hundred Graphic can be used to help students with the concept of rounding to the hundreds place. TEACHER NOTE Have students who have difficulty determining which place to use when rounding 4-digit numbers, place the number in a place value chart and then have them consider the place to which they are rounding. Struggling students could also use the curved number line by placing their car on the rollercoaster hill. page 15 of 132

16 Enhanced Instructional Transition Guide Grade 3/ Unit 02: Suggested Duration: 13 days Suggested Day Suggested Instructional Procedures Is 672 closer to the lower number, 600, or the higher number, 700, on the number line? (700, the higher number on the number line.) If 672 is rounded to the nearest 100, what number would 672 be rounded to? How do you know? (700, because it is closer to the higher number on the number line.) Which digit in the number 672 helps you find the nearest 100? (the 7 in the tens place) 7. Display the number 1,246 for the class to see. Ask: If 1,246 is rounded to the nearest 100, which digit should be considered to determine the value of the hundreds place? (the 4 in the tens place) What would the number line look like to show the multiples of 100 that are closest to this number? (The lower number would be 1,200 and the higher number would be 1,300.) What number is halfway between the lower and higher number? How do you know? (1,250; 250 in this number is between 200 and 300; etc.) Notes for Teacher Note that the number 1,246 will slide down the hill to 1,200 (not to 1,300). ADDITIONAL PRACTICE Additional practice can be assigned by using the handout (optional): Rounding to the Nearest Ten or Hundred Practice. 8. Instruct students to record the numbers 1,200, 1,250, and 1,300 on handout: Blank Number Lines. 9. Facilitate a class discussion about the number line. Ask: Where would the number 1,246 be placed on the number line? Answers may vary. page 16 of 132

17 Enhanced Instructional Transition Guide Grade 3/ Unit 02: Suggested Duration: 13 days Suggested Day Suggested Instructional Procedures Between 1,200 and 1,250; closer to 1,250; etc. Invite a student volunteer to demonstrate how to mark the approximate location of 1,246 on the number line. Ask: Notes for Teacher Which two numbers does 1,246 lie between? (1,200 and 1,250) Is 1,246 closer to the lower number, 1,200, or the higher number, 1,300, on the number line? (1,200, the lower number on the number line.) If 1,246 is rounded to the nearest 100, what number does 1,246 round to? How do you know? (1,200, because it is closer to the lower number on the number line.) Which digit in the number 1,246 helps you find the nearest 100? (the 4 in the tens place.) 10. Facilitate a class discussion about the similarities in rounding to the nearest 100 and rounding to the nearest 10. Allow time, 1-2 minutes, for students to reflect before responding. Ask: How is rounding to the nearest 100 like rounding to the nearest 10? Answers may vary. 11. Place students in pairs. Instruct student pairs to generalize a rule for rounding whole numbers to the nearest 100. Allow time for students to discuss and write their generalization. Monitor and assess students to check for understanding. Facilitate a class discussion regarding their generalizations. Explain to students that if the number to be rounded is at least halfway between the tens or hundreds, round to the larger number. If the number is less than halfway between the tens or hundreds, round to the smaller number. page 17 of 132

18 Enhanced Instructional Transition Guide Grade 3/ Unit 02: Suggested Duration: 13 days Suggested Day Suggested Instructional Procedures Notes for Teacher 12. Instruct student pairs to discuss their generalizations and consider if their generalization can be used for rounding numbers to the thousands place or greater. Allow students time to complete their discussions. Monitor and assess student pairs to check for understanding. Facilitate a class discussion regarding their generalizations. Ask: Do you think the generalization you made for rounding to 10 and rounding to 100 will work for rounding numbers to the thousands place or greater? Explain. Answers may vary. Explain to students that when you know the place to which you are rounding, look at the digit to the right of that place. If that digit to the right is less than 5, the digit in the rounding place stays the same or if the digit to the right is 5 or greater, the digit in the rounding place increases by 1 of that place. 13. Distribute handout: Place Value Rounding to the Nearest Hundred to each student and display teacher resource: Place Value Rounding to the Nearest Hundred. 14. Facilitate a class discussion about the similarities and differences of the handout and the students generalizations. 15. Distribute handout: Rounding Building Heights to each student to complete as independent practice. 3 Topics: Rounding as an addition estimation strategy Spiraling Review page 18 of 132

19 Enhanced Instructional Transition Guide Grade 3/ Unit 02: Suggested Duration: 13 days Suggested Day Suggested Instructional Procedures Notes for Teacher Explore/Explain 3 Students use rounding as an estimation strategy to solve addition problems. Instructional Procedures: 1. Distribute handout: Number Line to each student and display teacher resource: Number Line Instruct students to locate the numbers 28 and 64 on the number line on handout: Number Line Invite a student volunteer to model where these numbers are on the number line. Ask: If you were to round the two numbers in the problem to the nearest 10, what would the rounded numbers be? How do you know? (28 would round to 30, and 64 would round to 60.) Answers may vary. Twenty-eight is closer to thirty than it is to twenty; sixty-four is closer to sixty than it is to seventy; etc. If you didn t have a number line to model these two numbers, how could you determine how to round them to the nearest 10? (I could use the rounding rules and look at the ones place to determine how close or far away the numbers are from their multiples of ten.) ATTACHMENTS Teacher Resource: Number Line (1 per teacher) Handout: Number Line (1 per student) Teacher Resource: Cool Joe s Hamburgers & Hot Dogs (1 per teacher) Teacher Resource: Rounding Sums Notes & Practice KEY (1 per teacher) Handout: Rounding Sums Notes & Practice (1 per student) MATERIALS math journal (1 per student) whiteboard (student sized) (1 per student) dry erase marker (1 per student) TEACHER NOTE Remind students that estimation is meant to be a quick way to solve a problem when an exact sum/difference is not needed. 3. Distribute a whiteboard and marker to each student. Instruct students to use the left side of their whiteboard to estimate Invite a volunteer to share his/her solution with the class (30 + page 19 of 132

20 Enhanced Instructional Transition Guide Grade 3/ Unit 02: Suggested Duration: 13 days Suggested Day Suggested Instructional Procedures 60 = 90). Instruct students to use the right side of their whiteboard to write and solve Invite a student volunteer to share his/her strategy and solution with the class ( = 92). Ask: Notes for Teacher Was the estimate close to the actual sum? (yes) Which problem was the easiest (or quickest) to solve? Explain. Answers may vary. The problem with the rounded addends was easier to solve; etc. What is the value of finding the estimate and the actual computation? Explain. (The estimate and the actual solution should be close; the estimate and actual answers verify the reasonableness of the solution.) Explain to students that estimating numbers prior to computation helps in finding reasonable estimates to solve problems. It is relatively easier to add numbers that are multiples of 10 or Display teacher resource: Cool Joe s Hamburgers & Hot Dogs. Invite a student volunteer read the problem aloud to the class. Ask: Does this problem ask you to find out exactly how many hamburgers and hot dogs were sold? Explain. (No; the problem asks me to find out about how many hamburgers and hot dogs were sold to the nearest 10.) What does about how many and round to the nearest 10 mean? (estimate by using rounding) How could you round the numbers 367 and 72? (Round each number to the nearest 10.) 5. Instruct students to use their whiteboards to round 367 and 72 to the nearest 10, write the page 20 of 132

21 Enhanced Instructional Transition Guide Grade 3/ Unit 02: Suggested Duration: 13 days Suggested Day Suggested Instructional Procedures original addends of the problem, and the rounded addends. Instruct students to solve only the problem with the rounded addends. Invite a student volunteer to share his/her strategy and solution with the class. Notes for Teacher 6. Instruct students to add the original addends. Ask: How many hamburgers and hot dogs were sold altogether? (439) How close was the estimate to the actual number of hamburgers and hot dogs sold? (The estimate was close; there was only one hamburger or hot dog more.) Could you round the numbers 367 and 72 to the nearest 100? (yes) 7. Instruct students to use their whiteboards to round 367 and 72 to the nearest 100, write the original addends of the problem, and the rounded addends. Instruct students to solve only the problem with the rounded addends. Invite a student volunteer to share his/her strategy and solution with the class. page 21 of 132

22 Enhanced Instructional Transition Guide Grade 3/ Unit 02: Suggested Duration: 13 days Suggested Day Suggested Instructional Procedures Notes for Teacher Ask: Does rounding to the nearest 10 or rounding to the nearest 100 give a more reasonable estimation? (rounding to the nearest 10) Facilitate a class discussion as to why rounding to the nearest 10 gave a more reasonable estimation. When might you need to round to the nearest 100 instead of the nearest 10? Answers may vary. Rounding to the nearest 100 involves fewer operational steps and is, therefore, faster to acquire an answer. 8. Distribute handout: Rounding Sums Notes & Practice to each student to complete as independent practice. Allow time for students to complete the handout. Monitor and assess students to check for understanding. Facilitate a class discussion for students to share their solutions. 4 Topics: Compatible numbers as an addition estimation strategy Explore/Explain 4 Students use compatible numbers as an estimation strategy to solve addition problems. Instructional Procedures: Spiraling Review ATTACHMENTS Teacher Resource: Compatible Number Search (1 per teacher) Teacher Resource: Compatible Number page 22 of 132

23 Enhanced Instructional Transition Guide Grade 3/ Unit 02: Suggested Duration: 13 days Suggested Day Suggested Instructional Procedures 1. Display teacher resource: Compatible Number Search. Place students in pairs. Instruct student pairs to match as many pairs of numbers that they think will be easy to add and record their pairs in their math journal. Allow time for students to complete their pairs. Monitor and assess student pairs to check for understanding. Facilitate a class discussion about the activity. Ask: Do you see any two numbers that would be easy for you to add together mentally in your head? Answers may vary ; ; ; ; etc. Notes for Teacher Sums KEY (1 per teacher) Handout: Compatible Number Sums (1 per student) MATERIALS math journal (1 per student) whiteboard (student sized) (1 per student) dry erase marker (1 per student) 2. Facilitate a class discussion about compatible numbers. Record and display student responses for the class to see. Title the list as Friendly or Compatible Numbers. Ask: Why were these numbers so easy for you to add quickly in your head? Answers may vary. Adding with zeros; adding two fives makes tens/zeros; finding combinations that make 10, which make the computations easy to do in my head; etc. Remind students of the rounding problems they previously completed and the relative easiness of working with numbers that end in zero. 3. Explain to students that in addition to rounding numbers, friendly numbers or compatible numbers may be used as well to make solving a problem easier. Compatible numbers are numbers that are easy to compute mentally. Instruct students to record this definition along with some examples in their math journal. TEACHER NOTE As students are learning to add 2- and 3-digit numbers, it is important that they learn estimation skills. This allows them to avoid errors that may result from reliance upon rote procedures. Also, many real-life situations require only estimates of sums. TEACHER NOTE Be sure to write the example problems ( ) in horizontal format to ensure that students are truly estimating and not actually calculating the sum. TEACHER NOTE page 23 of 132

24 Enhanced Instructional Transition Guide Grade 3/ Unit 02: Suggested Duration: 13 days Suggested Day Suggested Instructional Procedures 4. Display the problem for the class to see. Ask: How can you change these numbers to make the numbers friendly in order to estimate the sum mentally? Answers may vary. Could different compatible numbers be used? Why or why not? (Yes, because there is more than one way to select a numbers that are compatible with 13 and 16.) Demonstrate how to make these numbers compatible or friendly. In this case, one example of using compatible numbers could be 15 and 15. Remind students that when using compatible numbers, you do not have to change both numbers. Another example of compatible numbers could be = 30; = 30; etc. Explain to students that using compatible numbers can be used for problems with several addends. 5. Distribute a whiteboard and marker to each student. Display the following example for the class to see. Instruct students to replicate the example on their whiteboards. 6. Instruct students to not give an answer, but to think about different ways to add the numbers as efficiently as possible. Remind students that the numbers can be paired to make tens, 1 + 9; 7 + 3; and Explain to students that instead of adding each number one at a time and in order, they can use pairings of numbers as a shortcut to find the sum by counting 3 tens, or 30. Allow time for students to pair the numbers. Monitor and assess students to check for understanding. Facilitate a class discussion for students to share how they paired their Notes for Teacher Estimation using compatible numbers does not have rigid rules like rounding. Using compatible numbers to estimate allows more flexibility in choice of numbers according to student s understanding of number relationships such as the adding of hundreds and tens, using 0 s and 5 s, 25 s, etc. State Resources MTR K-5: Just Make It Easy!; Let s Get Friendly! may be used to reinforce these concepts. RESEARCH Estimations will vary due to the number of estimation strategies. According to John A. Van De Walle (2004), there is no one right answer for estimation; we need to be open to the range of estimation responses and focus on the flexible methods. page 24 of 132

25 Enhanced Instructional Transition Guide Grade 3/ Unit 02: Suggested Duration: 13 days Suggested Day Suggested Instructional Procedures Notes for Teacher numbers. 7. Display the following example for the class to see. 8. Facilitate a class discussion for students to share ideas of how to add the numbers accurately and efficiently. Students should realize that pairing numbers to make 100s, ; ; and , is an efficient shortcut to find the sum by counting 3 hundreds, or Place students in pairs and distribute handout: Compatible Number Sums to each student. Instruct pairs to complete the handout. Monitor and assess students to check for understanding. 10. Display teacher resource: Compatible Number Sums. Facilitate a class discussion for students to share their responses and circle the correct compatible numbers. 5 Topics: Rounding as a subtraction estimation strategy Explore/Explain 5 Students use rounding as an estimation strategy to solve subtraction problems. Instructional Procedures: Spiraling Review ATTACHMENTS Teacher Resource: Number Line (1 per teacher) Handout: Number Line (1 per page 25 of 132

26 Enhanced Instructional Transition Guide Grade 3/ Unit 02: Suggested Duration: 13 days Suggested Day Suggested Instructional Procedures 1. Distribute handout: Number Line to each student and display teacher resource: Number Line Instruct students to locate the numbers 33 and 76 on the number line on handout: Number Line Invite a student volunteer to model where these numbers are on the number line. Ask: If we were to round the two numbers in the problem to the nearest 10, what would the rounded numbers be? How do you know? (33 would round to 30, and 76 would round to 80.) Answers may vary. I know that 33 is closer to 30 than it is to 20; I know that 76 is closer to 80 than it is to 70; etc. If you didn t have a number line to model these two numbers, how could you determine how to round them to the nearest 10? (I could use the rounding rules and look at the ones place to determine how close or far away the numbers are from their multiples of 10.) Notes for Teacher student) Teacher Resource: Baseball Seating (1 per teacher) Teacher Resource: Rounding Differences Notes & Practice KEY (1 per teacher) Handout: Rounding Differences Notes & Practice (1 per student) MATERIALS whiteboard (student-sized) (1 per student) dry-erase marker (1 per student) 3. Distribute a whiteboard and marker to each student. Instruct students to use the left side of their whiteboard to estimate Invite a volunteer to share his/her solution with the class (80 30 = 50). Instruct students to use the right side of their whiteboard to write and solve Invite a student volunteer to share his/her strategy and solution with the class (76 33 = 43). Ask: Was the estimate close to the actual difference? (yes) page 26 of 132

27 Enhanced Instructional Transition Guide Grade 3/ Unit 02: Suggested Duration: 13 days Suggested Day Suggested Instructional Procedures Which problem was the easiest (or quickest) to solve? Explain. Answers may vary. Most students should agree that the problem with the rounded numbers was easier to solve; etc. What is the value of finding the estimate and the actual computation? Explain. (The estimate and the actual solution should be close; the estimate and actual answers verify the reasonableness of the solution.) Explain to students that estimating numbers prior to computation helps in finding reasonable estimates to solve problems. It is relatively easier to subtract numbers that are multiples of 10 or 100. Notes for Teacher 4. Display teacher resource: Baseball Seating. Invite a student volunteer to read the problem aloud to the class. Ask: Does this problem ask you to find out exactly how many more fans were seated on the home team side than on the visitor s side? Explain. (No; the problem asks me to find out about how many more fans were seated on the home teams side than on the visitor s side.) To find out about how many, what could you to do? (estimate or round the numbers) How could you round the numbers 123 and 87? (round each number to the nearest 10) 5. Instruct students to round both numbers to the nearest 10, and to use their whiteboards to write the original numbers of the problem including the rounded numbers. Instruct students to solve only the problem with the rounded numbers. Invite a student volunteer to share his/her strategy and solution with the class. page 27 of 132

28 Enhanced Instructional Transition Guide Grade 3/ Unit 02: Suggested Duration: 13 days Suggested Day Suggested Instructional Procedures Notes for Teacher 6. Instruct students to subtract the original numbers. Ask: How many more fans were seated on the home team side than on the visitor s side? (36) How close was the estimate to the actual difference of the number of fans? (The estimate was close; only a difference of 6 fans.) 7. Distribute handout: Rounding Differences Notes & Practice to each student to complete as independent practice. Allow time for students to complete the handout. Monitor and assess students to check for understanding. Facilitate a class discussion for students to share their solutions. 6 Topics: Compatible numbers as a subtraction estimation strategy Explore/Explain 6 Students use compatible numbers as an estimation strategy to solve subtraction problems. Spiraling Review ATTACHMENTS Teacher Resource: Fastest Birds in the World (1 per teacher) page 28 of 132

29 Enhanced Instructional Transition Guide Grade 3/ Unit 02: Suggested Duration: 13 days Suggested Day Suggested Instructional Procedures Instructional Procedures: 1. Remind students that compatible numbers help them solve addition problems. Explain to students that now they will use compatible numbers to help them solve subtraction problems. Ask: What is a compatible number? (A number that is easy to compute mentally.) Can you use compatible numbers in subtraction? How do you know? (yes) Answers may vary. The definition says that they are numbers that are easy to compute, and subtraction is a form of computation; etc. Notes for Teacher Teacher Resource: Estimation Differences Practice KEY (1 per teacher) Handout: Estimation Differences Practice (U03L01) MATERIALS whiteboard (student-sized) (1 per student) dry erase marker (1 per student) 2. Display the problem 63 7 for the class to see. 3. Distribute a whiteboard and marker to each student. Instruct students to think of as many different ways to estimate this problem using compatible numbers as possible. Allow 2 3 minutes for students to complete this activity. Facilitate a class discussion for students to share their estimates and explain why they consider their numbers to be compatible. Ask: How many different ways can 63 7 be represented using compatible numbers? Answers may vary could be 60 7 = 53; 65 5 = 60; = 55; 67 7 = 60; 63 3 = 60; etc. When you use compatible numbers to estimate the difference, how do you decide which numbers to use? Answers may vary. Select numbers that are close to the original numbers but that are easy to subtract mentally; etc. Which pairs were the easiest to solve? Explain. Answers may vary. Remind students that the easiest way one person chooses to solve the problem may not be TEACHER NOTE Look for students that used compatible numbers and others that used rounding. Have students share their work and discuss how their estimates are similar and how they are different. TEACHER NOTE If some students struggle with compatible numbers that are multiples of 25, remind these students that multiples of 25 can be counted quickly if they think in terms of using quarters. page 29 of 132

30 Enhanced Instructional Transition Guide Grade 3/ Unit 02: Suggested Duration: 13 days Suggested Day Suggested Instructional Procedures the easiest way for another person to solve the same problem. Why were these numbers so easy for you to subtract quickly in your head? Answers may vary. Subtracting with zeros; subtracting two fives makes zeros; finding combinations that make zero, which makes the computation easy to do in my head; etc. Remind students of the rounding problems they worked previously and the relative easiness of working with numbers that end in zero. Notes for Teacher 4. Explain to students that in addition to rounding numbers, friendly numbers or compatible numbers may be used as well to make solving a problem easier. 5. Place students in pairs and display teacher resource: Fastest Birds in the World. Instruct student pairs to summarize how to use estimation to determine the difference between the two bird s speeds, and record the summaries in their math journal. 6. Display the following possible solutions. Facilitate a class discussion about the possible solutions. Ask: Why are 175 and 150 compatible numbers? Answers may vary. They are easy (think of money) to compute mentally; etc. Which estimate, rounding to 10 or using compatible numbers, is closer to the actual difference? Is this always true? Explain. (Using rounding to 10; No, because it depends page 30 of 132

31 Enhanced Instructional Transition Guide Grade 3/ Unit 02: Suggested Duration: 13 days Suggested Day Suggested Instructional Procedures on the compatible numbers used and how close the original numbers are to the rounded numbers.) How many different ways can be represented using rounding or compatible numbers? Answers may vary = 30; = 31; = 30; etc. Can you say that one estimation strategy always gives a closer estimate than another? Why or why not? (no) Answers may vary. The numbers in the problem help determine the estimation strategy to use, which means that there is not just one way to always determine the strategy that will give the closer estimate; etc. Notes for Teacher 7. Distribute handout: Estimation Differences Practice to each student. Instruct students to complete the handout independently. Allow time for students to complete the handout. Monitor and assess students to check for understanding. 7 Topics: Estimate sums and differences Elaborate 1 Students solve problems by estimating sums and differences using either rounding or compatible numbers. Instructional Procedures: 1. Prior to instruction, create a card set: Estimation Dominoes for every 2 students by copying on cardstock, cutting apart along the bold lines, and placing each set in a plastic zip bag. Spiraling Review ATTACHMENTS Card Set: Estimation Dominoes (1 set per 2 students) Teacher Resource: Estimation Dominoes Directions (1 per teacher) Teacher Resource: Estimating Sums and/or Differences Evaluation KEY (1 per teacher) page 31 of 132

32 Enhanced Instructional Transition Guide Grade 3/ Unit 02: Suggested Duration: 13 days Suggested Day Suggested Instructional Procedures 2. Facilitate a class discussion to debrief previously assigned handout: Estimation Differences Practice. 3. Place students in pairs and distribute card set: Estimation Dominoes to each pair. Use teacher resource: Estimation Dominoes Directions to explain the game to the class. 4. Instruct student pairs to play the game. Allow time for students to complete the word problems. Monitor and assess student pairs to check for understanding. Remind students that solving problems using estimation can result in several possible answers. Facilitate a class discussion for students to share their responses. Notes for Teacher Handout: Estimating Sums and/or Differences Evaluation (1 per student) MATERIALS cardstock (4 sheets per 2 students) scissors (1 per teacher) plastic zip bag (sandwich sized) (1 per 2 students) 5. If time allows, use teacher resource: Estimation Dominoes Directions to explain the directions listed as Alternative Instructions for Cooperative Groups. Explain to students that the goal of this version of the game is to complete a chain using all dominoes. If a student pair is unable to complete the chain, remind students that because solving problems using estimation can result in several possible answers, they may need to analyze each of their solutions to determine if other compatible numbers could be used to solve each problem in order to complete the chain. 6. Distribute handout: Estimating Sums and/or Differences Evaluation to each student. Instruct students to complete it independently. Allow time for students to complete the handout. Monitor and assess students to check for understanding. Facilitate a class discussion for students to share their responses. 8 Topics: Expanded notation as a form of 3-digit addition Spiraling Review page 32 of 132

33 Enhanced Instructional Transition Guide Grade 3/ Unit 02: Suggested Duration: 13 days Suggested Day Suggested Instructional Procedures Notes for Teacher Engage 2 Students use base-ten blocks and their knowledge of place value as well as expanded notation to add up to 3-digits. Instructional Procedures: 1. Place students in pairs and distribute a set of base-ten blocks to each student. Display flat, 2 10-longs, and 2 units for the class to see. Instruct student pairs to replicate the model using their base-ten blocks. Ask: What value do these base-ten blocks represent? Explain. (122) Explain to students that they have represented 122 with the fewest number of base-ten blocks possible. What addends are represented by the base-ten model? (100, 20, and 2) How could you use your base-ten blocks to show other addends that still represent 122? Answers may vary. Exchanging the base-ten blocks to create new addends; etc. Instruct student pairs to find as many different ways as possible to represent 122 using their base-ten blocks and to record the drawings of their base-ten models and addends in their math journals. Remind students of the shorthand way to draw base-ten blocks. Allow student pairs 3 5 minutes to complete their models and drawings. Facilitate a class discussion for students to share their responses. Ask: What are some of the different ways you represented 122 using the base-ten blocks? Answers may vary long and 22 units; long, 1 10-long, and 12 units; etc. MATERIALS base-ten blocks ( cubes, flats, longs, 10 units) (1 set per student, 1 set per teacher) (previously created in Unit 01 Lesson 01 Engage 1) math journal (1 per student) TEACHER NOTE The words trade, regroup, and exchange will be used interchangeably throughout this lesson to demonstrate how the two words are related. TEACHER NOTE While the small, solid square is a more accurate representation of a unit, it may be difficult for young students to draw. Therefore, allow students to use a page 33 of 132

34 Enhanced Instructional Transition Guide Grade 3/ Unit 02: Suggested Duration: 13 days Suggested Day Suggested Instructional Procedures 2. Display the vocabulary words exchange, regroup, trade, and total for the class to see. Instruct students to use their math journals to relate each word to the model of 122 represented with flat, 2 10 longs, and 2 units (e.g., the total number of units in the flat, 2 10 longs, and 2 units is 122. You could regroup 1 10 long into 10 units; or you could exchange the group of 10 units for 1 10-long.) Facilitate a class discussion for students to share and model their responses with base-ten blocks as necessary. Notes for Teacher small, solid dot to represent the unit. Topics: ATTACHMENTS Base-ten model for 3-digit addition Explore/Explain 7 Students use base-ten blocks to model and solve 3-digit addition problems. Instructional Procedures: 1. Remind students that sometimes numbers in the ones or tens place have to be regrouped when adding. Ask: How do you know when you need to regroup ones when adding? (You need to regroup when the sum in the ones place is more than 9.) Ten ones equal how many tens? (1 ten) Ten tens equal how many hundreds? (1 hundred) How do you know if you need to regroup tens when adding? Answers may vary. The Teacher Resource: Addition Model Connecting to the Procedure Recording Sheet KEY (1 per teacher) Handout: Addition Model Connecting to the Procedure Recording Sheet (1 per student) Teacher Resource: Modeling 3-Digit Addition Practice KEY (1 per teacher) Handout: Modeling 3-Digit Addition Practice (1 per student) Handout (optional): Addition of 3-Digit Numbers with Base-Ten Blocks Notes (1 per student) MATERIALS page 34 of 132

35 Enhanced Instructional Transition Guide Grade 3/ Unit 02: Suggested Duration: 13 days Suggested Day Suggested Instructional Procedures need to regroup happens when the sum in the tens place is more than 90; etc. 2. Place students in pairs and distribute base-ten blocks to each pair. 3. Instruct student pairs to use base-ten blocks to model 138 and 164 using the least amount of base-ten blocks. Allow time for student pairs to create their model representations of the numbers. 4. Using base-ten blocks, display a model of 138 and 164 for the class to see. Remind students to keep the hundreds, tens, and ones aligned. Notes for Teacher base-ten blocks ( cubes, flats, longs, 10 units) (1 set per 2 students, 1 set per teacher) (previously created) TEACHER NOTE For struggling students, use the handout (optional): Addition of 3-Digit Numbers with Base-Ten Blocks Notes to assist them in understanding each step of the addition process while using base-ten blocks. 5. Instruct student pairs to use their model of base-ten blocks to find the sum of 138 and 164. Allow a few minutes for student pairs to explore how to combine the base ten blocks. Invite 2 3 students to model how they determined their sum using their base-ten blocks. Facilitate a class discussion of the different ways students are able to model their solution strategies. 6. Remind students that when they use base-ten block models for addition, they will add the ones, the tens, and then the hundreds and regroup when needed. Facilitate a class discussion about regrouping. Ask: Do the ones need to be regrouped? How do you know? (Yes; because there are more TEACHER NOTE When student pairs add 138 and 164, some students may have not regrouped at all, but simply combined the blocks and counted. Others may have regrouped only the units (or 10-longs) and then counted. However, some students may have discovered that both the ones and the tens needed to be regrouped. Use these students regrouping examples to explain the process of finding the sum of page 35 of 132

36 Enhanced Instructional Transition Guide Grade 3/ Unit 02: Suggested Duration: 13 days Suggested Day Suggested Instructional Procedures than 9 ones altogether.) How will you regroup the ones? (Exchange 10 ones for 1 ten.) Instruct students to use their base-ten blocks to model this exchange. Demonstrate the same process for the class to see. Ask: Notes for Teacher Do the tens need to be regrouped? How do you know? (Yes; because the sum in the tens place is more than 90.) How will you regroup the tens? (Trade 10 tens for 1 hundred.) Instruct students to use their base-ten blocks to model this exchange. Demonstrate the same process for the class to see. Ask: Do the hundreds need to be regrouped? How do you know? (No; because the sum in the hundreds place is less than 900.) How many times and in which places did we need to regroup for this problem? (2 times; in the ones place and in the tens place.) Can the sum of two 3-digit numbers be a 4-digit number? How do you know? (yes) Answers may vary. The hundreds place may need to be regrouped and exchanged = 1,700; etc. 7. Remind students of the shorthand way to draw base-ten blocks. Instruct students to work with their partner and use handout: Addition Model Connecting to the Procedure Recording Sheet to draw each step of this addition problem using the shorthand base-ten drawings and connecting each step to the addition problem including using words to describe each step. Demonstrate the same process for the class to see. Use teacher resource: Addition Model page 36 of 132

37 Enhanced Instructional Transition Guide Grade 3/ Unit 02: Suggested Duration: 13 days Suggested Day Suggested Instructional Procedures Connecting to the Procedure Recording Sheet KEY for examples of how to model using base-ten blocks. 8. Distribute handout: Modeling 3-Digit Addition Practice to each student. Instruct student pairs to complete the handout. Allow time for students to solve the problems. Monitor and assess students to check for understanding. Facilitate a class discussion for students to share their responses. Notes for Teacher 9 Topics: Connect base-ten model to place value and traditional addition algorithm Explore/Explain 8 Students use base-ten blocks to model a 3-digit addition problem and to connect the numbers from that model to a place value chart. The place value chart is used to facilitate student understanding of the addition algorithm procedures, including regrouping. Instructional Procedures: 1. Facilitate a class discussion to debrief handout: Modeling 3-Digit Addition Practice. 2. Place students in pairs and distribute base-ten blocks to each student. 3. Display teacher resource: George s Travels. Instruct student pairs to solve the problem using base ten blocks and to record their base-ten drawings and solution processes in their math journals. Allow 3 5 minutes for students to complete the handout. Monitor and assess students to check for understanding. Facilitate a class discussion regarding student responses. Spiraling Review ATTACHMENTS Teacher Resource: George s Travels KEY (1 per teacher) Teacher Resource: George s Travels (1 per teacher) Teacher Resource: Place Value Chart Addition (1 per teacher) Teacher Resource: Modeling Word Problems Three Ways Part 1 KEY (1 per teacher) Handout: Modeling Word Problems Three Ways Part 1 (1 per student) MATERIALS page 37 of 132

38 Enhanced Instructional Transition Guide Grade 3/ Unit 02: Suggested Duration: 13 days Suggested Day Suggested Instructional Procedures Ask: What operation do you need to perform in order to solve this problem? How do you know? (addition) Answers may vary. We want to know the total miles he traveled altogether; etc. How could this problem be represented using base-ten blocks? Answers may vary. Encourage students to give you the addends represented in the fewest number of base-ten blocks possible, e.g., flats, 6 10-longs, and 3 units for 463, and flats, longs, and 8 units for 298 with a sum of flats, 6 10-longs, and 1 unit or 761. What number sentence could be used to solve this problem? = 761 Is George correct? Why or why not? (No, because he traveled 761 miles, not 661 miles.) What error did George most likely make in determining the number of miles he traveled altogether? (He forgot to regroup the hundreds or he forgot to add-in the regrouped hundred.) What could George have done to check to see if his answer was reasonable? Explain. (He could have used estimation.) Answers may vary. Estimation including the use of compatible numbers or rounding to determine if the answer was reasonable such as = 750; etc. What steps did you use to solve this problem? Answers may vary. We added the ones first, regrouped as necessary. Then we added the tens and regrouped as necessary, and finally added the hundreds; etc. Why do you begin adding in the ones place first? Answers may vary. In addition, regrouping renames smaller units as larger units. So, we add from right to left starting with the smallest place value and work toward the greatest place value; etc. Notes for Teacher base-ten blocks ( cubes, flats, longs, 10 units) (1 set per student, 1 set per teacher) (previously created) math journal (1 per student) page 38 of 132

39 Enhanced Instructional Transition Guide Grade 3/ Unit 02: Suggested Duration: 13 days Suggested Day Suggested Instructional Procedures 4. Explain to students that they can use the place value chart to help them add 3-digit numbers. Notes for Teacher 5. Display teacher resource: Place Value Chart Addition. Instruct students to determine where the digits in the numbers of George s problem should be placed. 6. Using, teacher resource: Place Value Chart Addition, demonstrate placing the digits of the first number on the second empty row. Ask: Why did I skip the first row of the chart? (The first row will be used to show any regrouping that may take place in the problem.) Use the following steps to model how students connect their models to addition on the place value chart: 7. Distribute handout: Modeling Word Problems Three Ways Part 1 to each student. Ask: page 39 of 132

40 Enhanced Instructional Transition Guide Grade 3/ Unit 02: Suggested Duration: 13 days Suggested Day Suggested Instructional Procedures Notes for Teacher What is the first way you will show this addition problem? The second way? The third way? (Shorthand base-ten drawings; place value chart; write the problem vertically and solve.) 8. Place students in pairs. Instruct pairs to complete the handout. Allow time for students to solve the word problems. Monitor and assess students to check for understanding. Facilitate a class discussion for students to share their responses. 10 Topics: Use open number lines to solve addition and/or subtraction problems. Explore/Explain 9 Students solve multi-step addition and subtraction problems using open number lines. Instructional Procedures: 1. Distribute handout: Blank Number Lines to each student and display teacher resource: Blank Number Lines. 2. Using the displayed teacher resource: Blank Number Lines, record the problem above one of the number lines. Explain to students that blank number lines may be used to solve addition problems by finding benchmark (or compatible) numbers from which to count on. Model how to use an open number line to solve the problem. Spiraling Review ATTACHMENTS Teacher Resource: Blank Number Lines (2 per teacher) Handout: Blank Number Lines (2 per student) Teacher Resource: Adding and Subtracting Using Number Lines KEY (1 per teacher) Handout: Adding and Subtracting Using Number Lines (1 per student) page 40 of 132

41 Enhanced Instructional Transition Guide Grade 3/ Unit 02: Suggested Duration: 13 days Suggested Day Suggested Instructional Procedures Notes for Teacher 3. Instruct students to use their handout: Blank Number Lines and explore different ways to solve Invite student volunteers to model how they solved the problem on their number lines. Ask: TEACHER NOTE By using a number line to illustrate the student s thinking, the teacher gives all students in the class access to a visual representation of a particular strategy. Representing addition and subtraction strategies on a number line also helps students to develop a sense of quantity, by thinking about the relative position of numbers on a number line. How did you model using an open number line? Answers may vary. I modeled to get 130, then added 10 to get 140, and then 5 to get 145; I modeled 128 plus 20 to get 148 and then subtracted the 3 extra that I added to get 145; etc. Although the open number line models were different, was the sum the always the same? (yes) 4. Facilitate a class discussion on the similarities and differences between an open number line and number lines with all the numbers labeled. Explain to students that in contrast to number lines where all the counting numbers are shown, the open number line only shows the result of operations and it can be used to represent strategies such as skip counting, adding on, removing, or differences. 5. Using the displayed teacher resource: Blank Number Lines, record the problem above another number line. Ask: page 41 of 132

42 Enhanced Instructional Transition Guide Grade 3/ Unit 02: Suggested Duration: 13 days Suggested Day Suggested Instructional Procedures What type of problem is this? (subtraction) In a subtraction problem, what are you trying to find? (the difference) Explain to students that the difference on a number line is the distance between the two points (or numbers) given. Ask: Notes for Teacher Which is the smaller of the two numbers in this problem? (49) Do we place that on the right or the left of the number line? How do you know? (On the left; because on a number line, the whole numbers get smaller as we go right to left and larger as we go left to right.) 6. Instruct students to place a tick mark at one end of the number line and another at the other end of the number line. 7. Using the displayed teacher resource: Blank Number Lines, model where to place each of the numbers on the number line and instruct students to replicate the model on their number lines on their handout: Blank Number Lines. 8. Explain to students that in order to find the difference on the number line, they are not going to jump the entire distance from 49 to 207 at once. They will jump in numbers that can be easily calculated mentally. 9. Using the displayed teacher resource: Blank Number Lines, model a possible solution as shown below beginning with the smaller number and building to the larger number, calculating the sum of all the jumps to find the difference: page 42 of 132

43 Enhanced Instructional Transition Guide Grade 3/ Unit 02: Suggested Duration: 13 days Suggested Day Suggested Instructional Procedures Notes for Teacher 10. Using the displayed teacher resource: Blank Number Lines, model another possible solution as shown below beginning with the larger number and decreasing to the smaller number, calculating the sum of all the jumps to find the difference: 11. Instruct students to use their handout: Blank Number Lines and explore different ways to solve Invite student volunteers to model how they solved the problem on their number lines. Ask: How did you model using an open number line? Answers may vary. I began with 207 and subtracted 7 to get 200, subtracted 50 to get 150, and subtracted 100 to get 50, and then subtracted 1 to get 49; etc. Although the open number line models were different, was the sum always the same? (yes) 12. Facilitate a class discussion on the many ways to subtract on an open number line. Explain to page 43 of 132

44 Enhanced Instructional Transition Guide Grade 3/ Unit 02: Suggested Duration: 13 days Suggested Day Suggested Instructional Procedures students that when using an open number line, they need to be concerned with the size of the jumps, so they need to show a difference in jumps between single digit and double digit numbers. 13. Display the following multi-step problem below for the class to see. Chad s plant was 54 inches tall. Marcie s plant was 74 inches taller than Chad s. Nancy s plant was 14 inches taller than both Chad s and Marcie s plant heights together. How tall is Nancy s plant? Ask: Notes for Teacher What type of problem is this? (addition; multi-step) 14. Explain to students that even multi-step problems can be solved using a number line. Instruct students to follow along on their own number lines as you model a possible solution for the problem. 15. Place students in pairs. Instruct student pairs to discuss another possible way to find the same solution to this problem using the blank number line. Invite student volunteers to model how they solved the problem on their number lines. page 44 of 132

45 Enhanced Instructional Transition Guide Grade 3/ Unit 02: Suggested Duration: 13 days Suggested Day Suggested Instructional Procedures 16. Distribute handout: Adding and Subtracting Using Number Lines to each student. Instruct student pairs to complete the handout. Remind students to model and label their solution process for each problem on the open number line. Allow time for student pairs to solve the addition and subtraction problems. Monitor and assess students to check for understanding. Facilitate a class discussion to debrief their processes and solutions. Invite students to demonstrate and explain their open number lines model for the class. Notes for Teacher 11 Topics: Base-ten model for 3-digit subtraction Hundreds grids model for 3-digit subtraction Explore/Explain 10 Students use base-ten blocks and hundreds grids to model and solve 3-digit subtraction problems. Instructional Procedures: 1. Place students in pairs. Distribute bags of base-ten blocks to each student. Explain to students that base-ten blocks can also be used to model subtracting numbers. Instruct student pairs to show the least number of blocks needed to model the number 338. Ask: How many blocks did you use? Describe the blocks used. (14; three 100-flats, three 10- longs, and 8 units) Spiraling Review ATTACHMENTS Teacher Resource: Subtraction Model Connecting to the Procedure Recording Sheet KEY (1 per teacher) Teacher Resource: Subtraction Model Connecting to the Procedure Recording Sheet (1 per teacher) Handout: Subtraction Model Connecting to the Procedure Recording Sheet (1 per student) Teacher Resource: Modeling Subtraction with Hundreds Grids KEY (1 per teacher) Teacher Resource: Modeling Subtraction page 45 of 132

46 Enhanced Instructional Transition Guide Grade 3/ Unit 02: Suggested Duration: 13 days Suggested Day Suggested Instructional Procedures 2. Instruct student pairs to model finding using their base ten blocks. Allow time for students to explore how to use their base-ten blocks to model subtraction. Monitor and assess student pairs to check for understanding, listening to conversations of their thinking processes for subtraction. Facilitate a class discussion, inviting 2-3 students to model their process of finding for the class to see. 3. Remind students that when subtracting base-ten block models for subtraction, they will subtract the ones, the tens, and then the hundreds and exchange when needed. Instruct students to look at the ones place. Ask: Do the ones need to be regrouped? How do you know? (No; because 8 ones > 3 ones. So, 3 can be subtracted from 8.) Do the tens need to be regrouped? How do you know? (Yes; because 3 tens < 5 tens.) How will you regroup the tens? (Trade one 100-flat for ten 10-longs.) Instruct students to use their base-ten blocks to show this exchange. Demonstrate this process for the class to see. Notes for Teacher with Hundreds Grids (1 per teacher) Handout: Modeling Subtraction with Hundreds Grids (1 per student) Teacher Resource: Modeling 3-Digit Subtraction Practice KEY (1 per teacher) Handout: Modeling 3-Digit Subtraction Practice (1 per student) Handout (optional): Subtraction of 3-digit Numbers with Base-Ten Blocks Notes (1 per student) MATERIALS base-ten blocks ( cubes, flats, longs, 10 units in each set) (1 set per student, 1 set per teacher) (previously created) Ask: TEACHER NOTE When student pairs subtract 338 and 153, some page 46 of 132

47 Enhanced Instructional Transition Guide Grade 3/ Unit 02: Suggested Duration: 13 days Suggested Day Suggested Instructional Procedures Do the hundreds need to be regrouped? How do you know? (No; because 2 hundreds > 1 hundred. So, 1 can be subtracted from 2.) How many times did we need to regroup for this problem? Explain. (1 time; in the tens place) How does regrouping in subtraction compare with regrouping in addition? Answers may vary. In subtraction you regroup 10 or 100 and add it to the place value position to the right. In addition you regroup a 10 or 100 and add it to the place value position to the left; etc. 4. Distribute handout: Subtraction Model Connecting to the Procedure Recording Sheet to each student. Instruct student pairs to use the recording sheet to draw each step of this subtraction problem in shorthand base-ten drawings. Students should also connect and describe each step using words to describe their solution process. Allow time for students to complete the activity. Monitor and asses students to check for understanding. Facilitate a class discussion regarding student responses. 5. Using page 2 of teacher resource: Subtraction Model Connecting to the Procedure Recording Sheet KEY model how to subtract across zeroes. Instruct student pairs to replicate the model with their base-ten blocks. 6. Distribute handout: Modeling Subtraction with Hundreds Grids to each student and display teacher resource: Modeling Subtraction with Hundreds Grids. 7. Using the displayed teacher resource: Modeling Subtraction with Hundreds Grids, reference the problem under the grids. Ask: Notes for Teacher students may have exchanged all the hundreds to tens and then subtracted, while other students may have discovered that only one hundred needed to be regrouped. Use these students examples to discuss, refine, and explain the process. TEACHER NOTE For struggling students, use the handout (optional): Subtraction of 3-digit Numbers with Base-Ten Blocks Notes to assist them in understanding each step of the subtraction process while using base-ten blocks. page 47 of 132

48 Enhanced Instructional Transition Guide Grade 3/ Unit 02: Suggested Duration: 13 days Suggested Day Suggested Instructional Procedures How could we use these grids to show the number 147? (We could shade 147 small squares on the grids, or shade one large grid and 47 small squares on another grid.) Instruct students to shade their grids on handout: Modeling Subtraction with Hundreds Grids to show 147. Using teacher resource: Modeling Subtraction with Hundreds Grids, demonstrate the process for the class to see. Notes for Teacher Ask: How could I subtract 129 from the number I just created on the grid? (You could cross out 129 of the small shaded squares, or you could cross out one large shaded grid and 29 small squares on the other grid.) Instruct students to cross out 129 on handout: Modeling Subtraction with Hundreds Grids. Ask: How many small shaded squares remain? (18) What do the remaining shaded (uncrossed-out) squares represent? (the difference) Explain to students that the remaining shaded squares represent the difference. Ask: How is modeling 147 using a hundreds grid similar to modeling the number with base-ten blocks? Answers may vary. The hundreds grid is like a 100-flat; the columns on the hundreds grid are like the 10-longs; and the individual small squares are like the units; etc. If you modeled this problem with base-ten blocks, would you have to regroup? page 48 of 132

49 Enhanced Instructional Transition Guide Grade 3/ Unit 02: Suggested Duration: 13 days Suggested Day Suggested Instructional Procedures Explain. (yes) Answers may vary. The 7 ones in 147 were not greater than the 9 ones in 129. So, you would need to regroup the ones place in order to subtract in this problem; etc. Remind students that regrouping occurs when the digits in the number being subtracted are greater than the digits in the number being subtracted from. Notes for Teacher 8. Distribute handout: Modeling 3-Digit Subtraction Practice to each student. Instruct student pairs to complete the handout. Allow time for student pairs to complete the subtraction problems. Facilitate a class discussion for students to share their responses. 12 Topics: Connect base-ten model to place value and traditional subtraction algorithm Explore/Explain 11 Students use base-ten blocks to model a 3-digit subtraction problem and to connect the numbers from that model to a place value chart. The place value chart is used to facilitate student understanding of the subtraction algorithm procedures, including regrouping. Instructional Procedures: 1. Facilitate a class discussion to debrief handout: Modeling 3-Digit Subtraction Practice. 2. Place students in pairs and distribute base-ten blocks to each student. 3. Display teacher resource: Pencil Factory for the class to see. Instruct student pairs to solve the problem using base-ten blocks and record all work, including their base-ten model graphics, in their math journals. Allow student pairs 3 5 minutes to complete the problem. Monitor and Spiraling Review ATTACHMENTS Teacher Resource: Pencil Factory KEY (1 per teacher) Teacher Resource: Pencil Factory (1 per teacher) Teacher Resource: Place Value Chart Subtraction (1 per teacher) Teacher Resource: Modeling Word Problems Three Ways Part 2 KEY (1 per teacher) Handout: Modeling Word Problems Three Ways Part 2 (1 per student) page 49 of 132

50 Enhanced Instructional Transition Guide Grade 3/ Unit 02: Suggested Duration: 13 days Suggested Day Suggested Instructional Procedures assess students to check for understanding. Facilitate a class discussion, clarifying any misconceptions. Ask: What operation is needed to solve this problem? How do you know? (subtraction) Answers may vary. We are trying to find how many more pencils were packed; etc. How could Jasmin s pencils be represented using the least amount of base ten blocks? Answers may vary. (2 100-flats, 7 10-longs, and 3 units for 273) How many pencils did Coryn pack? (196 pencils) What is the next step (using base-ten blocks) in determining if Jasmin is correct? (Start with the units and begin by removing or subtracting the number of units in Coryn s number. Continue to remove the blocks and regroup as necessary by moving to the tens and then to the hundreds.) What number sentence might represent Jasmin s solution? = 177 Is Jasmin correct? Why or why not? (No; because she packed only 77 more pencils than Coryn, not 177 more pencils.) What error did Jasmin most likely make in determining how many more pencils she packed than Coryn? (She forgot to regroup the hundreds or she forgot that she had exchanged one 100 for ten 10 s when regrouping and therefore subtracted the hundred incorrectly.) What could Jasmin have done to check to see if her answer was reasonable? Explain. (She could have used estimation.) Answers may vary. Used compatible numbers or rounding to determine if the answer was reasonable, such as =75; etc. What steps did you use to solve this problem? Answers may vary. We subtracted the ones first, and exchanged as necessary. Then we subtracted the tens and exchanged as necessary and finally we subtracted the hundreds; etc. Notes for Teacher MATERIALS base-ten blocks ( cubes, flats, longs, 10 units) (1 set per student, 1 set per teacher) (previously created) math journal (1 per student) State Resources MTR K-5: Just Make It Easy!; Let s Get Friendly! may be used to reinforce these concepts. page 50 of 132

51 Enhanced Instructional Transition Guide Grade 3/ Unit 02: Suggested Duration: 13 days Suggested Day Suggested Instructional Procedures Why do you begin subtracting in the ones place first? Answers may vary. In subtraction, exchanging renames smaller units as larger units. So, we subtract from right to left starting with the smallest place value and work toward the left with the greater place values; etc. Notes for Teacher 4. Remind students that they can use a place value chart to subtract 3-digit numbers just as they did for addition. 5. Display teacher resource: Place Value Chart Subtraction for the class to see. Instruct students to determine where the digits in Jasmin s problem should be placed. Ask: How should the number of Jasmin s pencils be recorded on the place value chart? (2 in the hundreds, 7 in the tens, and 3 in the ones; according to each digit s place value.) 6. Using teacher resource: Place Value Chart Subtraction, demonstrate by placing the digits of the first number on the second empty row. Ask: Why did I skip the first row of the chart? (The first row will be used to show any exchanging that may take place in the problem.) page 51 of 132

52 Enhanced Instructional Transition Guide Grade 3/ Unit 02: Suggested Duration: 13 days Suggested Day Suggested Instructional Procedures Use the following steps to show students how to connect their models to addition on the place value chart: Notes for Teacher 7. Distribute handout: Modeling Word Problems Three Ways Part 2 to each student. Ask: What is the first way you will show this subtraction problem? The second way? The third way? (Hundreds grid; place value chart; write the problem vertically and solve.) 8. Place students in pairs. Instruct pairs to complete the handout. Allow time for students to solve the word problems. Monitor and assess students to check for understanding. Facilitate a class discussion for students to share their responses. Topics: ATTACHMENTS Identify multiple representations of addition and/or subtraction problem situations Elaborate 2 Students identify addition and/or subtraction problem situations in word, model, and number sentence form. Teacher Resource: Addition/Subtraction Match-up KEY (1 per teacher) Card Set: Addition/Subtraction Match-up (1 per student group) Teacher Resource: Addition/Subtraction page 52 of 132