number development Level 5 6 MMSD Number and Operations Instructional Guide Summer 2011 Edition

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1 number development Level 5 6 MMSD Number and Operations Instructional Guide Summer 2011 Edition

2 Madison Metropolitan School District Number and Operations Instructional Guide: Number Development, Level 5 6 Summer 2011 Edition Copyright 2011 by Madison Metropolitan School District More information Madison Metropolitan School District Math Division 545 West Dayton Street, Madison, WI Recommended citation Madison Metropolitan School District (2011). Madison Metropolitan School District Number and Operations Instructional Guide: Number Development, Level 5 6. Madison, WI: Madison Metropolitan School District. Page 2 Number Development Level 5 6

3 Table of contents Student portrait: Sources: Toolkit: Blacklines: Forward number word sequence: 1-10, FWD.6.1 Provide Practice 9 FWD.6.2 Sliding Forward 10 FWD.6.3 Count Some More 10 FWD.6.4 After (& Before) 10 Backward number word sequence: 10, BACK.6.1 Provide Practice 11 BACK.6.2 Sliding Back 12 BACK.6.3 Count Some More 12 BACK.6.4 (After &) Before 12 Number word sequences: skip counting by 10s, 25s, 100s...13 SKIP.6.1 Provide Practice 13 SKIP.6.2 Sliding Forward and Back 14 SKIP.6.3 Count Around (Say Hello to the Floor) 14 SKIP.6.4 Changing Places 14 SKIP.6.5 How Many Miles to 1,000? 14 Number identification: 1-10, #ID.6.1 Making a 10,000 Chart 15 #ID.6.2 Number Building with Digit Cards 15 #ID.6.3 Provide Written Practice 16 Sequencing/ordering: 1-10, SEQ.6.1 Order Them 17 Number line/magnitude: MAG.6.1 Number Squeeze or Guess My Number 18 MAG.6.2 Who Am I? 18 MAG.6.3 Who Could They Be? 19 MAG.6.4 Close, Far, and In Between 19 Number Development Level 5 6 Page 3

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5 Student portrait: 5 6 The student at this level has the ability to perform the tasks of The student at this level is working to develop the ability to perform the tasks of LEVEL 5 LEVEL 6 Can count by 1s from any number Can name the number directly after for numbers Can count back within (starting from any number). Can name the number directly before for numbers Can count by 2s, 3s, 4s, and 5s starting from any multiple. Can count forward and backward by 10s from any 2-digit number. Can identify and write numerals Can sequence and order numbers in the range Can accurately place numbers on an empty or nearly empty number line. Can count or make sets of up to 1000 using base-ten materials (100s, 10s and 1s). Can count by 1s from any number 1-10,000. Can name the number directly after for numbers 1-10,000. Can count back within 10,000-0 (starting from any number). Can name the number directly before for numbers 1-10,000. Can count forward and backward by 10s and 100s from any 2- or 3-digit number. Can count forward and backward by 25s from any multiple. Can identify and write numerals 1-10,000. Can sequence and order numbers in the range 1-10,000. Can accurately place numbers on an empty or nearly empty number line. Number Development Level 5 6 Page 5

6 Sources: 5 6 Specific activities Many activities in this resource were created for this document or appear in MMSD s Learning Mathematics in the Primary Grades or Learning Mathematics in the Intermediate Grades. The following exceptions were reproduced or adapted from other sources: TERC (2008): Changing Places, 14; How Many Miles to 1,000?, 14; Making a 10,000 Chart, 15 Van de Walle & Lovin: Close, Far, and In Between, 19; Who Am I?, 18; Who Could They Be?, 19 Wright, et al. (2006a): Provide Practice, 9, 11, 13 Wright, et al. (2006b): Count Around (Say Hello to the Floor), 14 Complete citations Madison Metropolitan School District (2006). Learning Mathematics in the Primary Grades. Madison, WI: Madison Metropolitan School District. Madison Metropolitan School District (2007). Learning Mathematics in the Intermediate Grades. Madison, WI: Madison Metropolitan School District. TERC (2008). Investigations in Number, Data, and Space, 2 nd edition. Boston, MA: Pearson, Scott Foresman. Van de Walle, J. A., & Lovin, L. H. (2006). Teaching Student-Centered Mathematics: Grades 3-5. Boston, MA: Allyn and Bacon Pearson Education, Inc. Wright, R. J., Martland, J., Stafford, A. K., & Stanger, G. (2006a). Teaching Number: Advancing Children s Skills & Strategies, 2nd edition. Thousand Oaks, CA: Sage Publications, Inc. Wright, R. J., Martland, J., Stafford, A. K., & Stanger, G. (2006b). Teaching Number in the Classroom with 4-8 Year-olds. Thousand Oaks, CA: Sage Publications, Inc. Page 6 Number Development Level 5 6

7 Toolkit: 5 6 Sliding card Number Development Level 5 6 Page 7

8 Blacklines: 5 6 Number cards Number cards (0-10) Number strips Number strips (25s to 250) Number strips (100s to 10,000) Page 8 Number Development Level 5 6

9 Forward number word sequence: 1-10,000 FWD.6.1 Provide Practice To explore the base-ten patterns within 1-10,000, students need multiple opportunities to think through and work out the patterns of counting by 1s, 10s, 100s, and 1000s within 1-10,000. Particular attention should be paid to crossing 10s, 100s, and 1000s. Notice that with large numbers, some students may need the numbers written down to keep track of them in their minds. Examples: First, discuss and practice counting by 1000s up to 10,000. Let s take turns counting by 1000s. I ll say (write) 1000, then you say (write) 2000, then I ll say (write) Ready? (Teacher and student alternate.) Then switch. This time, you start. You say (write) 1000, and I ll say (write) (Student and teacher alternate.) Next, discuss and practice counting by 100s in intervals between 1000 and 10,000. Now let s take turns counting by 100s after I ll say (write) 1000, then you say (write) 1100, then I ll say (write) Ready? (Teacher and student alternate.) Then switch. This time, you start. You say (write) 1000, and I ll say (write) (Student and teacher alternate.) By 1s: Start from 1988 and count up by 1s to (Student counts verbally or in writing.) Now start from 2995 and count up to By 10s: I m going to count by 10s from a number, and I want you to say (write) the next two (or three) numbers after I stop. Ready? Say or write, 2960, 2970, 2980? I m going to start counting. When I stop, I want you to say (write) what number comes next. Say or write, 1395, 1396, 1397, 1398? (Gradually shorten the string of numbers before the student needs to respond.) I m going to say (write) a number, and I want you to tell (show) me what number comes next. Say or write, 1349? 2998? Number Development Level 5 6 Page 9

10 FWD.6.2 Sliding Forward Toolkit: Sliding card Blacklines: Number strips (100s to 10,000) Position a number strip in the sliding card opening. As the student counts forward by 100s, reveal the numbers in the opening by sliding the number strip through the card so the student can confirm or correct answers. Number strips will give students practice crossing 1000s (e.g., 2800, 2900, 3000, 3100, 3200 ). FWD.6.3 Count Some More Blacklines: Number cards (0-10) optional; use only 0-9 for this activity To determine the starting number, have one student write out a four-digit number or draw four digit cards to make a four-digit number. After the student identifies the starting number, have the group count on from that number either verbally or by writing in their math journals. FWD.6.4 After (& Before) With the group sitting in a circle, have each student write a four-digit number in her/his math journal (or individual dry-erase board, etc.) and place the number face down on the floor. The first student turns over his/her number, reads it aloud, and says, One after or Two after (student choice). The next student in the circle tells the number that is one (or two) after, and the first student confirms whether the number is correct. The second student then turns over his/her number, reads it aloud, and says One after or Two after to the next student in the circle. Continue until all students have had a turn. To begin another round, have each student write a new number. Page 10 Number Development Level 5 6

11 Backward number word sequence: 10,000-0 BACK.6.1 Provide Practice To explore the base-ten patterns within 1-10,000, students need multiple opportunities to think through and work out the patterns of counting back by 1s, 10s, 100s, and 1000s within 1-10,000. Particular attention should be paid to crossing 10s, 100s, and 1000s. Notice that with large numbers, some students may need the numbers written down to keep track of them in their minds. Examples: Back by 1000s: Let s take turns counting backward by 1000s. I ll say (write) 10,000, then you say (write) 9000, then I ll say (write) Ready? (Teacher and student alternate.) Then switch. This time, you start. You say (write) 10,000, and I ll say (write) (Student and teacher alternate.) Back by 100s in intervals between 1000 and 10,000: Now let s take turns counting backward by 100s. I ll say (write) 2100, then you say (write) 2000, then I ll say (write) Ready? (Teacher and student alternate.) Then switch. This time, you start. You say (write) 2100, and I ll say (write) (Student and teacher alternate.) Back by 1s: Start from 3,004 and count backward by 1s to (Student counts verbally or in writing.) Now start from 4002 and count backward to Back by 10s: I m going to count backward by 10s from a number, and I want you to say (write) the next two (or three) numbers after I stop. Ready? Say or write, 2980, 2970, 2960, 2950, 2940? (Gradually shorten the string of numbers before the student needs to respond.) I m going to start counting backward. When I stop, I want you to say (write) what number comes next. Ready? Say or write, 1507, 1506, 1505, 1504? I m going to say (write) a number, and I want you to tell (show) me what number comes right before it. Say or write, 1572? 2004? Number Development Level 5 6 Page 11

12 BACK.6.2 Sliding Back Toolkit: Sliding card Blacklines: Number strips (100s to 10,000) Position a number strip in the sliding card opening. As the student counts back by 100s, reveal the numbers in the opening by sliding the number strip through the card so the student can confirm or correct answers. Number strips will give students practice crossing 1000s (e.g., 3200, 3100, 3000, 2900, 2800 ). BACK.6.3 Count Some More Blacklines: Number cards (0-10) optional; use only 0-9 for this activity To determine the starting number, have one student write out a four-digit number or draw four digit cards to make a four-digit number. After the student identifies the starting number, have the group count back from that number either verbally or by writing the in their math journals. BACK.6.4 (After &) Before With the group sitting in a circle, have each student write a four-digit number in her/his math journal (or individual dry-erase board, etc.) and place the number face down on the floor. The first student turns over his/her number, reads it aloud, and says, One before or Two before (student choice). The next student in the circle tells the number that is one (or two) before, and the first student confirms whether the number is correct. The second student then turns over his/her number, reads it aloud, and says One before or Two before to the next student in the circle. Continue until all students have had a turn. To begin another round, have each student write a new number. To increase complexity, allow students to prompt each other for the number one or two before or one or two after. Page 12 Number Development Level 5 6

13 Number word sequences: skip counting by 10s, 25s, 100s SKIP.6.1 Provide Practice Students at this level are practicing counting forward and backward by 25s. They also are learning to count forward and backward by 10s and 100s from any two-digit or three-digit number. Students should be given plenty of opportunities to practice these count by skills in written as well as verbal formats. Examples: By 25s: I m going to count by 25s from 100 to 300. Listen so you can count after me. 100, 125, Now you try. (Student counts.) Next, alternate. Let s take turns counting by 25s. I ll say 100, then you say 125, then I ll say 150. Ready? (Teacher and student alternate.) Then switch. This time, you start. You say 100, and I ll say 125. (Student and teacher alternate.) By 10s: I m going to count by 10s from different numbers. Listen so you can count after me. 117, 127, 137, 147, 157. Now you try. (Student counts.) Next, alternate. Let s take turns counting by 10s. I ll say 117, then you say 127, then I ll say 137. Ready? (Teacher and student alternate.) Then switch. This time, you start. You say 117, and I ll say 127. (Student and teacher alternate.) By 100s: I m going to count by 100s from different numbers. Listen so you can count after me. 512, 612, 712, 812, 912, Now you try. (Student counts.) Next, alternate. Let s take turns counting by 100s. I ll say 512, then you say 612, then I ll say 712. Ready? (Teacher and student alternate.) Then switch. This time, you start. You say 512, and I ll say 612. (Student and teacher alternate.) Number Development Level 5 6 Page 13

14 SKIP.6.2 Sliding Forward and Back Toolkit: Sliding card Blacklines: Number strips (25s to 250) Position a number strip in the sliding card opening. As the student counts forward or backward by 25s, reveal the numbers in the opening by sliding the number strip through the card so the student can confirm or correct answers. SKIP.6.3 Count Around (Say Hello to the Floor) Have students stand in a circle. Announce by which number you ll be counting (25s), the first number (any multiple), and the last number (any multiple). For example, We re going to take turns counting by 25s from 100 to 200. Here s how we play. You may also wish to write these numbers where students can see them. Students take turns counting around in the circle by multiples of 25. At each turn, the student can choose to say one or two multiples in the sequence. The student who says the last multiple in the counting sequence sits down. Some groups like to say, Say hello to the floor! as the student sits down. (This is dependent upon a healthy classroom community.) Repeat with the same sequence until only one student is standing. That last student standing is the winner. SKIP.6.4 Changing Places Follow instructions and materials lists for Changing Places from the Investigations series (Grade 4, Unit 5, Session 1.3, pages 37 to 44). SKIP.6.5 How Many Miles to 1,000? Follow instructions and materials lists for How Many Miles to 1,000? from the Investigations series (Grade 4, Unit 5, Session 1.4, pages 45 to 50). Page 14 Number Development Level 5 6

15 Number identification: 1-10,000 #ID.6.1 Making a 10,000 Chart Follow instructions and materials lists for Making a 10,000 Chart from the Investigations series (Grade 4, Unit 5, Session 3.1, pages 100 to 106). In this activity, students will construct a 10,000 chart. This is a good anchor tool for continued number development as well as addition and subtraction tasks. #ID.6.2 Number Building with Digit Cards Blacklines: Number cards (0-10) four sets of 0-9 Take four of the single-digit cards and make a four-digit number. Have students read the number and write it down. Allow one student to rearrange the number cards, and then have students read and write the new number. Continue until four numbers have been recorded or until each student has had a turn. Repeat with new cards or ask students more questions about the first four cards. Examples: What is the largest number we could make with these four cards? Discuss why. What is the smallest number we could make with these four cards? Discuss why. Select one of the four cards in play. From these four digit cards, can you make two different numbers that both have this number in the 100s place? Select one of the four cards in play. From these four digit cards, can you make two different numbers that both have this number in the 10s place? Number Development Level 5 6 Page 15

16 #ID.6.3 Provide Written Practice Students need written practice counting within the range 1-10,000. Particular attention should be paid to crossing 10s, 100s and 1000s. Use student counting booklets (available in MMSD) and/or ask students to write numbers in their math journals. Examples: What number comes right before 4380? What number comes two before 7591? What are the next three numbers after 9248? Write the numbers counting forward within different number ranges (e.g., or ) Write the numbers counting backwards within different number ranges (e.g., or 2316 to 2280) Count by 25s (e.g., from 300 to 600 or from 1000 to 1300) Count by any number 2-10 or by 100 from any number within 1-10,000 (e.g., -7 from 3379 to 3239). Students at this level are working to become fluent with cross-ten subtraction facts, so this is an opportunity to extend that learning. Page 16 Number Development Level 5 6

17 Sequencing/ordering: 1-10,000 SEQ.6.1 Order Them Write an appropriate mixed-up set of numbers in the 1-10,000 range. Have the student re-write the numbers in order from least to greatest and then name each number. The set of numbers may follow a sequence (e.g., 4123, 4223, 4323, 4423, 4523 or 5671, 5681, 5691, 5701, 5711 or 1575, 2575, 3575, 4575, 5575), or it may not follow a sequence (e.g., 1123, 1132, 3120, 3201, 3301). Number Development Level 5 6 Page 17

18 Number line/magnitude: MAG.6.1 Number Squeeze or Guess My Number Draw a number line where everyone in the group can see. Ask one student to choose a secret number between 1 and Have remaining students take turns asking questions using before, after, and between to narrow the possibilities for the secret number. (For example, Is it before 500? ) When the first student answers, visually narrow the remaining choices by labeling and marking off the portion of the number line representing the range eliminated by the first answer. Have students continue asking questions and marking answers until they can be 100% sure they have the correct number. Do not allow random guessing. Challenge students to discover the number using the fewest questions they can. When the final answer is known, have the student who said the correct number choose the next number. Variation: To make this activity more challenging, have students sketch a line representing the given number range in their journals. As students guess at the secret number, have them practice labeling and crossing off eliminated numbers in their own journals. MAG.6.2 Who Am I? Sketch a line labeled 0 at one end and 1000 at the opposite end. Write a? at a point that corresponds to your secret number. (Estimate the position as best you can.) Have students try to guess your secret number. On the number line, place and label a mark representing the first guess. Continue marking each guess until your secret number is discovered. Page 18 Number Development Level 5 6

19 MAG.6.3 Who Could They Be? Use numbers to label two points on a number line, not necessarily the ends. Label other points with letters. Ask students what numbers they think the points labeled with letters might be and why they think that. In the example shown here, A and B are less than 500, but probably more than 250. C could be about 900. You could also ask where 750 or 250 might be. Explore with students as they justify their placement of numbers. 0 A B 500 C D MAG.6.4 Close, Far, and In Between Write any three numbers (e.g., 490, 520, 810). With these three numbers as referents, ask questions such as the following, and encourage discussion of all responses. Examples: Which two are closest? Why? Which is closest to 500? To 750? Name a number between 520 and 490. Name a number that is more than all of these. Name a number that is less than all of these. How far apart are 490 and 520? Number Development Level 5 6 Page 19