Patterns in 100s Chart

Transcription

1 Second Grade Unit: 04 Lesson: 01 Suggested Duration: 2 days Patterns in 100s Chart Lesson Synopsis: This lesson will introduce the 100s chart as a tool for identifying patterns in numbers. TEKS: 2.5 Patterns, relationships, and algebraic thinking. The student uses patterns in numbers and operations. 2.5A Find patterns in numbers such as in a 100s chart. Process TEKS: 2.12 Underlying processes and mathematical tools. The student applies Grade 2 mathematics to solve problems connected to everyday experiences and activities in and outside of school. 2.12C Select or develop an appropriate problem-solving plan or strategy including drawing a picture, looking for a pattern, systematic guessing and checking, or acting it out in order to solve a problem. GETTING READY FOR INSTRUCTION Performance Indicator(s): Select and demonstrate addition and subtraction of two-digit numbers utilizing patterns within a 100s chart and mathematically communicate those actions using words and numbers on the given recording sheet. (2.3B, 2.3C; 2.5A) ELPS Data: 1E, 2E, 2I, 3D, 3H, 4E, 5B, 5G Competency with this performance indicator may not be fully exhibited by all students until Unit 04 Lesson 04. Therefore, the evaluation component will not appear until Unit 04 Lesson 04. Key Understandings and Guiding Questions: The addition/subtraction patterns used in a 100s chart can be mathematically represented with number sentences. What happens to the value of the numbers when you move right to left or left to right within the 100s chart? What happens to the value of the numbers when you move up or down a row on the 100s chart? What happens to the value of the numbers when you move diagonally from left to right or right to left on a 100s chart? Vocabulary of Instruction: 100s chart number line digit place value horizontal vertical diagonal core repeating pattern increase decrease additive pattern Materials: chart tablet counters overhead manipulatives (i.e., color tiles, base ten blocks, counters) math journals or paper Resources: SPIRALING REVIEW A new lesson component, Spiraling Review, will be introduced with this lesson. It is designed to provide a spiraling review of previously introduced concepts. It is recommended that students be given 5 6 minutes to complete the daily questions using their math journals. Approximately four minutes should be used for discussion. 2008, TESCCC 08/11/08 page 1 of 9

2 Two days of each week are called Fact Time and are devoted to developing quick recognition of basic addition and subtraction fact families. Teachers may use supplementary materials such as flashcards based on the needs of each student in the classroom. Advance Preparation: 1. Handout: 100s Chart cut apart horizontally by rows into 10 rows. Tape the rows to the board so that consecutive ends are aligned end to end to create a horizontal number line. However, do not tape the ends together (i.e.,, row ending with 10 taped to row beginning with 11, etc.) because the number line will later be broken apart by rows and moved to create a 100s Chart (1 per teacher). 2. Transparency: 100s Chart Cut one transparency apart by rows, and keep the other transparency chart as a whole. (2 per teacher) 3. Handout: 100s Chart. Laminate for continuous use. (1 per student) 4. Handout: 100s Chart Pattern Pieces (1 per student) 5. Transparency: 100s Chart Pattern Pieces (1 per teacher) Background Information: Students will have prior experience in recognizing, extending, and creating new patterns using sounds, physical movement, and concrete objects (K.5) and identifying, describing, and extending repetitive and additive patterns (1.6A). This lesson will serve as an introduction of patterns found in numbers through the use of the 100s chart. GETTING READY FOR INSTRUCTION SUPPLEMENTAL PLANNING DOCUMENT Instructors are encouraged to supplement, and substitute resources, materials, and activities to differentiate instruction to address the needs of learners. The Exemplar Lessons are one approach to teaching and reaching the Performance Indicators and Specificity in the Instructional Focus Document for this unit. A Microsoft Word template for this planning document is located at If a supplement is created electronically, users are encouraged to upload the document to their Lesson Plans as a Lesson Plan Resource in your district Curriculum Developer site for future reference. INSTRUCTIONAL PROCEDURES Instructional Procedures ENGAGE 1. Using overhead manipulatives, create a color pattern on the overhead (i.e.,, red, green, red, green, etc.). What pattern do you see? How can you continue the pattern? (red, green, red, green, red, green; keep adding red, green) What is the core of this repeating pattern? (red, green) NOTE: 1 Day = 50 minutes Suggested Day 1 SPIRALING REVIEW MATERIALS overhead manipulatives FOR REPEATING PATTERN Students may describe the pattern as an AB pattern. Paraphrase student responses to describe the actual pattern such as red, green. The core of a repeating pattern is the actual pattern being repeated. The core is made up of elements. In this case, red and green. 2. Create an additive (growing) pattern on the overhead. (i.e.,, 1 st stage will have one block; 2 nd stage will have two blocks; 3 rd stage will have three blocks, etc.) What pattern do you see? How can you continue the pattern? (One block is being added each time. One block, two blocks, three blocks, four blocks, five blocks, six blocks, etc.) What do you call this type of pattern? (additive) Why is the pattern called an additive pattern? (The pattern changes with each repetition.) Additive Pattern: Blocks 2008, TESCCC 08/11/08 page 2 of 9

3 Instructional Procedures 3. Create a directional pattern on the overhead. (i.e., horizontal line, vertical line, diagonal line, horizontal line, vertical line, diagonal line, etc.). How can you describe the pattern on the overhead? Answers may vary. Possible answers may include: Repeating pattern or Line going across, line going up and down, line slanting, line going across, line going up and down, line slanting, etc. What would be the next two stages or repetitions? Answers may vary. Possible answers may include: It would be the same pattern repeated twice; it would be across, up and down, slant, across, up and down, slant, etc. Paraphrase student responses to include the proper use of the vocabulary: horizontal, vertical, and diagonal. 4. Create a repetitive chant. (i.e., snap your fingers three times, clap your hands twice, stomp your foot once, snap your fingers three times, clap your hands twice, stomp your foot once, etc.) How would you describe the sound pattern? Can you continue the pattern? Answers may vary. Possible answers may include: You snapped your fingers three times, clapped your hands twice, stomped your feet once, snapped your fingers three times, clapped your hands twice, stomped your feet once, etc. How could the pattern be represented using letters or numbers? AAABBC or EXPLORE/EXPLAIN 1. Teacher will explain to the students that patterns also exist within numbers. 2. Write a number pattern on the board (i.e., 12, 22, 32, 42, 52, etc.). How can you describe the number pattern? Answers may vary. Possible answers may include: The digit in the tens place value Possible answers may include: The digit in the tens place increases by one each time, while the digit in the ones place value stays the same; The numbers are increasing by 10 each time, etc Make sure students understand if they say the digit is increasing by one that means the value is increasing by ten. What would be the next two steps or repetitions? (62, 72) 3. Referencing the number line on the board (created from the 100s chart cut into rows of ten), students will observe the number line What patterns do you see on the number line? Answers may vary. Possible answers may include: The digit in the ones place value increases by one as you move to the right; The sections of the number line are divided into ten sections, etc. 4. Model drawing arrows to represent the number pattern 12, 24, 36, 48, 60, etc., over the number line on the board. Repeating Pattern: Directional Pattern MATERIALS Handout: 100s Chart made into a number line and taped to the board (1 per teacher) math journals or blank paper Transparency: 100s Chart (1 per teacher) one copy that is whole and another that has been cut into rows of ten. Handout: 100s Chart (1 per student) counters chart paper Point to the number line as you skip count by tens following the number pattern As you draw each arrow, have the students say the ending number with you and write each number in their math journal. Look at the numbers you wrote in your journal. What patterns do you see? Answers may vary. The arrows are the same length; The arrows are skip counting by 12; The tens are increasing by one ten and the ones are increasing by two each time, etc. Erase the arrows and explain that you are going to be drawing new arrows. 2008, TESCCC 08/11/08 page 3 of 9

4 Instructional Procedures 5. Referencing the number line on the board (created from the 100s chart cut into rows of ten), model drawing arrows to represent the number pattern 11, 22, 33, 44, 55 over the number line on the board. The students are to name each stopping point and write the numbers in their math journal. How can you describe the number pattern? Answers may vary. Possible answers may include: The digit in the tens and ones place value are the same; The digit in the tens place increases by one each time, while the digit in the ones place also increases by one each time; The value of the numbers increase by a sum of 11, etc. What would the pattern be if I extended it four more times? (66, 77, 88, 99) Draw arrows to show the extensions. 6. The teacher will explain to the students that number lines tend to take up too much space so you are going to rearrange the number line to be more user-friendly. Show how the number line is sectioned off into groups of ten. Demonstrate how the second row of tens (numbers 11 20) will wrap around by placing the strip directly under the first row of tens (numbers 1 10). Continue demonstrating the attachment of each row of ten to create the 100s chart. MISCONCEPTIONS It is essential to show the students how the 100s chart is created from a number line. Some students have difficulty understanding how the number at the end of a row wraps around to the beginning of the next row. You may need to use the overhead precut rows of the number line to demonstrate so the whole class can see how the numbers flow within a 100s chart The teacher will model how to locate a number utilizing the overhead transparency: 100s chart. To locate the number 62, we must identify the number of tens and ones. The number 62 has six tens and two ones. As you move your finger down a row, skip count by tens on the 100s chart: 10, 20, 30, 40, 50, 60. Continue moving your finger horizontally as you count by ones 61, The teacher will generate several two-digit numbers for students to practice locating numbers on a 100s chart. Each time students will count by tens as you move down each row and count by ones as you move horizontally. (ex: 48, 74, 92) 9. Distribute counters and the handout: 100s Chart to each student. Write the number pattern 12, 22, 32, 42, 52, etc. on the board. Ask students to locate the pattern on their handout: 100s chart using counters and look for a pattern. What pattern do you see? Answers may vary. Possible answers may include: The counters are moving down in a straight line; The numbers are increasing by ten each time; All of the numbers have 2 ones, etc. 10. Repeat this process with the remaining number pattern: 11, 22, 33, 44, 55, etc., and have the students describe the movements and pattern. 11. Divide students into pairs. Instruct students to discuss with their partner how locating numbers and patterns on a number line and a 100s chart are alike and different. Select one student from each partnership to share their findings with the whole class. How is locating numbers on a number line and 100s chart alike and different? Answers may vary. Possible answers may include: Using a number line, the numbers align horizontally and we skip count by tens and ones on the number line to locate a number. On a 100s chart, the numbers wrap around every ten numbers and we skip count by tens and one by moving vertically and horizontally to locate a number. How is finding patterns on a number line and 100s chart alike and Paraphrase and record student responses to include the proper directional vocabulary of vertical and horizontal, and properly identifying the changes in place value being described within the pattern. (i.e., A student may say the second number is changing by one when you go across the 100s chart. Paraphrase the student by saying, you are saying the digit in the ones place value is changing by one as 2008, TESCCC 08/11/08 page 4 of 9

5 Instructional Procedures different? Answers may vary. Possible answers may include: Using a number line, arrows are drawn horizontally over each group showing how we skip count by tens or ones. On a 100s chart, we mark the pattern with counters and count the number of tens found in a vertical line (skip counting by tens) and then count the number of ones by moving horizontally. 12. Instruct students to study the handout: 100s chart with their partners to look for any other patterns they see in the chart. Can you describe to your partner the number patterns you observed? Answers may vary. 13. Select one student from each partnership to share their findings with the whole class and record student findings on a chart tablet with an example of each. 14. Students may not recognize the diagonal number pattern within the 100s chart. Using the transparency: 100s chart, teacher will cover-up two sections of the overhead transparency to focus student attention to numbers moving diagonally. 15. Students will study the transparency: 100s chart with their partners. How can you describe the number patterns observed moving diagonally to your partner? Answers may vary, but should include changes in the tens and ones places. How many patterns can you find? Answers may vary. Allow students time to investigate the patterns. 16. Select one student from each partnership to share their findings with the whole class and record on the chart tablet. Possible responses may include: The digit in the tens place and the ones place change by one as you move diagonally on the 100s chart; Possible responses may include: The digit in the ones place value changes by one as you move horizontally on the 100s chart; and Refer to the chart tablet and discuss all of the patterns the students have discovered within the 100s chart focusing on the changes within the digits. How are the patterns within the 100s chart affecting the value of the numbers? Answers may vary. Possible answers may include: The patterns found always include a change in value for the tens and/ or ones place(s). 18. Select one student from each group to share their findings with the whole class. Answers may vary. Possible answers may include: The value of the number increases by one when moving horizontally from left to right on the 100s chart, but decreases by one when moving horizontally from right to left.; the value of the number increases by one ten as you move vertically from top to bottom on the 100s chart and decreases by one ten when you move vertically from bottom to top; the value of the number increases by one ten and one unit or eleven as you move diagonally from left to right in the 100s chart and increases one ten and decreases one unit or nine as you move diagonally from right to left. you move horizontally within the 100s chart. ) ELABORATE Suggested Day Although identifying diagonal patterns is important for students to observe, the intent of this unit is for students to concentrate on changes in tens (vertically) and ones (horizontally). 2008, TESCCC 08/11/08 page 5 of 9

6 Instructional Procedures 1. Distribute the handout: 100s Chart Pattern Pieces to each student. 2. Model for students how to complete a missing hundreds pattern piece using the patterns discovered within the 100s chart. Reference the notes taken on the chart tablet to assist them in completing this assignment. 3. Students will work in partners to complete the remaining missing components of the 100s chart. EVALUATE 1. This individual lesson has no formal evaluation of the performance indicator until Unit 04 Lesson 04. SPIRALING REVIEW MATERIALS Handout: 100s Chart Pattern Pieces (1 per student) Transparency 100s Chart Pattern Pieces (1 per teacher) Monitor partners to check for understanding. Redirect those students that are just copying the numbers directly from the 100s chart to focus on the patterns to determine the missing numbers. 2008, TESCCC 08/11/08 page 6 of 9

7 100s CHART , TESCCC 08/11/08 page 7 of 9

8 Fill in the missing numbers from the 100s chart pieces. 100s Chart Pattern Pieces KEY , TESCCC 08/11/08 page 8 of 9

9 Fill in the missing numbers from the 100s chart pieces. 100s Chart Pattern Pieces , TESCCC 08/11/08 page 9 of 9