Task 2
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Western Governors University *
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NUMBER SEN
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Mathematics
Date
Jan 9, 2024
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docx
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Kyle Clinedinst
Student ID-001029234
BNM2 Task 2: Understanding and Teaching Patterns or Functions
Part A:
1. List three content standards from your state that apply to patterns or functions for grades K–6. The three selected standards must represent three different grade levels.
Grade 2: 2.NBT.2 “Count forward and backward within 1,000 by ones, tens, and hundreds starting at any number; skip-count by 5s starting at any multiple of 5.”-Ohio Learning Standards/Mathematics Grade 2
Grade 3: 3.OA.5 “Apply properties of operations as strategies to multiply and divide. For example, if 6 × 4 = 24 is known, then 4 × 6 = 24 is also known (Commutative Property of Multiplication); 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30 (Associative Property of Multiplication); knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56 (Distributive Property). Students need not use formal terms for these properties” -Ohio Learning Standards/Mathematics Grade 3
Grade 4: 4.OA.5 “Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.” -
Ohio Learning Standards/Mathematics Grade 4
2. Write a sample problem for each
of the three standards to illustrate the evolution of student understanding.
Grade 2: 2.NBT.2
Complete the table. 15
20
25
40
50
55
60
80
85
90
100
105
110
115
What is the rule for this table? ______________
Grade 3: 3.OA.5
George has a collection of blue and green marbles. He arranges them in an array below. Write a multiplication sentence for the green marbles and the blue marbles. Then show how many marbles he has in all by adding your products. ____x____=_____ ____+_____=____
____x____=_____ If George were to add 2 more rows of red marbles that follow this pattern, how many marbles would he have? _________________
Grade 4: 4.OA.5
Complete the input output table. In
3
4
7
10
12
Out
18
24
3. Provide a solution for each
problem that demonstrates each
step or explains the thinking process involved in determining the solution.
Grade 2: 2.NBT.2
Complete the table.
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
105
110
115
120
125
130
What is the rule for this table? ______
Skip count by 5 or add 5
________
Thinking- For this problem, the students will first need to find the skip counting pattern. They can do this by starting at 15 and counting until they get to 20. Many students will know that they count by 5 to get from 15 to 20. Once they realize the pattern, they will continue to skip count by 5’s. Grade 3: 3.OA.5
George has a collection of blue and green marbles. He arranges them in an array below. Write a multiplication sentence for the green marbles and the blue marbles. Then show how many marbles he has in all by adding your products. __
5
_x__
4
__=___
20
__ _
20
_+__
16
_=_
36
_
__
4
__x__
4
__=__
16
___ If George were to add 2 more rows of red marbles that follow this pattern, how many marbles would he have in all? ___4x2=8 36+8= 44
________
Thinking-For this problem, students will first need to know that an array is made up of equal rows and columns. Once this is established, students can use the skip counting pattern to help solve distributive property questions. As in the example above, students
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will need to see that the blue marbles are 5 rows of 4 or 5x4 and the green marbles are 4 rows of 4 or 4x4. Once this is determined, students can add the products to solve. Now, the last part of this is the main pattern focus. When it says “2 more rows of red marbles…” students need to know that it means 2 more rows of 4. They can either draw 2 more rows and count all the marbles or know that 2x4=8 and 36+8=44. Grade 4: 4.OA.5
Complete the input output table. In
3
4
7
10
12
Out
18
24
42
60
72
Thinking- For this problem students will need to first find the function of the input-output table. In order to do this, at least 2 outputs must be shown. If there was only one output, for example only in=3 and out=18, then a reasonable response for the formula would be either x6 or +15. But only x6 works for this problem because 4x6=24. Next, students will need to see that it doesn’t go in sequential order. The next input is 7. A common mistake will be that students think they can just count by 6 for the output. So, students will first need to find the function of x6, then use that function for each input to output number. 4. Discuss how the chosen standards and problems build student understanding of patterns or functions across the three K–6 grade levels selected in part A1.
I chose these standards because they build on the previous year’s prior knowledge of patterns from grades 2-4. This pattern knowledge helps complete the function table in grade 4.
First, the 2nd grade question shows the students understanding of numbers and skip counting as a pattern. Students learn that they can find the next number in a sequential
set by using a pattern or a formula. They may not know it as a formula at this age but will build on this knowledge. Next, in the 3rd grade question, students will continue building on their skip counting knowledge to solve a distributive property array question. Students will see that an array is a pattern. For example, when the students needed to add 2 more rows of red marbles, they would know that each row has 4 marbles. Finally,
once students learn these skip counting patterns, they can use them in functions. The 4th grade problem uses the same skip counting strategy as in 2nd and 3rd grade. Once
students learn the rule of the function on the formula, they can complete it by skip counting.
Part B.
Watch the video entitled “Discover Number Patterns with Skip Counting” and do the following:
1. Describe an instructional strategy the teacher used to accomplish the student learning goal of “reasoning and justifying arguments” or “sharing, talking out loud, and explaining their thinking.”
An instructional strategy that the teacher used in this video was “think, pause, share.” For this strategy, the teacher gives the whole class a question. In this video the teacher
was choral counting by 200’s starting at 5,000. They counted as a class up to 6,400 and the teacher stopped them to ask the whole class a question. “What do you think is going to be here?” She then gave them time to think. She said she likes to give about 10 seconds. Next, they share their ideas with a classmate. Finally, after everyone has had a chance to share, the students take turns sharing with the whole class. a. Explain how the teacher’s implementation of the described strategy was effective in achieving the goal, using examples from the video.
This strategy was effective in achieving the goal for many reasons. The question was clearly asked to the whole class allowing everyone to hear it and have time to think about their response. Then allowing the students to share their ideas gives everyone a voice. Each student was able to share their ideas, not just a few. I also believe that this
strategy allows for students to build confidence in their answers. For example, if she didn’t give time for students to share their ideas, some students they may be unsure of themselves would never volunteer to share their answers with the class. But allowing them to share with classmates helps validate their ideas. Also, when it’s time to share with the whole class, a student can rely on their partner to help explain if they get stuck. In the video, a little boy was asked to explain his thinking. He started explaining and then got lost for words or was unsure. He quietly asked his partner for help, and she jumped right in and helped. This is not only a great math strategy, but a good social/emotional strategy. 2. Explain how the teacher’s use of feedback encouraged student mathematical thinking, using specific examples from the video.
The teacher used different color markers as her feedback to encourage students' mathematical thinking. First, she used the green marker to show the jumps of 200. Many students said that the counting strategy is going up by 200, so she was showing their thinking to the whole class. She used red to show that each column is adding 1,000. I’m not sure if this was a student's idea or something that the teacher just wanted to show the students. Finally, she used red to underline the place value. A
student noticed that there were 5 5’s going down one column, 5 6’s going down the next…. This helps to validate student responses. Part C:
Prepare to create an original lesson plan on patterns or functions by doing the following:
1. Describe an evidence-based instructional strategy that will be incorporated into your original lesson plan. The evidence-based instructional strategy that I plan to incorporate into my lesson plan is called “Gallery Hop.” “Divide the class into groups of 4 or 5. Each group of students will receive a problem on
a large post-it paper. The post-it papers will be hanging around the room. Each group will work together to solve one of the problems or one post-it note. After every group has finished, they will take turns sharing their ‘gallery’ or post-it solutions with the class.”
-(Buffington, 2007, p.31)
For this lesson plan, it will be 4th grade function problems. Each group will first need to find the function rule and complete the function table. They will work together to solve then share with the class. a. Explain why the chosen instructional strategy would be beneficial in a lesson on patterns or functions, using evidence from a credible source to support your selection.
I chose to use this strategy for a few reasons. First, this strategy allows students to move around the classroom. Many students have a hard time staying seated for an extended period of time. If we can incorporate movement into our lessons, it will help them learn and stay on task. Next, this strategy allows students to work together and bounce ideas off each other. As we know, students learn best from their peers. Also, this lesson has diversity built right in. When grouping the students, I will make sure that each group has at least one student that is on grade level, below grade level, and above
grade level. The students that are below grade level can lean on their peers for assistance and ideas. The students who are above grade level will work on explaining their ideas. Many students can solve mathematical problems, or any problem, but struggle to explain their reasoning. This allows higher level thinkers the opportunity to explain their reasoning.
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Part E
:
Acknowledge sources, using in-text citations and references, for content that is quoted, paraphrased, or summarized.
Ohio Learning Standards Mathematics
. (2017). Ohio Department of Education. https://education.ohio.gov/getattachment/Topics/Learning-in-Ohio/Mathematics/
Ohio-s-Learning-Standards-in-Mathematics/MATH-Standards-2017.pdf.aspx?
lang=en-US
Buffington, B. B. (2007). Strategy Ring
. Knox County ESC.