respond to discussion 3TJ

brilliant answersMiss Professor

Respond to discussion 3

100 words per response

AUDREY

The CRA model of instruction uses concrete, representational, and abstract models to support students’ development of conceptual understanding. It allows teachers to take a big task and break it down, and then you can build on each station. It helps the teacher build upon prior knowledge. First, you’re working with your concrete station. This is where you will work with your manipulatives to tie them to real-world problems. Students can physically touch, which will help because students are hands-on.  Next, you will move to your representational station. Using what you’ve learned from the first station and making connections. They will be able to provide more evident reasoning for their answers because the familiarity of the physical station will come to mind. The last station is the end goa, abstract. Teachers end goal is to have students to work out math problems, knowing how they got their answers and providing details.

Working with manipulatives introduces familiarity. It provides a hand on experience that allows students to recollect the activity when providing answers for their representational and abstract stations. Students are comfortable with manipulatives, which provides for some nervousness and fear to be released because “it’s just a game.” When students aren’t provided with differentiated instruction, it can cause a loss of interest. I am in my fourth week of teaching Math, and this was my first time using manipulatives with my students. The connection to the problems was easier to convey because they had something in their hands to tie to their understanding. According to Dr. Jean Shaw, “Working with manipulatives deepens understanding of concepts and relationships, making skill practice meaningful, and lead to retention and application of information in new problem-solving situations (Shaw,2002).”  This allows the students to build upon their previous knowledge. Manipulatives are great for engagement. Teaching with manipulatives allows for teachers to reach students at any level. 

KENYATTA

How does the CRA model of instruction support students’ development of deep conceptual understanding? Be specific and cite evidence from this week’s reading or other sources in your response.

Utilizing the CRA approach has more advantages than disadvantages. The CRA technique will target each of those learning types, so students gain from using it whether students learn by seeing, performing, or understanding the knowledge. One of the primary and critically important steps in using the CRA approach in the classroom is choosing the appropriate physical objects to use to teach specific math concepts and skills. Single materials are highly helpful because they allow students to see and feel the qualities of the objects they are using.

Once the students have achieved the concrete level of achievement introduce appropriate drawing processes. Students will use plain drawings of the tangible items they have previously used to solve problems during these activities. By mimicking the movements they previously used with real items, simple drawings of such objects assist students in building their abstract comprehension of the concept or talent.

Three-dimensional models are used in the concrete phase of instruction so that students can use the metacognitive strategies to help students while they are mastering the new concept. Using manipulatives boosts a student’s utilization of sensory information when learning a new topic, which raises the likelihood that a student will recall the processes necessary to solve the problem.

Students are taught to depict the same ideas using two-dimensional drawings during the representational stage of learning.

Students can simplify conceptual mathematical operations into logical steps and clear definitions through manipulations in the concrete and representational stages. Students are able to create graphical representations of complex mathematical problems in order to help them solve them.

The representational stage necessitates planning because the teacher must choose how to depict the model’s concrete understanding in a picture, with the help of dots, or with sums that most closely correspond to the actual materials utilized. Despite the fact that the abstract stage may not call for as much originality, it nevertheless necessitates extensive planning because it links everything together. The teacher must therefore ensure that the students have a comprehensive understanding of how to solve the arithmetic issue individually following this stage’s presentation.

Titus 2:7-8 NIV

7 In everything set them an example by doing what is good. In your teaching show integrity, seriousness 8 and soundness of speech that cannot be condemned, so that those who oppose you may be ashamed because they have nothing bad to say about us.

CHRISTOPHER

The overarching purpose of the CRA instructional approach is to “ensure students develop a tangible understanding of the math concepts/skills they learn.” (Special Connections, 2005).  Concrete Representational Abstract (CRA) is a three step instructional approach that has been found to be highly effective in teaching math concepts. The first step is called the concrete stage. It is known as the “doing” stage and involves physically manipulating objects to solve a math problem. The first and most important step to apply the CRA approach in the classroom is to use a concrete object like beans or popsicle sticks. This helps the student learn by actually seeing and feeling the object. The second step in the CRA approach uses drawings and other images so students will be able to see what they are counting. An example would be tally marks or dots. The final step is the abstract phase in which students use actual numbers to solve a problem. CRA is a gradual systematic approach. Each stage builds on to the previous stage and therefore must be taught in sequence. This approach is most commonly used in elementary grades, but can be found in some middle and high school classrooms. Students are able to later use this foundation and add/link their conceptual understanding to abstract problems and learning. Having students go through these three steps provides students with a deeper understanding of mathematical concepts and ideas and provides an excellent foundational strategy for problem solving in other areas in the future. (Special Connections, 2005). 

Enhanced Multiple Choice

1. The dimension of the rectangular prism below are given in inches.

The total volume of the rectangular prism is 96 cubic inches. What is the value of x?

A. 4

B.

8

C. 10

D. 12

2. A set of books was shipped in a box shaped like the a rectangular prism with the dimensions shown below.

What is the volume of the box?

A. 25 cubic inches

B. 120 cubic inches

C. 24

0 cubic inches

D. 480 cubic inches

3. Mr. Mark is filling a box with 1-inch cubes. He filled the bottom layer as shown.

When the box is completely full, how many cubes will be in the box?

A. 18

B. 36

C. 72

D. 90

4. A toy box is 3 feet wide, 4 feet long, and 2 feet tall. What is the volume of the toy box?

A. 12 cubic feet

B. 18 cubic feet

C. 24 cubic feet

D. 30

cubic feet

5. Mary keeps a container of pencils of her desk. The container has a volume of 162 inches. Which container could be one of Mary’s desk?

A.

B.

C.

D.

6. Check all the ways to find the volume of the rectangular prism.

A. 3 x 4 x 9

B. 4 x12

C. 3 x 9 x 4

D. 4 x 27

E. 9 x 12

7. Look at the pencil case.

What is the volume of the pencil case?

A. 15 cm

B. 22 cm

C. 75 cm

D. 150 cm

8. The volume of the box shown below is 135 cubic inches.

What is the value of h?

A. 5

B. 6

C. 24
D. 30

9. A shoe box is 15 inches long, 9 inches wide, and 5 inches tall. What is the volume of the shoe box?

A. 24 cubic inches

B. 75 cubic inches

C. 135 cubic inches

D. 675 cubic inches

10. Dorothy has an fish tank with a length of 5 feet, a width of 3 feet, and a height of 3 feet.

What is the volume of Dorothy’s fish tank?

A.

11 cubic feet

B. 18 cubic feet

C. 45 cubic feet

D. 90 cubic feet

11. Adrianna is storing sweaters in boxes. She wants a box that has the same length and width as the one shown below, but she wants the box to have a greater height.

A. 150

B. 225

C. 300

D. 450

12. What is the volume of the rectangular prism?

A. 18 cubic centimeters

B. 27 cubic centimeters

C. 54 cubic centimeters

D. 90 cubic centimeters

Constructed response questions

13. Look at the rectangular prism below.

What is the volume of the rectangular prism in cubic centimeters? Show your work.

Write your answer on the line. _______________

14. A shoebox in the shape of a rectangular prism has a base with an area of 84 square inches. If the shoebox has a height of 5 inches, what is the volume of the shoebox, in cubic inches?

Show your work. Write your answer on the line. __________

___

15. Danielle has a container shaped like a rectangular prism. The container was 8 inches long, 3 inches wide, and 10 inches tall. What is the volume of the container?

Show your work. Write your answer on the line. _________

16. A moving company offers two sizes of moving trucks. Truck L can fit 25 boxes that measure 1 cubic yard. Truck M is three times as large.

What is the volume of Truck M in cubic yards?

Show your work and write your answer on the line. __________

17. Meghan gave Lynn a jewelry box for Christmas the length of 5 inches, 4 inches, and a height of 2 inches. What is the volume to the jewelry?

Show your work. Write the answer on the line. _______________

18. What is the volume the rectangular prism is 32 cubic centimeters?

Show your work. Write your answer on the line. __________

19. A left rectangular prism is 9 feet long, 4 feet wide, and 6 feet in length. What is the volume of the rectangular prism?

Show your work. Write your answer on the line. ___________

20. Harold needs to buy a new refrigerator, before he buys the refrigerator he needs to know the volume. What is the volume of the refrigerator?

Show your work and write your answer on the line. __________

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