ELED 4061 Spring Final Exam

Select all of the rational numbers.

-6 2.3 0 -7

A jet fighter travels 75 miles in 375 seconds. How fast is it traveling?

0.2 miles per second

A student drew this drawing to represent how much each person would get if 3 people shared 4 candy bars. How is the student most likely thinking about each share?

1 + 1/3

A police helicopter clocked an automobile for 60 seconds over a stretch of highway 1 mile long. At what rate was the automobile traveling?

1 mile per minute

Which statement about the group below illustrates a part-to-part ratio? (1 red star from 6 stars)

1 out of 6

Draw a picture to determine: How many times can you measure 2/3 out of 1?

1 ½

Prompt: What do you think Nick Bannister could or should have done differently in selecting and sequencing student responses (part 3), in making connections among responses, and with the mathematical ideas that were central to the lesson (part 4)? Why would you make these changes? What impact would you expect these changes to have on students' opportunities to learn? *(Please note that there are three parts to this prompt).

1. Many people have mentioned how putting the equation up first or the answer would have allowed for a better learning experience. However, I think the messy way in which group ideas were presented and the lack of connections and deeper discussions implemented might have caused this thinking that first pulling up the answer instead of working it out step-by-step as a class is the better teaching method. If Mr. Bannister had taken the time to allow for personal connections and create deeper discussions on the subject from students ideas, then putting the answer last would not have hindered his teaching. If he used a better form of directing the children's ideas and discussions then he would have allowed a deeper understanding and more pride and camaraderie as a class for being able to come up with the equation. 2. I would make these changes in order to develop the class atmosphere, by using this method then students would band together and acknowledge each other's strengths. It would also help the children remember this information during homework and test as hopefully something more than just a memorized equation. 3. By opening up more time for connections and discussions, the students will have an increase in learning opportunities, some math-based as well as social learning. It would also change the dynamic of the room from having the teacher be in charge of spouting information, and instead, the students would be the ones talking more and coming up with possible solutions as the teacher chimes in from time to time to help direct.

Prompt: Have you ever taught a class or been a student in a class where the teacher has used one or more of the five talk moves? What move was used and what were the results? What benefits do you see in incorporating some or all of these moves into your practice as an elementary mathematics teacher?

1. Repeating 2. Revoicing 3. Offering Wait Time 4. Asking Genuine Questions 5. Fostering Reasoning Skills

If the value of yellow is 1, what is the value of blue? Y-Hexagon an B- Diamond

1/3

Select all of the unit fractions.

1/3 1/4

Joe went on a bike ride. After 3 hours he was 33 kilometers from where we started. At what rate was he traveling?

11 kilometers per hour

Draw a picture to determine: How many 1/2s are there in 8?

16

Which is more 3/4 of a cherry pie or 7/10 of a cherry pie? How much more? (Use a method shown in the module to decide).

3/4 is more. 1/20 more.

A family of 6 shared 3 cheese pizzas and 4 veggie pizzas. How much of each kind did each person get if they shared fairly?

3/6 cheese and 4/6 veggie

What is the ratio of purple triangles to blue triangles in this group? (3 P to 7 B)

3:7

Where is the first place partitioning is mentioned in the Common Core State Standards for Mathematics?

3rd grade

The triangles are what part of the group of objects?

6/12

If a cake recipe calls for 2 1/2 cups of flour and you make 3 of these cakes, how many cups of flour will you need?

7 ½

Why is teaching one algorithm for a fraction operation (addition, subtraction, multiplication, and division) not in the best interest of students? (Choose all that apply).

Algorithms do not help students think conceptually about fractions Different algorithms often quickly become confused Students can't adapt to slight changes in the fractions

In the scenario you read, who was the new teacher given a positive introduction to the teaching profession?

Beth

How can these cakes be cut so that the cake in each pan will have pieces of the same size?

Cut them in to 20 pieces

How can these cakes be cut so that the cake in each pan will have pieces of the same size?

Cut them into 3 pieces

Students were asked to decide how 3 people might share 2 identical cakes. Which student drawings include fair shares? (Choose all that apply).

D A

Teachers should spend large amounts of time teaching children to draw more difficult partitions, such as thirds and fifths, correctly.

False

Consider the situation and choose a question that requires additive thinking. Situation: A pizza is cut into 8 slices. Three people each eat 2 slices and take the rest home.

How many slices did the people eat?

Prompt: Have you seen a PLC in action? If so, what were the benefits? If not, what benefits might it provide for teaching mathematics?

I have not seen a PLC in action. Some benefits might it provide for teaching mathematics is a way of gaining different viewpoints. For example, say a student in your class is not getting the material, but you have tried working with him/her every day. If you ask your college or a different professional, perhaps they might be able to give you a different technique to try as well as a fresh pair of eyes. Also if you meet and discuss what unit each classroom is on then perhaps you could align more or less depending if you want students to work together outside of their own class.

Why can drawing and shading fractions to compare fractions be problematic for students? (Choose all the apply).

Students base decisions on flawed drawings. It is sometimes difficult to divide into equal shares.

Hint: You may recognize this question from the Numbers Need Not Apply activity in the module. How does the following situation focus students' attention on relative thinking? Situation: Maria and Ann each have the same number of identical wooden (cube) blocks. Each girl is told to build a wall, using all of the blocks, so that there are no "holes" in the wall. Maria's wall is taller than Ann's. What can we say about Ann's wall?

Students can focus on the walls in relation to one another.

Suppose there are 3 children at Table A and 4 children at Table B. Is it fair if Table A receives 2 cookies to share and Table B receives 3 cookies to share? If not, who gets more?

The children at Table B get more.

Which animal eats the most in a day relative to its weight? A killer whale weighs 6096 kg and eats 227 kg. An elephant weights 4200 kg and eats 185 kg.

The elephant

What supports were given to Connie in the scenario you read? (choose 6)

The outcomes her students were to achieve and a background and how these outcomes had been determined A history of the school An explanation of the school's mission and vision statements A mentor Department meeting where they reviewed the scope and sequence for the entire year Knowledge of the resources available to her

Prompt: Find or create a partitioning task that could be given to students in K, 1st, 2nd, or 3rd grade. Your post should include: the task the objective of the task which grade the task is appropriate for and what materials would be needed

The task: You and your three friends want to buy two pizzas with two topping and the toppings can only be split 1/2 and 1/2 on the pizza. If the topping on the pizzas is Hawaiian (ham and pineapple), pepperoni, and mushrooms. How would you divide the pizza so that all four of you get equal amounts of each topping? Objective: To have them think through adding fractions, and discovering that there can be leftovers or an inability to be equal. Grade: 3rd Materials: Scratch paper that they can draw pizzas on, it could be circles or rectangles, as it was not specified in the prompt.

Equal shares do not have to have the same number of pieces.

True

True or False: Every rational number can be expressed as a fraction.

True

JS answered the question: which is larger 4/6 or 7/9. Is he correct?

Yes

In the Atlantean Dodgeball video, the coach of the Beluga team was at a disadvantage because he was looking at the number of team members using...

absolute thinking

What are the 3 big ideas of PLCs? (choose all that apply)

celebrations a culture of collaboration focus on results

American public schools were originally organized around __________________

the factory model

The compensatory principle states that...

the larger units of measure you use, the fewer of them it will take to quantify the same amount

What does author Rick DuFour suggest is the biggest obstacle to improving education?

tradition

If you wanted to students to work with 4 1/8 - 1/2, what would be the most appropriate task context that would encourage students to model using a length model?

wooden board being cut