What are the reasons that children have difficulty with fractions? Explain how teachers can help. 50 words

What are some manipulatives that can help students comprehend fractions and integers better than calculating with pencil and paper? 50 words

Provide a fourth-grade level explanation of the meaning of the top number and the bottom number in a fraction. What type of activity could be used to help explain this concept to children while teaching them how to write fractions meaningfully? 50 words

Do children have an understanding of negative numbers? If so, what is their understanding? If not, how might you help them develop an understanding of negative numbers? 50 words

lets say you give the students a problem like 3-4 to start with, maybe say, you have $3, but you need to pay your mom $4, what can you do? Give the students manipulatives and allow them to work and talk together and see what happens. Can you think of any other ways you could talk about it with students and give them a problem to work through on their own? 50 words

1)
How does knowing how to calculate probability help the safety professional in measuring safety performance? (No more than one paragraph.)
2)
Question has two parts. Suppose you a selecting a new vendor that inspects your facilities fire extinguishers, eye wash stations and stock first aid cabinets on a monthly basis. You could pay them an up-front, lump sum of $48,000 for three years worth of service, or pay monthly installments of $1473 for 36 months. In three years, at the end of the 36 month agreement, you will have paid $53,028. Part I (4 Points). If one were to ignore the fact that the $48,000 could be put in a high-interest investment, and simply consider inflation at 2.5% annually over the next three years, what is the future value of the $48,000 lump sum in three years? Part II (1 Point). In one or two sentences, state whether it makes sense to pay the new vendor a lump sum, cash payment of $48,000 up front, and why.

3)
Why is it important for safety professionals to know fundamental financial metrics when discussing safety performance? (No more than one paragraph.)

4)
Suppose a new ergonomic, safety intervention cost $405,000. Further suppose the intervention is certain to prevent all back injuries associated with the job. Over the last three years, the employer has averaged 14 injuries per year, with an average cost of $14,000 per injury. What would be the ROI for a three-year period for this intervention?

5)
Suppose a new initiative in safety cost $215,000. The investment saved the employer $278,000. What is the ROI for the new initiative?

6)
Suppose a chemical company has a pressure vessel (i.e., tank) for heating methyl ethyl doo doo. The pressure vessel is equipped with a sensor that sends a reading of the pressure to an operator employee in a control room. When the operator notices the pressure exceeding a safe level, the employee is to operate controls to transfer methyl ethyl doo doo from the vessel before an explosion occurs. The control room panel is also equipped with an alarm should the operator fail to notice the pressure is getting too high and fail to transfer methyl ethyl doo doo right away. As an additional backup to prevent an explosion, the pressure vessel is also equipped with a relief valve that should operate before pressure reaches a level that would cause the vessel to explode. In essence, assume there are three mechanisms in place to prevent explosion: 1) the sensor that sends a signal to the control panel; 2) the alarm on the control panel; and 3) the relief valve. All three must fail in order for an explosion to occur. Presume the failure rates of each are as follows: 1) sensor = 0.005; 2) the alarm = 0.003; and 3) the relief valve = 0.002. If one were to disregard probability of human error (i.e., the operator fails to notice the sensor because she/he is distracted), what is the probability of an explosion due to failure of the electronic and mechanical components of the pressure vessel system?

7)
Suppose a machine has two components that prevent injury; component A and component B. If either of the components fail, an employee will be injured. It is important to note that both A and B cannot fail at the same time. (In other words, they are mutually exclusive events.) If the failure rate for component A is 0.0005 and component B is 0.004, what is the probability an employee will be injured because of failure of these components?

Part I(short essay/discussion)
1. Please answer any one of the following three questions:
· Why is statistics an important course for business or social science majors to take? OR
· How has the use of statistics changed your life? OR
· How has Statistics affected you in the workplace?
2. What are some of the commonly used measures of variation in statistics?
Part II: Homework
See attached Microsoft word document

MODULE 2
A
How is sample size related to statistical tests and outcomes? Give a specific example. Why is it important to plan the sample size before collecting data?
B
Fill in the following for a possible study with one independent variable (IV) with two conditions/treatments and a dependent variable (DV) that is measured on a continuous scale (interval or ratio):
· Independent variable = ______________
· Condition A = ______________
· Condition B = ______________
· Dependent variable = _______________
· How do you know this DV is measured on a continuous scale?
· How would you word the null hypothesis for your sample study?
· How would you word the alternative hypothesis for your sample study?
· What alpha level would you set to test your hypothesis? Why?

MODULE 3
A
What is the primary purpose of inferential statistics? How might inferential statistics be applied to your intended research study? Explain.
B
Researchers often assume a normal distribution of data. Why is this significant in quantitative research? Explain.

MODULE 4
A
Mary is planning a study to see if learning of 6th graders on a math lesson is affected by background noise level. She wants to use a t-test for independent groups to analyze her results. Help her plan her study. What is her independent variable (IV) here? Describe two conditions she could create for the IV in her study. What is her dependent variable (DV) here? Describe a way to measure the DV so that each participant would have one score at the end. Would this DV measure be on a continuous scale of measurement? Why is this important? Explain and justify.
B
Consider Mary’s experiment regarding whether learning of 6th graders on a math lesson is affected by background noise level. Mary has collected her data. What is the null hypothesis for her study? What is the alternative hypothesis for her study? What are the assumptions that must be met about her data before she can correctly use an independent t-test to test the hypotheses? Why? How would she see if her data met these assumptions? How much room does she have to violate any of these assumptions and still get accurate results from the t-test? Explain and support your answers.

MODULE 5
A
In Module 4, we considered Mary’s interest in doing a study to see if learning of 6th graders on a math lesson is affected by background noise level. There, she was planning to use two noise conditions and then analyze her outcomes using a t-test for independent groups. Describe the study Mary might plan where she would use a one-way analysis of variance (ANOVA) for independent groups instead of a t-test to study differences between noise levels. What is her independent variable here? Describe the conditions she could create for this study. What is her dependent variable? Describe a way to measure the DV so that each participant would have one score at the end that would be on a continuous scale of measurement. Support your responses.
B
Consider Mary’s study of whether the learning of 6th graders on a math lesson is affected by background noise level. Describe the pros and cons of Mary using a repeated measures design for this study. What would you probably choose to do? Support your responses.

Ethics in Epidemiological Research
An Experimental Study in the Primary Prevention of Type 2 Diabetes
Imagine that researchers are conducting a randomized controlled trial of a high-fiber supplement as a preventive measure in persons at increased risk of type 2 diabetes. People enrolled in the study are disease-free at the time they agree to participate in the trial, but they all have a family history of type 2 diabetes and are considered at high-risk (80%) to develop the disease during their lifetime. The 10,000 participants who start the trial are healthy individuals who are randomly allocated to receive either high-fiber supplements or placebo for several years. As you can imagine, this study will be quite expensive and will require a large infrastructure of personnel and materials to carry it out successfully.
Because type 2 diabetes has reached epidemic proportions in the United States, the potential benefits of this research are important at a population level. Unfortunately, high-fiber supplements have also been shown in a few studies to be associated with gastrointestinal blockage (which can be life-threatening) and reduced nutrient absorption, which may lead to anemia, osteoporosis, and other debilitating chronic diseases. The supplements may also reduce absorption of certain medications and cause gastrointestinal distress. The potential side effects of continuous high-fiber supplementation are only partially understood, and long-term effects are unknown.
By Day 8
Post your initial response to at least two of the following questions:

What are the potential risks and benefits to be considered when designing this study?
When the side effects and long-term effects of a potential preventive measure are largely unknown, is it ethical to expose participants to these risks? Why or why not?
Is it ethical to deny the possible prevention benefits of high-fiber supplements to persons in the placebo group? Why or why not?
Do the potential benefits outweigh the potential risks to the participants and to society? Why or why not?