How can you create more culturally sustaining addition and subtraction problems for elementary students?

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Math Journal #6

  1. How can you create more culturally sustaining addition and subtraction problems for elementary students?
    1. Provide 3 examples. Include the problem and reasoning for its cultural sustainability.
  2. A carpenter has a board 200 inches long and 12 inches wide. They make 4 identical shelves and still have a piece of board 36 inches long left over. How long is each shelf?
    1. Solve the problem, and write down each step of your process. Why did you do each step?
  3. Albert ate 2 ¾ veggie dogs and Reba ate 1 ½ veggie dogs. What part of all of the hot dogs they consumed did Albert eat?
    1. Solve the problem, and write down each step of your process. Why did you do each step?
  4. Write a real-world math problem that fits naturally with the equation
    1. What method  of solving this would a student use?
  5. Write equations that correspond to the make-a-ten method for adding  depicted below. Your equations should make careful and appropriate use of parentheses.
    1. Which property of arithmetic do your equations illustrate?
  6. Zachary added 3.4 + 2.7 and got the answer 5.11.
    1. How might Zachary have gotten this incorrect answer? Explain to Zachary why this answer is not correct and why a correct method for adding 3.4+2.7 makes sense.
  7. The standard subtraction algorithm described in the text is not the only correct subtraction algorithm. The next subtraction algorithm is called adding the complement. For a 3-digit whole number, N, the complement of N is 999-N. For example, the complement of 486 is . Notice that regrouping is never needed to calculate the complement of a number. To use the adding-the-complement algorithm to subtract a 3-digit whole number, N, from another 3-digit whole number, start by adding the complement of N rather than subtracting N. For example, to solve , first add the complement of 486. . Then cross out the 1 in the thousands column, and add 1 to the resulting number: 1236 → 236 + 1 = 237. Therefore, according to the adding the complement algorithm, 723 – 486 = 237.
    1. Use the adding the complement algorithm to calculate 301-189 and 295-178. Verify that you get the correct answer.
    2. Explain why the adding the complement algorithm gives you the correct answer to any 3-digit subtraction problem. Focus on the relationship between the original problem and the addition problem in adding the complement. For example, how are the problems 723 – 486 and 723 + 513 related? Work with the complement relationship 513 = 999 – 486, and notice that 999 = 1000 – 1.
    3. What are some advantages and disadvantages of the adding the complement subtraction algorithm compared with the common subtraction algorithm described in Beckmann’s text?
    1. Show how to calculate the sum and show how to write the answer as a fraction and as a decimal.
    2. Show how to calculate the sum and show how to write the answer as a fraction and as a decimal.
    3. Discuss briefly what kinds of errors you think students who are just learning about fraction and decimal addition might make with the problems in parts a and b.
  9. Can the following problems about Sarah’s bead collection be solved by adding ¼ + ⅕? If so, explain why. If not, explain why not. Solve the problems if they can be solved. Write a different story problem about Sarah’s bead collection that can be solved by adding ¼ + ⅕.
    1. One-fourth of the beads in Sarah’s collection are pink. One-fifth of the beads in Sarah’s collection are long. What fraction of the beads in Sarah’s collection are either pink or long?
    2. One-fourth of the beads in Sarah’s collection are pink. One-fifth of the beads in Sarah’s collection that are not pink are long. What fraction of the beads in Sarah’s collection are either pink or long?

10.As we read about addition and subtraction, and you used mathematical reasoning to process through your thoughts, what things came up in your mind as you were solving problems? What was maybe difficult to comprehend at first, but became easier? How did you get to that point?  How did doing math with this level of attention feel in contrast to how you’ve done mathematics before?

Reflect on the importance of generating multiple strategies to guide thinkers to select appropriate strategies to find the best solution.

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Learning Objects (LOs) are varied topics (and file types) that can stand alone as learning units.

The Math-Music Competition

Creating the Scenario: Task 2

Module 2.

Using the Mathematics Mystery Contest scenario as a model, you will continue to design your own scenario-based game. You will incorporate best practices in problem solving and demonstrate your understanding of concepts from algebra in this module. You will create a component of the final game user guide to be submitted in Module 5.

  • Complete the Module 2 component of the game user guide in a Word document.
  • Use APA format for the guide components and their titles, references page, and in-text citations.
  • Submit the Module 2 component of the game user guide in this module. You will compile and submit your final guide in Module 5.

Step 1. Connect to Algebra
Continuing work on your game user guide, and using the component identified in the Module 1 assignment, Step 4, describe the task in detail which uses an algebraic concept. Clearly identify this connection to the branch of mathematics.

Step 2. Incorporate a Mathematical Practice
Reviewing the component, incorporate one aspect of mathematical practice which needs to be improved.

  • Identify the practice.
  • Create an aspect of Task 2 which models how to accomplish the practice.
  • Create a step in Task 2 which exercises the identified practice.

Step 3. Reflect
In two or three paragraphs, reflect on the importance of generating multiple strategies to guide thinkers to select appropriate strategies to find the best solution.

 

State if the following are exponential or linear. Then write the function equation.

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State if the following are exponential or linear. Then write the function equation.

1. (0,2), (1,6), (2,18), (3,54) 2. (0,2), (1,6), (2,10), (3,14) 3. (0,64), (1,32), (2,16), (3,8)

4. I start on week 0 with $50 and deposit $10 every week. x=weeks, y=$

5. I start on day 0 with 1024 cookies and eat 12 every day. x=days, y=cookies left

6. I start on day 0 with 64 almonds and eat half every day. x=days, y=almonds left

7. I start with $5000 on year 0 and earn 4% interest every year. x=years, y=$

Calculating:

y=100(1.05)^x Find y when x=50

Give 2 to 3 points that struct you from the video/Ian Stewarts’ Nature’s Numbers.

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Give 2 to 3 points that struct you from the video/Ian Stewarts’ Nature’s Numbers.
Expound on at least 1 or 2 points but you can do more if you like. But don’t forget that the audio recording does not exceed 2 minutes.

Demonstrate how accumulated interest will depend on the APR, compounding intervals and term of a loan.

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Mathematics Portfolio for Project 1: This semester you will create a mathematics portfolio to research selected topics on the concepts in this course. For each topic, you will need to submit one page. There are three topics, which means the portfolio should have three pages. You will select three topics below in which you will investigate and demonstrate how the mathematics connects to the real world. This will require you to show at least one mathematical operation and explain the connection in your own words. Please be detailed in your explanation for your use of formulas with clear steps for another student reading this project to follow.

Please follow these general guidelines while working on your individual project:

Introduction

  • Write a brief introduction, about a paragraph or so. Explain the nature of your project and why it is relevant. Use the sources from the literature/google review to help you write the introduction.

Data Collection

  • Collect the data (from freely available sources like google or any other publications).
  • State where your data is collected from (include the author’s name and title of the book or internet source you used).

Data Presentation

  • Present the data collected (created).
  • The answer to this depends on the data. Data can be displayed via lists, tables, graphs, scatter plots, pie charts, bar charts, histograms, etc. Depending on the type of your problem you may use even combination of a few methods.

Performing a Project

  • Perform all the needed calculations to complete your project.

Conclusion

  • Write the concluding remarks summarizing all sections. Explain what your goal was, what kind of data you collected, what did you perform, what did you observe (calculated). Write your own interpretation or applicability of your result.

Topics: Topics you must address are the following three areas: ratios, proportions and percentages, and understanding of personal finance.

Each topic is worth 10 points, and there are 30 total points possible. Please see the rubric below for grading on this assignment.

You may create your own examples or use examples from the textbook to investigate such as the following examples:

  1. Find and discuss a published study (you may use a health journal, newspaper, magazine, or a government source) to interpret a ratio to compare two or more related quantities. Ratio shows the relationship between one part and another part, and therefore it can be used to compare amount of a certain ingredient relative to another. You can write about health benefits of a certain food as compared to others (e.g. amount Vitamin C in different fruits) or representation of a certain group of individuals in various industries or organizations (inclusion of people from diverse backgrounds in mathematics/technology as compared to other industries). See chapter 4, pp. 158-159.
  2. Find a recipe in a recipe book or on the internet with at least 8 ingredients. The recipe must suggest number of people the recipe is for. You need to cook this dish for a company of 9 adults. Recalculate the recipe ingredients list for 9 adults. Choose the appropriate unit depending on the amount you have.

Then cook this dish for a company of 12 children. The serving size should be definitely smaller.

Calculate recipe ingredients assuming that it is 2/3 of the original amount per person.

  1. Find two world records in athletics achieved in the same discipline. Find absolute change and percentage difference between these records. Then discuss the method of averaging percentages. Explain (with examples) which method is correct and which one should not be used. See chapter 4 p. 179.
  2. Create a scenario for a college graduate who receives an annual salary. Determine net income as well as a monthly budget plan that will include reasonable expenses (e.g. rent, gas, utilities, insurance, student’s loans and food/entertainment). See chapter 9, pp. 462-463. You may use a spreadsheet such as Microsoft Excel to demonstrate your calculations.
  3. Demonstrate how accumulated interest will depend on the APR, compounding intervals and term of a loan. Use at least three different scenarios for the same loan amount to compare which scenario will lead to a lower accumulated interest on the loan.  See chapter 9, exercise 36 p. 521.
  4. Discuss compound interest frequency (e. g. monthly, quarterly, yearly, continuous). Find real-world examples in which each of the frequencies is being used.  Find and discuss the maximum amount of interest possible in one year.  See chapter 9 pp. 477-478.

Discuss what information about an endpoint and the paths leading to it can be gathered from the length of its binary strings and the number of 1s in them.

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Suppose you want to create a path between each number on Pascal’s Triangle. For this exercise, suppose the only moves allowed are to go down one row either to the left or to the right.
We will code the path by using bit strings. In particular, a 0 will be used for each move downward to the left, and a 1 for each move downward to the right. So, for example, consider the first five rows of Pascal’s Triangle below, and the path shown between the top number 1 (labelled START) and the left-most 3.
07_12_44.jpg
This path involves starting at the top 1 labelled START and first going down and to the left (code with a 0), then down to the left again (code with another 0), and finally down to the right (code with a 1). Hence, this path would be coded with binary string 001. This code is then recorded at the ending location on the triangle.
For Option #1, complete the following tasks based on the coding scheme described above:
Determine if there are additional paths between the START (number 1 at the top) and end point (leftmost 3). If so, describe them in words, by tracing the path on the triangle, and as binary strings. Then record all such binary strings at the ending location.
Find and record at least 5 paths using binary strings between the START location and numbers in rows 4 and 5. Compare the binary strings for each number and discuss why those similarities and differences might exist. Also, explain any connections you notice between the number of possible paths ending at each location and the corresponding entry of Pascal’s Triangle.
Discuss what information about an endpoint and the paths leading to it can be gathered from the length of its binary strings and the number of 1s in them.
Explain the addition rule of Pascal’s Triangle in your own words in terms of the path coding scheme you worked with in this assignment.
Note the type of symmetry that Pascal’s Triangle has and explain it in terms of the paths.
Additional Requirements:
Paper must be written in third person.
Your paper should be 3-4 pages in length (not counting the title page and references page) and cite and integrate at least one credible outside source. The CSU Global Library (Links to an external site.) is a great place to find resources. Your textbook is a credible resource.
Include a title page, introduction, body, conclusion, and a reference page.
The introduction should describe or summarize the topic or problem. It might discuss the importance of the topic or how it affects you or society as a whole, or it might discuss or describe the unique terminology associated with the topic.
The body of your paper should answer the questions posed in the problem. Explain how you approached and answered the question or solved the problem, and, for each question, show all steps involved. Be sure this is in paragraph format, not numbered answers like a homework assignment.
The conclusion should summarize your thoughts about what you have determined from the data and your analysis, often with a broader personal or societal perspective in mind. Nothing new should be introduced in the conclusion that was not previously discussed in the body paragraphs.
Include any tables of data or calculations, calculated values, and/or graphs associated with this problem in the body of your assignment.
Document formatting, citations, and style should conform to the CSU Global Library’s CSU Global Writing Center (Links to an external site.). A short summary containing much that you need to know about paper formatting, citations, and references is contained in the APA7 Papers & Essay section (Links to an external site.). In addition, information in the CSU Global Library (Links to an external site.) under the Writing Center/APA Resources tab has many helpful areas (Writing Center, Writing Tips, Template Examples/Papers Essays, and others).

A pipet delivers 9.98 g of water at 20 °C. What volume does the pipet delivers?

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Description

1. Carry out the following operations, and express the answer with the appropriate number of significant figures and units:
a. (5,23 mm)(6.1 mm) =
b. 72.3 g/1.5 mL =
c. 12.12 g + 0.0132 g =
d. 31.03 g + 12 mg =
2. Drug medications are often prescribed on the basis of body weight. The adult dosage of Elixophyllin, a drug used to treat asthma, is 6 mg/kg of body mass. Calculate the dose in milligrams foe a 150-lb person?
3. A pipet delivers 9.98 g of water at 20 °C. What volume does the pipet delivers?
4. A141-mg sample was placed on a watch glass that weighed 9.203 g. What is weight of the watch glass and sample in grams>

Determine the mean and the standard deviation for your grouped data.

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Task 2 – Applications of Statistical Techniques

  1. The length in millimetres of a batch of 36 electrical components are as shown below:

2.10 2.29 2.32 2.21 2.14 2.22

2.26 2.15 2.21 2.17 2.28 2.15

2.15 2.25 2.23 2.11 2.27 2.35

2.24 2.05 2.29 2.18 2.24 2.16

2.15 2.22 2.14 2.27 2.19 2.21

2.23 2.05 2.13 2.26 2.16 2.12

  1. Form a frequency distribution table of the lengths having four classes.
  2. Form a cumulative frequency distribution table.
  • Determine the mean and the standard deviation for your grouped data.

 

Describe the characteristics of a discrete random variable and its probability distribution.

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  • CONTENT: Your understanding of important concepts and mathematical techniques taught in the required courses in the major.
  • ANALYSIS: Your ability to see the connectivity (internal links) among the different areas of mathematics.
  • RESEARCH: Your aptitude for extending your mathematical repertoire beyond what you have been taught – to deal with unfamiliar topics, but related to areas you have studied.
  • COMMUNICATION: Your skill in communicating mathematics – to present your analysis in a clear and coherent manner reflecting the mathematical style and sophistication appropriate to your mathematical level.

Directions:

  1. Answer five out of six questions.
  2. Use at least three pages for each question; use only one side of the paper, double spaced. Word must be used, as well as MathType for math symbols.  Use Times New Roman font size 12.  Also, type (or copy and paste) in the question using bold font for each problem (the questions may remain single spaced).  The parts of each question may be typed in (or copied and pasted), again using bold font, at the appropriate part in the paper.
  3. Work independently. If you have any question, you may meet with any department faculty.  Otherwise, you may not collaborate, give or receive any assistance of any form from anyone else.  Failure to comply will result in a failing grade for this course, in addition to the other consequences for violating the Academic Integrity Policy.
  4. Cite all the sources you use for the report. You may use the examples in the sources as a guide for any examples you give.  Except for examples of proofs from Question 3, do not use the same examples in the sources.  You must cite any examples you use or modify.
  5. You will present one question to the faculty. As indicated in the syllabus, you may not present question #2.  While your work should be the basis of your presentation, the presentation should not be a duplicate of your work.
  6. When draft before presentation is approved, provide copies of each question to each faculty member. The copies should be provided at least one week before presentation.  Also, reserve a room with the Registrar’s Office for the arranged time.  Be sure you get a room equipped with the appropriate technology.
  7. After presentation, make any final corrections suggested by faculty, and provide one more copy to the department. Also, this final copy is to be burned onto a CD or flash drive and submitted to the department.  PowerPoint, or other presentation software, must be used for the presentation, this should be copied onto a flash drive and submitted to the department.

1)   Differentiation and integration are considered inverse operations, but they were invented separately and have different geometric interpretations.

  1. Give the formal definition of derivative. Using a specific example, compute the derivative using the definition.  Show how the derivative can be interpreted algebraically and graphically.
  2. Give the formal definition of integral. Using a specific example, compute the definite integral using the definition, or approximate the integral using a Riemann sum.  Show how the integral can be interpreted algebraically and graphically.
  3. Discuss at least two applications using derivatives. Use an example for each application.
  4. Discuss at least two applications using integrals. Use an example for each application.
  • In probability theory, there are two kinds of random variables, discrete and continuous.
  1. Explain the difference between discrete and continuous random variables. Give examples of each.
  1. b) Answer the following questions on discrete random variables:
  1. Describe the characteristics of a discrete random variable and its probability distribution.
  2. How do you find the probability of an event involving a discrete random variable? Use an example to help illustrate.
  • What purpose do the mean, median, and standard deviation serve in describing the characteristics of the distribution of a discrete random variable? How do you find the mean, median, and standard deviation?  Use the example in part ii) to help illustrate.
  1. The binomial distribution is the most famous of the discrete distributions. Describe the properties of this distribution and how you find the mean, and standard deviation. How do you find the probability of an event?  Provide an example.
  2. c) The study of the distribution of continuous random variables is the part of probability theory most closely related to calculus.  Associated with each continuous random variable is a function called a probability density function. Answer the following questions on continuous random variables:
  3. Define a probability density function. Give an example.
  4. How is the probability density function used to find the probability of an event? Use example from part i) to illustrate.
  • Give formulas for finding the mean, median, and standard deviation for the distribution of a continuous random variable. Use example from part i) to illustrate.
  1. Many important random continuous phenomena are modeled by a normal distribution. What is the probability density function for the normal distribution?
  • The art of mathematics is creating proofs. Just as a painter has some basic modes of painting, such as oils and watercolors; so the mathematician has some basic modes of proof.
  • Proving by direct conditional proof.  We assume P with the explicit intention of deducing Q.
  • Proving by contrapositive.  We assume  with the explicit intention of deducing , i.e.,  using the equivalence .
  • Biconditional proof. Proving sentences of the type  using the equivalence
  • Proof by cases. Proving sentences of the type  using the equivalence
  • Proof by contradiction. A proof by contradiction of a sentence P is a proof that     assumes  and yields a sentence of the type , i.e., using the equivalence
  1. a) Show that the pairs of logical statements in the last four bullets are logically equivalent.
  2. Give two examples of each type of proof. You may select proofs from Calculus, Linear Algebra, Abstract Algebra, Geometry, Number Theory, Introduction to Real Analysis, and Foundations of Mathematics.There should be a variety of examples, i.e., the proofs should not be similar in form, and should include a variety of different topics.  (Note:  For these examples, you need not modify the proof, but be sure to cite the source.)
  3. Direct conditional proof.
  4. Conditional proof using contrapositive.
  • Biconditional proof.
  1. Proof by cases.
  2. Proof by contradiction.
  • The concept of infinity has been studied in Calculus, Modern Geometry, and Foundations of Mathematics. Discuss the uses of infinity in these courses as indicated below.
  1. In Calculus, infinity has been used in some limits, improper integrals, sequences, and series. Give examples of the different ways that infinity is used.
  2. In Geometry, points of infinity or ideal points were discussed in hyperbolic geometry.
  3. In Foundations of Mathematics, infinity played a major role in sets and cardinality. Give examples of sets of each infinite cardinality.
  • A function is one of the key concepts in many areas of mathematics.
  1. Define a function, a 1-1 function, an onto function, an inverse of a function. Provide examples for each as you define them.
  2. Functions were also studied in various mathematics courses. In these courses, the functions had additional properties.  Discuss these functions, including their additional properties, and provide examples.  Note:  Some of these functions may have different names in different courses.
  3. Linear Algebra.
  4. Abstract Algebra.
  • Modern Geometry.
  • Algebraic systems relate sets of elements with binary operations.
  1. Describe the algebraic systems setting up a hierarchy beginning with groups, then abelian groups, rings, integral domains, and fields. Explain how each additional more restrictive system is an extension of a previous system with additional properties.  Give examples for each of these five algebraic systems.  Be sure to include examples of groups that are not abelian.  Also, provide examples of rings that are not integral domains, and examples of integral domains that are not fields.
  2. Consider the set with operations matrix addition and multiplication. Discuss the properties of an algebraic system that  Is a group and/or an abelian group?  Is  a ring and/or an integral domain?  Show, by examples, which properties of a field this algebraic system does not have.
  3. Define a vector space. Is a vector space a group and/or an abelian group with respect to vector addition?  Is a vector space a ring, integral domain, and/or field with respect to addition and scalar multiplication?  Pay particular attention to the definitions of the arithmetic operations for each of the algebraic systems.

 

 

 

 

Make a quick plot for yourself to “eyeball” whether the data exhibit a relatively linear trend.

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Choose a particular type of food. (Examples: Fish sandwich at fast-food chains, cheese pizza, breakfast cereal) For at least 8 brands, look up the fat content and the associated calorie total per serving. Make a quick plot for yourself to “eyeball” whether the data exhibit a relatively linear trend. (If so, proceed. If not, try a different type of food.) After you find the line of best fit, use your line to make a prediction corresponding to a fat amount not occurring in your data set.) Alternative: Look up carbohydrate content and associated calorie total per serving.