Math Methods Test 2

Describe the probability continuum, including examples that help elementary and middle school students understand what it means for an event to be on the continuum from impossible to certain.

0 to 1

A general instructional plan for measurement has three steps. Explain how the type of activity used at each step accomplishes the instructional goal

1) Make comparisons (longer/shorter, heavier/lighter) When it is clear that the attribute is understood there is need to continue. 2) Use physical models of measuring units (use physical models of measuring units to fill, cover...) 3) Use measuring instruments (make direct comparisons between the student-made tools and standard tools.

Types of ratios

1) Part to part-can relate one part of a whole to another part of a whole. (ex 6/8 as a ratio six to eight rather than a fraction) 2) Part whole- similarly, relate one part to the whole (ex 6/14 is six out of fourteen rather than the fraction six-fourteenths) 3) Ratios as Quotients because they can be seen as a division problem, the numerator divided into the denominator in a part whole ratio 4) Ratios as rates- in situations where there is a comparison between to measurements of different units. one compares the rate by which they grow in relation to one another.

Analyze strategies for teaching students about shapes and properties

1. show variety of shapes and have students compare both examples and nonexamples with a focus on critical characteristics. 2. facilitate student discussions about the properties of shapese, having them develop essential language along the way. 3. encourage the examination of an array of shape classes that goes beyond the tradtitional, allowing students to explore relationships and recognie different categories, orientations, and sizes. 4. provide students with a range of geometric experiences at every level having them use physical materials, drawings, and computer models page 494

Summarize the four major geometry goals for students

1.Shapes and properties- includes a study of the properties of shapes in two and three dimensions, as well as the relationships built on properties 2. Transformations-includes a study of translations, reflections, rotations, dilations, the study of symmetry and the concept of similarity 3. Location- includes a study of coordinate geometry or other ways of specifying how objects are located in the plane or in space. 4. Visualization-includes the recognition of shapes in the environment, developing relationships between two and three dimensional objects nd the ability to draw and recognize objects from different viewpoints

What are prime numbers?

A prime number is a whole number greater than 1, whose only two whole-number factors are 1 and itself. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29.

What are composite numbers?

A whole number that can be divided evenly by numbers other than 1 or itself. Example: 9 can be divided evenly by 3 (as well as 1 and 9), so 9 is a composite number.

Describe the best model for teaching elapsed time.

Have students sketch empty time lines (similar to the empty number line, discussed for computation)

Illustrate and explain the meaning of measures of center and measures of variability.

Measures of Center- mean, median, mode Measures of variability-Range, Mean Absolute deviation

Three reasons were offered for using nonstandard units instead of standard units in instructional activities. Which of these seem most important to you and why?

Nonstandard units provide a good rationale for using standard units. I believe this would be beneficial in all grades.

What strategies can you use to help students understand and appropriately use the order of operations?

Please excuse my dear aunt sally, Pedmas

What are the first ideas about probability that students should develop? How can you help students with these ideas?

Possible and not possible

Describe the essential features of a ratio, including how it relates to fractions, and articulate ways to help students understand and be able to use ratios.

Ratio- a number that relates two quantities or measures within a given situation in a multiplicative relationship

How would you explain the difference between a rational and irrational number to a middle school student.

Rational numbers are numbers that can be expressed as a ratio of two integers. They can be in fraction, decimal or whole number form. Irrational numbers are numbers that cannot be expressed as a ratio of two integers.

Give an example of a problem you might pose to students that would help them explore and compare the median and the mean.

Teachers start in Memphis making 38,000 Superintendents salary $270,000 yada yada

Explain the development of area formulas. (use geoboards)

The students first learn the area to be the number of squares on a geoboard or graph paper. If there is a chart, the length and width can be placed in the first two columns and the area in the last column. The students can be scaffolded until they realize that length times width is equal to area.

Explain how volume is measured in standard and nonstandard units.

The volume of a pyramid or cone is one third the volume of a prism or cylinder with the same base and same height. When filling up the prism using the pyramid as a "measuring cup" this would be an example of nonstandard units. The standard form would be using liters or gallons...

What does the "shape of data" mean

a sense of how data are spread out or grouped, what characteristics about the data set as a whole can be described and what the data tell us in a global way about the population from which they are taken.

Activities 22.3, 22.4, 22.5 are designed to help studnets see that some outcomes are more likely than others. What are the similarities and differences between these two activities? Why might this difference be useful in helping students gain insights about how likely an event is?

all three activities have students making predictions about the outcomes page 561. With each activities, more possibilities are given to the students. The top two activities include dice, the third has a spinner. The 1st uses 1 die with 3 (some repeated) numbers they are to see which number is rolled the most, the 2nd uses 2 die (or dice rolls) to come up with a sum,, they are to see which some comes up the most., the 3rd uses a spinner seperated into unequal parts of 3 colors. They are to find out which color it will land on the most.

Describe geometric transformations.

changes in position or size of a shape.

Compare quantity and number line visuals for teaching integers, and contrast the different contexts for teaching about positive and negative numbers

counters and number lines-intergers involve two concepts-magnitude and direction. Magnitude is modeled by the number of counters or the length of the arrows. Direction is represented as different colors or directions. height=numberline

What is covariation? Give an algebraic and geometric example of covariation.

covariation means that two different quantities (a ratio) vary together? example in book says- 5 mangos cost $2 ... as the numbers of mangos varies so does the price. and as the cost changes so does the number of mangoes you will get. (thats an algebraic) I think a geometry one would be if side a and side b get bigger in a triangle then side c would grow too?

Explain the law of large numbers. Describe an activity that might help students appreciate this idea.

if you repeat a random experiment, such as tossing a coin or rolling a die, many, many, many times, your outcomes should on average be equal to the theoretical average.

Use a context to explain each of the following (-10) + (+13) = +3 (-4.5) - (-9.2) = +4.7 4 x -3=-12 -82.5/5 = -16.5

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Describe the idea of a ratio in your own words. Explain how your idea fits with each of the following statements: a. A fraction is a ratio b. Ratios can compare things that are not at all alike c. ratios can compare two parts to the same whole d. rates such as prices or speeds are ratios

ratio= the ratio of girls to boys is 2/5 that means there is 7 total. the fraction of girls is 2/7, the fraction of boys is 5/7 unless one gets murdered by a girl. This is also like letter C. letter D 2 Kiwis for $2 this means if you has 4 kiwis you would spend $4. Rates would be like miles/gallon

Compare questions to determine which ones are statistical questions.

statistical questions-used to summarize mathematics..analysis of mathematics...it focuses on variability of data in statistical reasoning.

Contrast theoretical probability and experiments, including how to integrate both into instruction to better develop a strong understanding of probability

theoretical probability-is the number of ways that the event can occur, divided by the total number of outcomes. experimental probability-is the ratio of the number of times an event occurs to the total number of trials or times the activity is performed.

What does "bivariate data" mean?

two things are varying together(number of people attending and the number of hotdogs sold)