Math study guide

The mean and median are not always data points.

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Using measuring instruments, and the activity should involve making measuring instruments to see how the tool is performing the same function as the individual units.

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When students have the knowledge of how to find the area of a parallelogram, which can always be transformed into a rectangle with the same base and height, they can use two identical copies of a triangle.

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All other graphs are used for numerical data

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One of the best approaches to teaching an analog clock is to start with a one handed clock. Then students can focus on the movement of the little hand as they watch the movement during the hour and even predict when it is half past the hour. With just one hand.

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When students use skills in classification, they are grouping by a common attribute and sorting the shapes into categories.

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Example

1 yard = 36 inches

Three reasons for using non standard units instead of standard units in instructional activities.

1. Non standard units focus directly on the attribute being measured. 2. The use of non standard units avoids convicting objectives in instructional activities. 3. Non standard units provide a good rationale for using standard units.

Rates

A dollar fifty per can of corn

Describe the idea of a ratio in your own words. Explain how your idea fits with each of the following statements.

A fraction as a ratio. Ratios can compare things that are not at all alike. Rates such as prices or speeds are ratios.

In statistics this data is gathered using scatter plots.

A line of best fit might then be drawn to show the relationship between the two variables

The empty number line is ideal for linking the computation required for elapsed time problems to the task of adding or comparing times.

A number line is also suggested by the common core state standards for student use on this type of problem.

Which sport is safest to play is not a statistical question because it's not clear what data might be gathered to answer the question.

Adapting the question to something like how many injuries do athletes in various sports get can be explored using the process of doing statistics.

One of the best approaches for teaching elapsed time is which?

An empty number line

When using cubes, one can make a layer of cubes on the bottom, and then calculate how many layers one would need to fill the prism.

Another approach would be to fill the entire box with neat layered cubes.

Tangrams

Area models that demonstrate how figures can have the same area composed of different shapes

2 ways to interpret ratios.

As composed units or as rates

What kinds of graphs can be used for data that can be put into categories.

Bar graphs, picture graphs, and pie charts

Ratios show the relationship between two quantities of something.

Because you can have four parts out of a whole

The natural progression for teaching students to understand and read analog clocks includes

Begin with a one handed clock that can be read with reasonable accuracy.

What is the cognitive skill that helps students recognize and group shapes according to their attributes and properties.

Classification.

When students build larger shapes from smaller shapes it is called

Composing shapes

When students explore how shapes fit together to form larger shapes it is called

Composing shapes

When they break apart a large shape into smaller parts it is called

Decomposing shapes

Which of the following transformations is a non rigid transformation

Dilation

Teaching key words that can support students in effectively setting up proportions correctly

Does not teach proportions

Line plots are graphs in which a line connects data points on a coordinate axis.

False

Consider this problem.

If 50 gallons of fuel oil cost 56.95, how much can be purchased for 100 dollars?

The broken ruler will cause some students to say that it is impossible to measure when beginning and end units are cut off, because there is no starting point.

If students fully understand the ruler they will know they only need the units and can count the matching units from any point on a ruler.

Standard unit of measurement

Inches. Centimeter, Ruler

Key words are not effective in helping students understand a story situation. A careful reading is needed in order to recognize when a situation is multiplicative.

It is important to discuss what in the story tells students that it is a multiplicative comparison and therefore a proportional situation.

How can one obtain an accurate measure of the volume of a rectangular prism when given a set of the same sized cubes?

Layer the cubes on the bottom of the box to find the dimensions and then see how many layers are needed.

Costumary unit of measurement

Length of football field by yards not inches. Length of a table by inches not feet

An evening out for leveling of data

Mean

A good task to use to assess their understanding of the use of a standard ruler is

Measuring with a broken ruler

A value in the data set that is the center of the data

Not the mean

Ratios are a subset of fractions

Not true

Ratios are only part part comparisons and fractions are part whole comparisons.

Not true

Ratios can be interpreted as additive or multiplicative situations.

Not true.

Rates can be prices or ounces..

Or almost anything

Non standard unit of measurement

Paperclips

Students should explore the area of a triangle after they have a conceptual understanding of the area of a

Parallelogram

Various types of graphs can provide different snapshots of the data

Pie charts focus more on the relative value of this data , whereas bar graphs add a dimension of quantity.

Ratios can be written as fractions , but they are not the same as fractions

Ratios describe the relationship between two different units.

When a shape can be folded on a line so that the two halves match that fold line is also known as a line of

Reflection

Four content goals in geometry

Shapes and properties, transformation, location, and visualization.

Covariation examples in geometry

Similar figures in which corresponding sides vary by a scale factor.

Composed units

Six cans of corn for four dollars

One of the basic ideas of length measurement is that when the unit is longer, the measure is

Smaller

Use models of measuring units and the activity should use physical models of measuring units to make the desired comparison of the attribute with the unit.

Step 3

A general instructional plan for measurement has three steps.

Step one

Make comparisons, and the activity should require students to make direct comparisons of an object based on the attribute of interest ( such as shorter or longer)

Step two

Tangrams have seven different pieces, all of which can be represented with a smaller triangular unit. By creating figures with all of the seven different pieces, the figures will each have the same area regardless of the use of different shapes.

Tangrams

Emphasizing within and between relationships among the units that covary

Teaches proportion

Encouraging students to use reasoning strategies to compare ratios that occur in stories and visuals.

Teaches proportions

Providing opportunities for students to compare additive, constant, and multiplicative situations.

Teaches proportions

Teach experiments and theoretical probability together, focusing on the number of trials needed

Teaching experiments and theoretical probability together is important in order for students to understand the value of both and to realize there is sometimes no way to determine an expected value other than gathering empirical data.

Balance point of the data

The mean

One measure that describes the center of data

The mean

What does the shape of data mean

The shape gives a sense of how data is spread out or grouped; the characteristics about the data set as a whole can then be described.

Probability can be introduced in the first grade and should be integrated into fraction instruction in grades three through five

Thinking about how likely an event is makes for interesting discussion about fractions and percents.

When a shape has line of symmetry also known as mirror symmetry it can be folded on a line in which the halves match.

This is a line of reflection in which the portion of the shape on one side of the line is reflected onto the other side

Line plots, like dot plots, are a form of bar graphs in which individual data is plotted above a number line using X's

This is different from a line graph which is what is described in the statement.

Box plots are used to display both measures of center and the spread of data

True

Histogram are different from bar graphs because they display continuous data

True

Picture graphs can be created so that the picture represents one piece of data or a group of data

True

Ratios can be interpreted as composed units or as rates.

True

What does bivariate data mean?

Two things vary together. Ex. Height and weight

Example of covariation

When the number of mangoes goes up, the price goes up. This can be written as p = k times m. In which p is the total price, m is the number of mangoes, and k is the rate or price of the mango.

Covariation

When two things vary together.

Which of the following questions is not statistical in nature.

Which sport is safest to play

60 miles per hour

You are relating two different variables