Last updated: 6/10/2015

## Math-8 Core Quarter 4

Bivariate statistics

Pythagorean Theorem applications

Solids-basic review (prisms, pyramids)

Volume of Prisms and Pyramids

Cones, cylinders, spheres, hemi-sphere (Nets-Volume)

Volume of composite figures

Surface area of cones and cylinder

Real number sets and subsets

Classifying numbers

Approximating and ordering irrational expressions

Solving equations using square and cubed roots

Quarter 4

Statistics

Bivariate Quantitative Data

Bivariate Statistics-based on two variables

Building scatter plots from bivariate data

Lines of best fit/trend lines

Drawing lines of best fit through data

Positive, negative, or no  association

Clustered data

Non-linear patterns of data

Outliers

Writing Equations of lines of best fit

Predicting using line of best fit

Interpolation and extrapolation

Qualitative Data

Categorical data

Building two-way tables

Interpreting two way-tables

Joint frequencies

Marginal frequencies

Relative joint frequenies

Ralative joint frequencies

Applied Geometry

Pythagorean Theorem Applications

Two-dimensional applications

Three-dimensional applications

Solids

Solids-Basic Review (Prisms, Pyramids)

Volume of Prisms and Pyramids

Volume of cylinder, sphere, hemisphere, cones

Composite figure volume

Cones, cylinders, spheres (Nets)

Surface Area of cones and cylinder

Changes in dimension-similar figures

Number System

Real number sets and subsets

Classifying numbers

Approximating and ordering irrational expressions

Solving square root equations

Solving cubic root equations

Cumulative Vocabulary Project

Statistics

Quantitative Data

How does bivariate data differ from univariate data?

How can we display data with two different variables?

Should we connect the data points in a scatter plot?

How does having accurate and appropriate scales help us understand the bivariate data?

What types of words can we use to describe how data is plotted on a scatter plot?

What does a clustering of data points indicate?

Can we determine from the scatter plot if we have a positive, negative or no association?

What is an outlier?

How does an outlier affect the data?

How would the points look if there was a strong association? Weaker association?

How can we describe a pattern of data?

How can we draw a trend line to best represent the data?

Will the trend always be linear?

Can we use the trend line to make predictions?

How can we make predictions for data that is well outside the scope of the scatter plot?

Which two points should we use to develop our line of best fit?

Will everyones equations of the line of best always be the same?

Qualitative Data

How can we use a table to demonstrate associations between categorical data?

Does it matter which variables are rows or column?

What does each cell represent?

How can we determine marginal frequencies?

Can we determine percents of joint frequencies out of total?

Can we determine percents of marginal frequencies out of total?

What would you need to do to find percents of single categories?

What does relative mean?

What are relative joint and marginal frequencies?

Applied Geometry

How can we use our knowledge of Pythagorean Theorem to prove given lengths are those of a right triangle?

How can we apply Pythagorean Theorem to find measures of real life situations in two dimensions?

How can we use Pythagorean Theorem for direct measurement in our three dimensional world?

Solids

What is a solid?

How do solids differ from other figures you have learned?

How can we classify solids?

How do we name solids?

How can we determine the amount of space within a solid?

What unit of measure would we use?

Why can't we measure using squares like we did with area?

What is the general concept of volume?

Can we create a general formula for volume of solids?

Are their solids the general formula does not apply to?

How do pyramids and cones volumes compare to prisms and cylinders of same bases?

How can we determine the formula of a sphere? Hemi-sphere?

How can we determine the volume of composite figures?

Is it important to state the units you measured volume in?

What does stating cubic units show you understand?

How does surface area differ from volume?

Can you draw the nets of a cone and a cylinder?

Can you devleop a formula to cover the total surface area of the solid?

What units do we use to measure surface area?

If two figures are similar, how does the scale factor afffect the dimensions of the figure?

What is the relationship between two figures dimensions, area and volume, in reference to its scale factor?

Can we just use the scale factor, to determine a similar figures area and volume?

If given area or volume of similar figures, can we determine a missing dimesion?

Number System

How can we determine the sets of real numbers a numerical value belongs to?

Can we classify a number as rational and irrational?

How can we approximate the value of irrational numbers written as square roots?

How can we determine which two consecutive integers an irrational number lies between?

How will you determine if it is shy or past the halfway mark between two integers?

Can we place all real number sets on a number line?

Are their any sets that cannot be displayed on a real number line?

How many numbers lie between integers on a number line?

When solving equations with square and cubed roots, how can you determine if your results will be rational or irrational?

 (1) 8.G.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. (1) 8.G.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. (1) 8.G.9 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. (1) 8.NS.1 Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. (1) 8.NS.2 Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π2). For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations. (1) 8.SP.1 Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. (1) 8.SP.2 Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. (1) 8.SP.3 Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height. (1) 8.SP.4 Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?

Statistics

Quantitative Data

Construct scatter plots from given data points

List data from scatter plot

Determine if data displayed has a positive, negative or no association

Determine if data is clustered or not

Determine if there is an outlier

Draw a trend line through data - appears linear

Draw a trend line though curved data

Determine the slope of trend line

Determine the y-intercept of the trend line using y = mx + b

Write the equation of the line of best fit (trend line)

Use the line of best fit to make predictions(interpolate, extrapolate)

Qualitative Data

Recognize the difference between quantitative and qualitative variables

Interpret categorical data in two way tables

Establish difference between rows and columns

Determine joint frequencies of categorical data

Determine marginal frequencies of categorical data

Determine relative joint frequencies of categorical data

Determine relative marginal frequencies of categorical data

Convert relative frequencies to percentages

Build two-way frequency tables

Applied Geometry

Use converse of Pythagorean theorem to prove given lengths are those of right triangle

Find missing side of a right triangle in two dimensional description of real life situation (indirect measurement)

Create real life use of Pythagorean theorem, for indirect measurement.

Slice three dimensional figures to determine lengths drawn in solids, based on right triangles

The Number System

Determine subsets of real number sets

Describe and list the elements in each subset of real numbers

Classify a given numerical value by stating all sets (subsets) it is an element of

Determine approximations of irrational numbers

State two consecutive integers each irrational number lies between

Ordering real numbers on a number line

Solving equations using square and cubed roots

Determine if solutions to an equation are rational or irrational

Statistics

display

scatter plot

line of best fit

qualitative data

quantitative data

association

positive association

negative association

strong association

no association

linear association

non-linear (curved) association

clustering

outlier

categorical data

interpolation

extrapolation

prediction

row

column

two-way table

joint frequency

marginal frequency

relative joint frequency

relative marginal frequency

indirect measure

slicing

solids

nets

volume

prism

pyramid

cylinder

cone

sphere

hemi-sphere

composite figure

surface area

square units

cubic units

real numbers

rational numbers

irrational numbers

integers

whole

natural/counting numbers

Math Chat

Writing prompt

Classroom assessments

Pass paper

Judy Dodge exits

Exit tickets

Daily and weekly spirals

Benchmarks

IXL

Glencoe Course 3 Text