Last updated: 6/25/2015 ## Math-7 Core Map Quarter 4

Statistics

Populations

Samples

Bias/Unbiased

Quartiles

Five number summary

Box and whisker plots

Dot- Plots

Comparing Data

Making Predictions

Probability

Probability of simple events

Complementary events

Theoretical and Experimental Probability

Fair and unfair games

Probability of compound events

Simulations

Simulate compound events

Fundamental Counting Principle

Permutations

Dependent and Independent Events

Geometry

Basics: plane, point, line, segments and rays

Angles-classifying

Triangles-classifying by sides

Triangles-classify by angles

Interior sum of triangles

Finding missing interior angle/s of triangles (using equations)

Finding missing interior angle/s of quadrilaterals (using equations)

Classifying quadrilaterals with more than 4 sides

Determining the sum of interior angles by creating triangles

Constructing triangles to determine relationships of sides that form unique triangle

Describe two dimensional figures from slicing solids

Quarter 4

Statistics

Difference between population and sample

Differences in types of populations

Bias in samples or populations

Five number summary

Box and whisker plots

Dot plots

Histograms

Comparing data through data displays

Comparing data using centers and ranges

Make predictions using proportions

Determine if data or data displays are bias

Probability

Probability of simple events-single event

Complementary events-one or the other must happen

Theoretical Probability-ideally what should happen

Experimental Probability-what actually occurred during experiment

Fair and unfair games-equal chance of winning

Probability of compound events-two or more simple outcomes

Simulations-experiment to describe model

Simulate compound events

Fundamental Counting Principle-product of each single events outcomes

Permutations-number of ways items can be ordered (order matters)

Geometry

Basics: plane, point, line, segments and rays

Naming geometric shapes and labeling point, segments, lines, rays and angles

Angles-classifying

Triangles-classifying by sides

Triangles-classify by angles

Interior sum of triangles (180)

Finding missing interior angle/s of triangles (using equations)

Exterior angles of triangles and relationship to two non-adjacent interior angles

Finding missing interior angle/s of quadrilaterals (using equations)

Classifying quadrilaterals with more than 4 sides

Determining the sum of interior angles by creating triangles (number of triangles is always two less than the number of sides)

Constructing triangles to determine relationships of sides that form unique triangle-sum of two sides must always be greater than the third

Describe two dimensional figures from slicing solids

Statistics

How can you gather information from a large population of people?

How can we determine which sample represents the population the best?

How can we determine if a sample has a bias?

When there is only one variable, what type of data is that called?

How can we find the centers of the data list?

How does having an outlier in the data affect the centers?

How do you know if a data point is a true outlier?

Why should we determine the range? What does it tell us about the data?

Can we divide the data and use other markers to help make sense of the data?

Why is it necessary to place dot and box plots over a strict number line?

How can we use different displays to compare data collected?

How can data be skewed to represent data more favorably?

How can you determine if a display is misleading?

Probability

How does understanding probability help us understand and predict future events?

How can we describe an event that will never occur?

How can we describe an event that will absolutely occur?

How do you think we would describe an event that is equaliy likely to occur?

What about less or more than equaly likely?

Why do complementary events have to have a sum of 1?

How come there is a difference between theoretical and experimental probability?

How can knowing the probability of an experiment help predict future events?

As you complete more experiments, how do you think the experimental and theoretical probability will compare?

What do you think a fair game is (vs. unfair)?

How do you think we can determine the probability of compound events?

How does drawing a sample space tree diagram help find probability of compound events?

How does the Fundamental Counting Principle become useful with compound events?

How can we determine how many ways items or numbers can be arranged? Where order matters?

How do perumutations relate to real life?

How do dependent and independent events differ?

Geometry

How can we label (name) geometric figures?

What is a plane?

What are all angles based off of?

Can we examine a full circular rotation and determine that an angle is a portion of that rotation?

How can we classify angles, based on their size?

How can we estimate the size of angles?

When two lines intersect, how many angels are formed?

Is their a relationship between them?

Are all angles in the intersection adjacent?

Can we name special pairs of angles?

What is a triangle?

How can we classify angles by sides and then by angles?

Can we determine the number of interior angles in all triangles?

Can we use equations to find missing angles?

How does knowing the size of an angle affect the opposite side?

How does knowing the size of the opposite size help you determine information about the opposite angles?

How can we find the missing angles of quadrilaterals?

Can we use equations to determine the missing angles of quadrilaterals?

How do we name polygons that have more than 4 sides?

How can we determine the sum of the interior angles of a polygons?

Can we construct triangles using compass and straight edge?

Is there a general rule that must be followed for a triangle to be formed?

If we slice solids to reveal two dimensional figures, could you name the two dimensional figure?

 (1) 7.SP.1 Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. (1) 7.SP.2 Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be. (1) 7.SP.3 Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable. (1) 7.SP.4 Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book. (1) 7.SP.5 Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. (1) 7.SP.6 Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times. (1) 7.SP.7 Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. (1) 7.SP.7.a Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected. (1) 7.SP.7.b Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies? (1) 7.SP.8 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. (1) 7.SP.8.a Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs. (1) 7.SP.8.b Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., "rolling double sixes"), identify the outcomes in the sample space which compose the event. (1) 7.SP.8.c Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?

Statistics

Determine a sample of a population

Understand the difference between random, stratified, convenience & systematic sampling

Determine if a sampling is bias or unbias

Examine data using quartiles

Examine interquartile ranges

Find fivenumber summary

Build box and whisker plots

Compare data displayed in box and whisker plots

Determine if the range or the interquartile range describes the data best

Determine when the mean or the median is the best center

Determine the affect of outliers in centers and display

Make predictions using proportions and data display

Probability

Determine probabilty of simple event

Understand random results - equally likely to occur

Understand that probability can be written as a fraction, decimal or percent

Determine the complement of a given event

Determine probability form charts and bar graphs

Determine the theortical and experimental probability of given situation

Verbally describe the difference between theoretical and experimental probability

Use theoretical or experimental probability to predict outcomes of future events

Determine if a game is fair or unfair

Determine the probability of compound events

State sample space - draw probability tree

Predict the outcome of future events

Use Fundamental Counting Principle to determine outcomes

Apply Fundemental Countiing Principle to determine probability of compound accounts

Use permutations to determine the number of ways can be ordered

Determine probability of independent events

Determine probability of dependent events

Geometry

Label point, line, segment, ray and angles (Multilple methods)

Examine a full rotation, three quarter, half and quarter degree markers

Examine angles acute, right, obtuse, straight and reflexive

Estimating the number of degrees in an angle

Understand the relationships of complementary and supplementary angles

Determine the number of degrees in a complement or supplement of a given angle

Determine the difference between the supplement and complement of a given angle

Describe the difference between supplementary angles and linear pairs

Examine the relationship between angles formed in a single intersection

Determine the meause of vertical angles

Solve equations to find missing variable given a pair of angles in a single intersection

Classify triangles by sides

Classify trianlges by angles

Determine the sum of interior angles is 180-using a straight angle model

Find missing angle of a given triangle

Solve equations to find the missing variable given a measures of the angles of a triangle

Determine the smallest and largest sides of a given triangle

Determine the relationship between base angles of isosceles triangles and their opposite sides

Read and create markings to decipher specific quadrilaterals (congruence, parallelism, right angles)

Determine the sum of the interior angles of a quadrilateral by slicing into two triangles

Determine the missing angle in a quadrilateral

Use equations to find missing variable when interior angles are expressions

Determine which angles are always congruent in specific quadrilaterals

Classify polygons with more than 4 sides

Determine the sum of the interior angles of polygons based on the number of tirangles formed

Construct triangles-discover the sum of two sides must always be longer than the third to create a unique triangle

Describe the two-dimesional figure sthat result from slicing three dimesional figures

biased samples

box-and-whisker plot

convenience sample

interquartile range

lower quartile

upper quartile

mean

median

mode

outlier

population

random sample

range

sample

upper quartile

systematic random sample

voluntary response sample

simple random sample

stratified samples

convenience sampling

systematic sample

survey

dot plot

probability

complementary events

compound events

dependent events

experimental probability

fair

Fundamental Counting Principle

independent events

outcome

permutation

random

sample space

simple event

simulation

theoretical probability

tree diagram

unfair

plane

point

line

line segment

ray

angle

acute angles

obtuse angles

right angles

straight angles

reflex angles

degrees

intersection

complementary

supplementary

linear pairs

parallelograms

rectangle

rhombus

square

trapezoid

isosceles trapezoid

congruent

interior angles

exterior angles

parallel lines

transversals

constructions

protractor

compass

2-dimensional

3-dimensional

Writing Assessment

Unit Assessment

Benchmark Assessment

IXL-technology informal assessment

Glencoe Course 2 Text

State Modules

IXL

Big Ideas Accelerated -Ron Larson 