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# NJPEP

By Lauren Greene,2014-05-07 12:27
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NJPEP

STANDARD 4.4 (DATA ANALYSIS, PROBABILITY, AND DISCRETE MATHEMATICS)

Strands and Cumulative Progress Indicators (CPIs)

4-8

Cumulative Progress Indicators by Grade

Strand 4 5 6 7 8 1. Collect, generate, 1. Collect, generate, 1. Collect, generate, organize, 1. Select and use 1. Select and use A. Data Analysis

organize, and display data in organize, and display data. and display data. appropriate appropriate representations response to questions, representations for sets of for sets of data, and ? Data ? Data generated

claims, or curiosity. data, and measures of measures of central generated from surveys

central tendency (mean, tendency (mean, median, ? Data collected from surveys 2. Read, interpret, select,

median, and mode). and mode). from the school 2. Read, interpret, select, construct, analyze, generate

environment construct, analyze, generate questions about, and draw ? Type of ? Type of 2. Read, interpret, construct, questions about, and draw inferences from displays of display most display most analyze, generate questions inferences from displays of data. appropriate appropriate for about, and draw inferences data. for given given data ? Bar graph, line

from displays of data. data ? Bar graph, graph, circle ? Box-and-

? Pictograph, bar line graph, graph, table, ? Box-and-whisker plot,

graph, line plot, circle graph, histogram whisker upper quartile,

line graph, table table plot, upper lower quartile ? Range, median,

quartile, ? Average ? Range, and mean ? Scatter plot

lower (mean), most median, and ? Calculators and ? Calculators

quartile frequent mean computers used and computer

(mode), middle 3. Respond to questions ? Scatter plot to record and used to record

term (median) about data and generate process ? Calculators and process

their own questions and information and information

hypotheses. 3. Respond to questions about computer ? Finding the

data, generate their own used to median and

questions and hypotheses, and record and mean formulate strategies for process (weighted

answering their questions and information average) using testing their hypotheses. 2. Make inferences and frequency

formulate and evaluate data.

arguments based on ? Effect of

displays and analysis of additional data

data. on measures of

central

tendency

2. Make inferences and

formulate and evaluate

arguments based on displays

and analysis of data.

1

Cumulative Progress Indicators by Grade

Strand 4 5 6 7 8

3. Estimate lines of best fit

and use them to interpolate

within the range of the data.

4. Use surveys and sampling

techniques to generate data

and draw conclusions about

large groups. 1. Use everyday events and 1. Determine probabilities 1. Determine probabilities of 1. Interpret probabilities 1. Interpret probabilities as B. Probability

chance devices, such as dice, of events. events. as ratios, percents, and ratios, percents, and coins, and unevenly divided decimals. decimals. ? Event, ? Event,

spinners, to explore concepts 2. Model situations 2. Determine probabilities probability of complementary

of probability. involving probability with of compound events. an event event,

simulations (using 3. Explore the probabilities ? Likely, probability of an ? Probability of

spinners, dice, calculators of conditional events (e.g., unlikely, event certain event

and computers) and if there are seven marbles in certain, is 1 and of ? Multiplication

theoretical models. a bag, three red and four impossible, impossible rule for

green, what is the improbable, ? Frequency, event is 0 probabilities

probability that two marbles fair, unfair relative 2. Determine probability ? Probability of picked from the bag, frequency ? More likely, using intuitive, certain event is 1 without replacement, are 3. Estimate probabilities less likely, experimental, and and of both red). and make predictions equally likely theoretical methods (e.g., impossible event 4. Model situations based on experimental using model of picking ? Probability of is 0 involving probability with and theoretical items of different colors tossing "heads" ? Probabilities of simulations (using spinners, probabilities. from a bag). does not event and dice, calculators and 4. Play and analyze depend on ? Given complementary computers) and theoretical probability-based games, outcomes of numbers of event add up to 1 models. and discuss the concepts previous tosses various types 2. Determine probability of fairness and expected ? Frequency, 2. Determine probabilities of of items in a using intuitive, experimental, value. relative simple events based on bag, what is and theoretical methods (e.g., frequency equally likely outcomes and the using model of picking items 5. Estimate probabilities and express them as fractions. probability of different colors from a bag). make predictions based on 3. Predict probabilities in a that an item ? Given numbers experimental and theoretical variety of situations (e.g., of one type of various types probabilities. given the number of items of will be picked of items in a bag, 6. Play and analyze each color in a bag, what is ? Given data what is the probability-based games, the probability that an item obtained probability that and discuss the concepts of picked will have a particular experimentallan item of one fairness and expected value. color). y, what is the type will be

? What students likely picked

think will distribution of ? Given data

happen items in the obtained

(intuitive) bag experimentally, what is the likely

2

Cumulative Progress Indicators by Grade

Strand 4 5 6 7 8

3. Model situations distribution of ? Collect data

involving probability using items in the bag and use that

simulations (with spinners, 3. Explore compound events. data to predict

dice) and theoretical 4. Model situations involving the probability

models. probability using simulations (experimental)

(with spinners, dice) and ? Analyze all

theoretical models. possible 5. Recognize and understand outcomes to

the connections among the find the

concepts of independent probability

outcomes, picking at random, (theoretical)

and fairness.

1. Represent and classify 1. Solve counting problems 1. Solve counting problems 1. Apply the 1. Apply the multiplication C. Discrete

data according to attributes, and justify that all and justify that all possibilities multiplication principle of principle of counting. Mathematics

such as shape or color, and possibilities have been have been enumerated without counting. Systematic Listing ? Permutations: relationships. enumerated without duplication. and Counting ? Permutationordered

duplication. ? Venn diagrams ? Organized lists, s: ordered situations with

? Organized charts, tree situations replacement ? Numerical and

lists, charts, diagrams, tables with (e.g., number alphabetical

tree diagrams, replacement of possible order ? Venn diagrams

tables (e.g., license plates) 2. Represent all possibilities 2. Apply the multiplication

2. Explore the number of vs. ordered for a simple counting principle of counting.

multiplication principle of possible situations situation in an organized way ? Simple situations

counting in simple license without and draw conclusions from (e.g., you can

situations by representing plates) vs. replacement this representation. make 3 x 4 = 12

all possibilities in an ordered (e.g., number ? Organized lists, outfits using 3

organized way (e.g., you situations of possible charts, tree shirts and 4

can make 3 x 4 = 12 outfits without slates of 3 diagrams skirts).

using 3 shirts and 4 skirts). replacement class officers ? Dividing into ? Number of ways (e.g., from a 23 categories (e.g., a specified number of student class) to find the total number of items possible ? Factorial number of can be arranged slates of 3 notation rectangles in a in order (concept class ? Concept of grid, find the of permutation) officers combinations number of ? Number of ways from a 23 (e.g., number rectangles of of selecting a student of possible each size and slate of officers class) delegations of add the results) from a class 2. Explore counting 3 out of 23 (e.g., if there are problems involving Venn students) 23 students and 3 diagrams with three 2. Explore counting officers, the attributes (e.g., there are problems involving Venn number is 23 x 15, 20, and 25 students diagrams with three 22 x 21)

3

Cumulative Progress Indicators by Grade

Strand 4 5 6 7 8

3. List the possible respectively in the chess attributes (e.g., there are 15,

combinations of two elements club, the debating team, 20, and 25 students

chosen from a given set (e.g., and the engineering respectively in the chess

forming a committee of two society; how many club, the debating team, and

from a group of 12 students, different students belong the engineering society;

finding how many handshakes to the three clubs if there how many different students

there will be among ten people are 6 students in chess belong to the three clubs if

if everyone shakes each other and debating, 7 students there are 6 students in chess

person's hand once). in chess and engineering, and debating, 7 students in

8 students in debating and chess and engineering, 8

engineering, and 2 students in debating and

students in all three?). engineering, and 2 students

3. Apply techniques of in all three?).

systematic listing, 3. Apply techniques of

counting, and reasoning in systematic listing, counting,

a variety of different and reasoning in a variety of

contexts. different contexts. 1. Follow, devise, and 1. Devise strategies for 1. Devise strategies for 1. Use vertex-edge 1. Use vertex-edge graphs D. Discrete

describe practical sets of winning simple games winning simple games (e.g., graphs to represent and and algorithmic thinking to Mathematics-

directions (e.g., to add two 2-(e.g., start with two piles of start with two piles of objects, find solutions to practical represent and find solutions VertexEdge

digit numbers). objects, each of two players each of two players in turn problems. to practical problems. Graphs and

2. Play two-person games in turn removes any removes any number of Algorithms ? Finding the ? Finding the and devise strategies for number of objects from a objects from a single pile, and shortest shortest winning the games (e.g., single pile, and the person the person to take the last network network "make 5" where players to take the last group of group of objects wins) and connecting connecting alternately add 1 or 2 and the objects wins) and express express those strategies as sets specified specified sites person who reaches 5, or those strategies as sets of of directions. sites ? Finding a another designated number, directions. 2. Analyze vertex-edge graphs ? Finding the minimal route is the winner). and tree diagrams. shortest that includes 3. Explore vertex-edge ? Can a picture or route on a every street graphs and tree diagrams. a vertex-edge map from (e.g., for trash

? Vertex, edge, graph be drawn one site to pick-up)

neighboring/adjwith a single another ? Finding the

acent, number line? (degree of ? Finding the shortest route

of neighbors vertex) shortest on a map from

? Path, circuit ? Can you get circuit on a one site to

(i.e., path that from any vertex map that another

ends at its to any other makes a tour ? Finding the

starting point) vertex? of specified shortest circuit 4. Find the smallest number (connectedness) sites on a map that of colors needed to color a makes a tour map or a graph. of specified sites

4

Cumulative Progress Indicators by Grade

Strand 4 5 6 7 8 3. Use vertex-edge graphs to ? Limitations of find solutions to practical computers problems. (e.g., the

? Delivery route number of

that stops at routes for a

specified sites delivery truck

but involves least visiting n sites

travel is n!, so

finding the ? Shortest route

shortest circuit from one site on

by examining a map to another

all circuits

would

overwhelm the

capacity of any

computer, now

or in the

future, even if

n is less than

100).

5

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