1.1.1: knows, explains, and uses equivalent representations for rational numbers expressed as fractions, terminating decimals, and percents; positive rational number bases with whole number exponents; time; and money.
1.1.2: compares and orders:
1.1.2.b: fractions greater than or equal to zero,
1.1.2.c: decimals greater than or equal to zero through thousandths place.
1.1.3: explains the relative magnitude between whole numbers, fractions greater than or equal to zero, and decimals greater than or equal to zero.
1.1.4: knows and explains numerical relationships between percents, decimals, and fractions between 0 and 1, e.g., recognizing that percent means out of a 100, so 60% means 60 out of 100, 60% as a decimal is .60, and 60% as a fraction is 60/100.
1.1.5: uses equivalent representations for the same simple algebraic expression with understood coefficients of 1, e.g., when students are developing their own formula for the perimeter of a square, they combine s + s + s + s to make 4s.
1.2.2: identifies prime and composite numbers and explains their meaning.
1.2.3: uses and describes these properties with the rational number system and demonstrates their meaning including the use of concrete objects:
1.2.3.a: commutative and associative properties of addition and multiplication (commutative - changing the order of the numbers does not change the solution; associative - changing the grouping of the numbers does not change the solution);
1.2.3.i: additive inverse property (every number has a value known as its additive inverse and when the original number is added to that additive inverse, the answer is zero), e.g., +5 + (-5) = 0.
1.2.4: recognizes and explains the need for integers, e.g., with temperature, below zero is negative and above zero is positive; in finances, money in your pocket is positive and money owed someone is negative.
1.3.2: uses various estimation strategies and explains how they were used to estimate rational number quantities or the irrational number pi.
1.4.1: computes with efficiency and accuracy using various computational methods including mental math, paper and pencil, concrete objects, and appropriate technology.
1.4.2: performs and explains these computational procedures:
1.4.2.b: adds and subtracts decimals from millions place through thousandths place;
1.4.2.f: adds, subtracts, and multiplies fractions (including mixed numbers) expressing answers in simplest form; e.g., 5 1/4 x 1/3 = 21/4 x 1/3 = 7/4 or 1 3/4
1.4.2.g: finds the root of perfect whole number squares;
1.4.2.h: uses basic order of operations (multiplication and division in order from left to right, then addition and subtraction in order from left to right) with whole numbers;
1.4.4: identifies, explains, and finds the prime factorization of whole numbers
1.4.5: finds prime factors, greatest common factor, multiples, and the least common multiple.
1.4.6: finds a whole number percent (between 0 and 100) of a whole number, e.g., 12% of 40 is what number?
2.1.1: identifies, states, and continues a pattern presented in various formats including numeric (list or table), visual (picture, table, or graph), verbal (oral description), kinesthetic (action), and written using these attributes include:
2.1.1.a: counting numbers including perfect squares, and factors and multiples (number theory).
2.1.1.e: things related to daily life, e.g., time (a full moon every 28 days), tide, calendar, traffic, or appropriate topics across the curriculum.
2.2.1: explains and uses variables and/or symbols to represent unknown quantities and variable relationships, e.g., x < 2.
2.2.2: uses equivalent representations for the same simple algebraic expression with understood coefficients of 1, e.g., when students are developing their own formula for the perimeter of a square they combine s + s + s + s to make 4s.
2.2.3.a: one-step linear equations (addition, subtraction, multiplication, division) with one variable and whole number solutions, e.g., 2x = 8 or x + 7 = 12
2.2.4: explains and uses equality and inequality symbols (=, not equal, <, less than or equal to, >, greater than or equal to) and corresponding meanings (is equal to, is not equal to, is less than, is less than or equal to, is greater than, is greater than or equal to) to represent mathematical relationships with positive rational numbers.
2.3.1: recognizes linear relationships using various methods including mental math, paper and pencil, concrete objects, and graphing utilities or appropriate technology.
2.3.2: finds the values and determines the rule with one operation using a function table (input/output machine, T-table).
2.3.3: generalizes numerical patterns up to two operations by stating the rule using words, e.g., If the sequence is 2400, 1200, 600, 300, 150, ..., what is the rule? In words, the rule could be split the number in half or divide the number before by 2.
2.3.4: uses a given function table (input/output machine, T-table) to identify, plot, and label the ordered pairs using the four quadrants of a coordinate plane.
2.4.1: knows, explains, and uses mathematical models to represent mathematical concepts, procedures, and relationships. Mathematical models include:
2.4.1.a: process models (concrete objects, pictures, diagrams, number lines, hundred charts, measurement tools, multiplication arrays, division sets, or coordinate planes/grids) to model computational procedures and mathematical relationships and to solve equations
2.4.1.b: place value models (place value mats, hundred charts, base ten blocks, or unifix cubes) to compare, order, and represent numerical quantities and to model computational procedures;
2.4.1.c: fraction and mixed number models (fraction strips or pattern blocks) and decimal and money models (base ten blocks or coins) to compare, order, and represent numerical quantities;
2.4.1.d: factor trees to find least common multiple and greatest common factor
2.4.1.e: equations and inequalities to model numerical relationships
2.4.1.f: function tables (input/output machines, T-tables) to model numerical and algebraic relationships;
2.4.1.g: two-dimensional geometric models (geoboards or dot paper) to model perimeter, area, and properties of geometric shapes and three-dimensional geometric models (nets or solids) and real-world objects to model volume and to identify attributes (faces, edges, vertices, bases) of geometric shapes;
2.4.1.h: tree diagrams to organize attributes and determine the number of possible combinations;
3.1.3: names and describes the solids [prisms (rectangular and triangular), cylinders, cones, spheres, and pyramids (rectangular and triangular)] using the terms faces, edges, vertices, and bases.
3.1.4: recognizes all existing lines of symmetry in two-dimensional figures.
3.1.6: recognizes and uses symbols for angle (find symbol for), line(<--->), line segment (---), ray (-->), parallel (||), and perpendicular (|_).
3.1.9: recognize that the sum of the angles of a triangle equals 180°.
3.1.10: determines the radius or diameter of a circle given one or the other.
3.2.1: determines and uses whole number approximations (estimations) for length, width, weight, volume, temperature, time, perimeter, and area using standard and nonstandard units of measure.
3.2.2: selects, explains the selection of, and uses measurement tools, units of measure, and level of precision appropriate for a given situation to find accurate rational number representations for length, weight, volume, temperature, time, perimeter, area, and angle measurements.
3.2.3.a: within the customary system, e.g., converting feet to inches, inches to feet, gallons to pints, pints to gallons, ounces to pounds, or pounds to ounces;
3.2.3.b: within the metric system, e.g., converting millimeters to meters, meters to millimeters, liters to kiloliters, kiloliters to liters, milligrams to grams, or grams to milligrams
3.2.5: recognizes and states perimeter and area formulas for squares, rectangles, and triangles.
3.2.5.a: uses given measurement formulas to find perimeter and area of: squares and rectangles,
3.2.5.b: figures derived from squares and/or rectangles.
3.2.7: finds the volume of rectangular prisms using concrete objects.
3.2.8: estimates an approximate value of the irrational number pi.
3.3.1: identifies, describes, and performs one or two transformations (reflection, rotation, translation) on a two-dimensional figure.
3.4.1: uses a number line (horizontal/vertical) to order integers and positive rational numbers (in both fractional and decimal form).
3.4.2: organizes integer data using a T-table and plots the ordered pairs in all four quadrants of a coordinate plane (coordinate grid).
3.4.3: uses all four quadrants of the coordinate plane to:
3.4.3.a: identify ordered pairs of integer values on a given graph;
3.4.3.b: graph ordered pairs of integer values.
4.1.1: recognizes that all probabilities range from zero (impossible) through one (certain) and can be written as a fraction, decimal, or a percent, e.g., when you flip a coin, the probability of the coin landing on heads (or tails) is 1/5,.5, or 50%. The probability of flipping a head on a two-headed coin? The probability of flipping a tail on a two-headed coin?
4.1.2: lists all possible outcomes of an experiment or simulation with a compound event composed of two independent events in a clear and organized way, e.g., Using a tree diagram or list to find all the possible color combinations of pant and shirt ensembles, if there are 3 shirts (red, green, blue) and 2 pairs of pants (black and brown).
4.1.3: recognizes whether an outcome in a compound event in an experiment or simulation is impossible, certain, likely, unlikely, or equally likely.
4.1.4: represents the probability of a simple event in an experiment or simulation using fractions and decimals, e.g., The probability of rolling an even number on a single number cube is represented by ½ or .5.
4.2.1: organizes, displays, and reads quantitative (numerical) and qualitative (non-numerical) data in a clear, organized, and accurate manner including a title, labels, categories, and rational number intervals using these data displays:
4.2.1.b: frequency tables and line plots;
4.2.1.c: bar, line, and circle graphs;
4.2.1.e: charts and tables;
4.2.1.f: single stem-and-leaf plots;
4.2.1.g: scatter plots;
4.2.2: selects and justifies the choice of data collection techniques (observations, surveys, or interviews) and sampling techniques (random sampling, samples of convenience, or purposeful sampling) in a given situation.
4.2.3: uses sampling to collect data and describe the results.
4.2.4: determines mean, median, mode, and range for:
4.2.4.a: a whole number data set,
Correlation last revised: 1/20/2017