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Massachusetts Math Standards - Grades 3-4
MathScore aligns to the Massachusetts Math Standards for Grades 3-4. The standards appear below along with the MathScore topics that match. If you click on a topic name, you will see sample problems at varying degrees of difficulty that MathScore generated. When students use our program, the difficulty of the problems will automatically adapt based on individual performance, resulting in not only true differentiated instruction, but a challenging game-like experience.
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Number Sense and Operations
4.N.1 Exhibit an understanding of the base ten number system by reading, modeling, writing, and interpreting whole numbers to at least 100,000; demonstrating an understanding of the values of the digits; and comparing and ordering the numbers. (Place Value )4.N.2 Represent, order, and compare large numbers (to at least 100,000) using various forms, including expanded notation, e.g., 853 = 8 x 100 + 5 x 10 + 3. (Place Value , Number Comparison , Order Numbers )
4.N.3 Demonstrate an understanding of fractions as parts of unit wholes, as parts of a collection, and as locations on the number line. (Fraction Pictures )
4.N.4 Select, use, and explain models to relate common fractions and mixed numbers (1/2, 1/3, 1/4, 1/5, 1/6, 1/8, 1/10, 1/12, and 11/2), find equivalent fractions, mixed numbers, and decimals, and order fractions. (Fraction Comparison , Basic Fraction Simplification , Fractions to Decimals )
4.N.5 Identify and generate equivalent forms of common decimals and fractions less than one whole (halves, quarters, fifths, and tenths). (Fractions to Decimals )
4.N.6 Exhibit an understanding of the base ten number system by reading, naming, and writing decimals between 0 and 1 up to the hundredths. (Decimal Place Value )
4.N.7 Recognize classes (in particular, odds, evens; factors or multiples of a given number; and squares) to which a number may belong, and identify the numbers in those classes. Use these in the solution of problems. (Odd or Even , Odd or Even Theory , Factoring , Perfect Squares )
4.N.8 Select, use, and explain various meanings and models of multiplication and division of whole numbers. Understand and use the inverse relationship between the two operations. (Understanding Multiplication , Understanding Division , Inverse Equations 2 )
4.N.9 Select, use, and explain the commutative, associative, and identity properties of operations on whole numbers in problem situations, e.g., 37 x 46 = 46 x 37, (5 x 7) x 2 = 5 x (7 x 2). (Associative Property 1 , Associative Property 2 , Commutative Property 1 , Commutative Property 2 )
4.N.10 Select and use appropriate operations (addition, subtraction, multiplication, and division) to solve problems, including those involving money. (Basic Word Problems , Arithmetic Word Problems , Basic Word Problems 2 , Making Change , Counting Money , Unit Cost )
4.N.11 Know multiplication facts through 12 x 12 and related division facts. Use these facts to solve related multiplication problems and compute related problems, e.g., 3 x 5 is related to 30 x 50, 300 x 5, and 30 x 500. (Fast Multiplication , Fast Multiplication Reverse , Multiplication Facts Strategies , Fast Division , Multiply By Multiples Of 10 )
4.N.12 Add and subtract (up to five-digit numbers) and multiply (up to three digits by two digits) accurately and efficiently. (Long Addition , Long Subtraction , Multiplication By One Digit , Long Multiplication )
4.N.13 Divide up to a three-digit whole number with a single-digit divisor (with or without remainders) accurately and efficiently. Interpret any remainders. (Long Division By One Digit , Division with Remainders , Word Problems With Remainders )
4.N.14 Demonstrate in the classroom an understanding of and the ability to use the conventional algorithms for addition and subtraction (up to five-digit numbers), and multiplication (up to three digits by two digits).
4.N.15 Demonstrate in the classroom an understanding of and the ability to use the conventional algorithm for division of up to a three-digit whole number with a single-digit divisor (with or without remainders).
4.N.16 Round whole numbers through 100,000 to the nearest 10, 100, 1000, 10,000, and 100,000. (Rounding Numbers )
4.N.17 Select and use a variety of strategies (e.g., front-end, rounding, and regrouping) to estimate quantities, measures, and the results of whole-number computations up to three-digit whole numbers and amounts of money to $1000, and to judge the reasonableness of the answer. (Estimated Addition , Estimated Subtraction , Money Addition , Money Subtraction )
4.N.18 Use concrete objects and visual models to add and subtract common fractions. (Requires outside materials )
Patterns, Relations, and Algebra
4.P.1 Create, describe, extend, and explain symbolic (geometric) and numeric patterns, including multiplication patterns like 3, 30, 300, 3000, …. (Patterns: Numbers )4.P.2 Use symbol and letter variables (e.g., Δ, x) to represent unknowns or quantities that vary in expressions and in equations or inequalities (mathematical sentences that use =, <, >). (Algebraic Sentences )
4.P.3 Determine values of variables in simple equations, e.g., 4106 - ∇ = 37, 5 = O + 3, and [] - O = 3. (Missing Factor , Missing Term )
4.P.4 Use pictures, models, tables, charts, graphs, words, number sentences, and mathematical notations to interpret mathematical relationships. (Function Tables , Function Tables 2 )
4.P.5 Solve problems involving proportional relationships, including unit pricing (e.g., four apples cost 80¢, so one apple costs 20¢) and map interpretation (e.g., one inch represents five miles, so two inches represent ten miles). (Unit Cost )
4.P.6 Determine how change in one variable relates to a change in a second variable, e.g., input-output tables. (Line Graphs , Function Tables , Function Tables 2 )
Geometry
4.G.1 Compare and analyze attributes and other features (e.g., number of sides, faces, corners, right angles, diagonals, and symmetry) of two- and three-dimensional geometric shapes.4.G.2 Describe, model, draw, compare, and classify two- and three-dimensional shapes, e.g., circles, polygons-especially triangles and quadrilaterals-cubes, spheres, and pyramids. (Quadrilateral Types , Polygon Names )
4.G.3 Recognize similar figures. (Congruent And Similar Triangles )
4.G.4 Identify angles as acute, right, or obtuse.
4.G.5 Describe and draw intersecting, parallel, and perpendicular lines. (Parallel and Perpendicular Lines )
4.G.6 Using ordered pairs of numbers and/or letters, graph, locate, identify points, and describe paths (first quadrant).
4.G.7 Describe and apply techniques such as reflections (flips), rotations (turns), and translations (slides) for determining if two shapes are congruent.
4.G.8 Identify and describe line symmetry in two-dimensional shapes.
4.G.9 Predict and validate the results of partitioning, folding, and combining two- and three-dimensional shapes.
Measurement
4.M.1 Demonstrate an understanding of such attributes as length, area, weight, and volume, and select the appropriate type of unit for measuring each attribute.4.M.2 Carry out simple unit conversions within a system of measurement, e.g., hours to minutes, cents to dollars, yards to feet or inches, etc.
4.M.3 Identify time to the minute on analog and digital clocks using a.m. and p.m. Compute elapsed time using a clock (e.g., hours and minutes since…) and using a calendar (e.g., days since…). (Time Intervals , Telling Time )
4.M.4 Estimate and find area and perimeter of a rectangle, triangle, or irregular shape using diagrams, models, and grids or by measuring. (Perimeter and Area of Composite Figures )
4.M.5 Identify and use appropriate metric and English units and tools (e.g., ruler, angle ruler, graduated cylinder, thermometer) to estimate, measure, and solve problems involving length, area, volume, weight, time, angle size, and temperature. (Time Intervals )
Data Analysis, Statistics, and Probability
4.D.1 Collect and organize data using observations, measurements, surveys, or experiments, and identify appropriate ways to display the data.4.D.2 Match a representation of a data set such as lists, tables, or graphs (including circle graphs) with the actual set of data.
4.D.3 Construct, draw conclusions, and make predictions from various representations of data sets, including tables, bar graphs, pictographs, line graphs, line plots, and tallies. (Tally and Pictographs , Bar Graphs , Line Graphs )
4.D.4 Represent the possible outcomes for a simple probability situation, e.g., the probability of drawing a red marble from a bag containing three red marbles and four green marbles. (Probability )
4.D.5 List and count the number of possible combinations of objects from three sets, e.g., how many different outfits can one make from a set of three shirts, a set of two skirts, and a set of two hats?
4.D.6 Classify outcomes as certain, likely, unlikely, or impossible by designing and conducting experiments using concrete objects such as counters, number cubes, spinners, or coins.
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