Grade 4 Math Michigan standards Standards

Number and Operations—Fractions

Geometry

Measurement and Data

Number and Operations in Base Ten

Operations and Algebraic Thinking

Standards for Mathematical Practice

Problem Solving

Students solve increasingly complex mathematical problems, making productive use of algebra and functions.

Using Measurement and Data

Students demonstrate increasingly complex understanding of measurement, data and analytic procedures.

Measurement and Data

Geometry

Students demonstrate increasingly complex spatial reasoning and understanding of geometric principles.

Number and Operations - Fractions

Number and Operations in Base 10

Operations and Algebraic Thinking

Students demonstrate increasingly complex understanding of number sense.

Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.

Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.

Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.

Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.

Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two column table.

Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

Apply the area and perimeter formulas for rectangles in real world and mathematical problems.

Represent and interpret data.

Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots.

Geometric measurement: understand concepts of angle and measure angles.

Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:

An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a "one-degree angle," and can be used to measure angles.

An angle that turns through n one-degree angles is said to have an angle measure of n degrees.

Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.

Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.

Generalize place value understanding for multi-digit whole numbers.

Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.

Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

Use place value understanding to round multi-digit whole numbers to any place.

Use place value understanding and properties of operations to perform multi-digit arithmetic.

Fluently add and subtract multi-digit whole numbers using the standard algorithm.

Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Extend understanding of fraction equivalence and ordering.

Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

Understand a fraction a/b with a > 1 as a sum of fractions 1/b.

Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model.

Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.

Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.

Understand a fraction a/b as a multiple of 1/b.

Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number.

Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem.

Understand decimal notation for fractions, and compare decimal fractions.

Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.

Use decimal notation for fractions with denominators 10 or 100.

Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.

Use the four operations with whole numbers to solve problems.

Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.

Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.

Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

Gain familiarity with factors and multiples.

Find all factor pairs for a whole number in the range 1—100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1—100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1—100 is prime or composite.

Generate and analyze patterns.

Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself.

Make sense of problems and persevere in solving them.

Reason abstractly and quantitatively.

Construct viable arguments and critique the reasoning of others.

Model with mathematics.

Use appropriate tools strategically.

Attend to precision.

Look for and make use of structure.

Look for and express regularity in repeated reasoning.

Recognize parallel lines and intersecting lines.

Describe the defining attributes of two-dimensional shapes.

Recognize that lines of symmetry partition shapes into equal areas.

The student can differentiate between parallel and intersecting lines/line segments.

The student can identify a straight line.

The student can recognize intersecting lines/line segments.

Identify the smaller measurement unit that comprises a larger unit within a measurement system (inches/foot, centimeter/meter, minutes/ hour).

Tell time using a digital clock. Tell time to the nearest hour using an analog clock.

Measure mass or volume using standard tools.

Use standard measurement to compare lengths of objects.

Identify coins (penny, nickel, dime, quarter) and their values.

Determine the area of a square or rectangle by counting units of measure (unit squares).

Represent data on a picture or bar graph given a model and a graph to complete.

Interpret data from a picture or bar graph.

Recognize angles in geometric shapes.

Identify angles as larger and smaller.

The student can identify the smaller unit of measure (limited to minutes/hour, inches/ foot), when presented with a real-world context.

The student can tell time to the nearest hour using an analog clock and the nearest half hour using a digital clock.

The student can identify and use appropriate tools to measure mass (ruler, scale, measuring tape) and volume (measuring cups, beaker, etc.).

The student can use standard units of measure (inches/feet) to compare the lengths of 2 objects.

The student can identify coins and their values (penny, nickel, dime, quarter).

The student can calculate the area of a rectangle by counting unit squares.

The student can use a pictograph or bar graph (with a scale of 1) to read data.

The student can compare angles in geometric shapes and describe them as larger or smaller.

The student can identify tools to measure time and length.

The student can relate activities with approximate time of the day.

The student can compare 2 masses or 2 volumes as more or less when presented with amounts that are extremely different.

The student can identify an object as being long or short when given two objects of vastly different lengths.

The student can recognize money when compared with other common objects.

The student can match the perimeter (outline) of a shape.

The student can recognize symbols as representing data on a simple graph (limited to 2 data points).

The student can identify which shape is the same when presented with a common two-dimensional shape.

The student can recognize minutes/hour as a measure of time and/or inches/foot as a measure of length.

The student can tell time to the hour using a digital clock.

The student can measure mass and volume using non-standard units.

The student can compare lengths of different objects and describe them as longer, longest, shorter, or shortest.

The student can name coins (penny, nickel, dime, quarter).

The student can differentiate between area and perimeter.

The student can recognize quantity of data as most or least in a bar graph or picture graph.

The student can match shapes with a common attribute (e.g., angles of the same size, same number of angles, same number of sides).

Compare whole numbers to 10 using symbols (<, >, =).

Round any whole number 0-30 to the nearest ten.

Add and subtract two-digit whole numbers.

The student can compare whole numbers to 10 using symbols (<, >, =).

The student can round whole numbers 0-30 to the nearest 10 using a number line.

The student can add and subtract numbers within 100 where both numbers are multiples of 10 and no regrouping is required.

The student can compare 2 sets of objects with extreme differences to determine which has more.

The student can identify which number comes next on a number line using numbers to 5.

The student can add 1 or subtract 1 from a number or quantity, using a number line and/or quantities of objects 1-5.

The student can compare whole numbers to 10 using “more than,” “less than”, and “equal to.”

The student can round whole numbers 0-20 to the nearest 10 using a number line.

The student can add and subtract whole numbers within 20 using a number line and/or objects.

Identify models of one-half (1/2) and one-fourth (1/4).

Differentiate between whole and half.

The student can recognize that two halves and four fourths equal one whole using a model.

The student can differentiate between one-half and one-fourth as related to one whole.

The student can identify one-half of a real-world object.

The student can differentiate between a whole object and a half of an object.

The student can recognize that two halves equal one whole using a model.

The student can differentiate between one half and one whole using a model/ representation of an object.

Demonstrate the connection between repeated addition and multiplication.

The student can solve one-step real-world problems using addition or subtraction within 100.

Show one way to arrive at a product.

Use repeating patterns to make predictions.

The student can use models of repeated addition to solve a multiplication problem.

The student can solve one-step problems using addition or subtraction within 100 without regrouping.

The student can create, describe, and extend simple number patterns.

The student can identify a group of objects or pictures with the same quantity as another group of objects or pictures.

The student can solve real-world addition and subtraction problems within 5 without regrouping with or without the use of manipulatives or a calculator.

The student can extend patterns involving objects or symbols.

The student can identify models that represent the sum of two sets of objects of the same quantity with sets of no more than 5.

The student can solve addition and subtraction problems within 20 without regrouping with or without the use of manipulatives, and/or a calculator.

The student can create, describe, and/or extend simple number patterns or patterns involving counting objects or symbols.