Grade 5 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

The student can replicate or identify an equal set from a model.

Number and Operations in Base 10

Students demonstrate increasingly complex understanding of number sense.

Graph points on the coordinate plane to solve real-world and mathematical problems.

Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).

Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.

Classify two-dimensional figures into categories based on their properties.

Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category.

Classify two-dimensional figures in a hierarchy based on properties.

Convert like measurement units within a given measurement system.

Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world 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). Use operations on fractions for this grade to solve problems involving information presented in line plots.

Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.

Recognize volume as an attribute of solid figures and understand concepts of volume measurement.

A cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume, and can be used to measure volume.

A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.

Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.

Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.

Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.

Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems.

Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.

Understand the place value system.

Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.

Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.

Read, write, and compare decimals to thousandths.

Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).

Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

Use place value understanding to round decimals to any place.

Perform operations with multi-digit whole numbers and with decimals to hundredths.

Fluently multiply multi-digit whole numbers using the standard algorithm.

Find whole-number quotients of whole numbers with up to four-digit dividends and two-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.

Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

Use equivalent fractions as a strategy to add and subtract fractions.

Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators.

Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers.

Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

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

Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b.

Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

Interpret multiplication as scaling (resizing), by:

Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.

Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n×a)/(n×b) to the effect of multiplying a/b by 1.

Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.

Interpret division of a unit fraction by a non-zero whole number, and compute such quotients.

Interpret division of a whole number by a unit fraction, and compute such quotients.

Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem.

Write and interpret numerical expressions.

Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them.

Analyze patterns and relationships.

Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane.

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.

Sort two-dimensional figures and identify the attributes (angles, number of sides, corners, color) they have in common.

The student can sort two-dimensional figures using attributes (e.g., angles, numbers of sides) they have in common.

The student can identify two-dimensional shapes (circle, square, star).

The student can identify two-dimensional figures with a common attribute.

Tell time using an analog or digital clock to the half or quarter hour.

Use standard units to measure weight and length of objects.

Indicate relative value of collections of coins.

Represent and interpret data on a picture, line plot, or bar graph.

Identify common three-dimensional shapes.

Determine the volume of a rectangular prism by counting units of measure (unit cubes).

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

The student can use an appropriate tool and customary units of measurement to measure length (inches/feet) and weight of objects (ounces/pounds).

The student can tell the amount of money using collections of coins up to and including $10.00.

The student can read and interpret data from charts, tables, graphs, tallies and pictographs.

The student can identify a sphere, cube, cone, and cylinder.

The student can determine the volume of a rectangular prism by counting unit cubes.

The student can associate activities with morning and afternoon.

The student can compare the lengths or masses of two objects to determine which one is longer or heavier, where the difference is vastly different.

The student can match coins of the same denomination (penny, nickel, dime, and quarter) when presented within a group.

The student can identify the category in a bar graph or picture graph that has the most or least when the quantities have extreme differences.

The student can differentiate between round and square or sphere and cube.

The student can differentiate between empty and full.

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

The student can identify the appropriate tool for measuring length and weight.

The student can identify an equivalent value of a nickel, dime, and quarter.

The student can identify what type or quantity of data are needed to answer a question, solve a problem, or complete a chart or pictograph.

The student can match objects to their outlines.

The student can demonstrate understanding that 3D shapes have volume.

Compare numbers up to 99 using base-ten models.

Use the number of zeros in numbers that are powers of 10 to determine which values are equal, greater than, or less than.

Compare whole numbers up to 100 using symbols (<, >, =).

Round two-digit whole numbers to the nearest 10 from 0—90.

Illustrate the concept of division using fair and equal shares.

The student can compare two quantities up to 99 using base-ten models.

The student can order numbers that are multiples of ten ranging from 0 to 10,000 in sequential order least to greatest.

The student can compare whole numbers up to 100 using symbols (=, <, >).

The student can round two-digit whole numbers (0-90) to the nearest ten using a number line indicating the tens.

The student can multiply numbers up to 5 x 5.

Multiply numbers up to 5 x 5.

The student can partition a set into equal subsets to solve a problem.

The student can compare two quantities of objects (0-10) with extreme differences to determine which set has more.

The student can identify the sequential order of numbers up to 10.

The student can identify which numeral, paired with a visual representation of its quantity, is greater than another numeral paired with a visual representation of its quantity (numerals 1-10).

The student can determine if a single-digit number is closer to 0 or 10 on a number line.

The student can combine two sets with an equal number of objects in each set.

The student can compare two quantities (0-20) using models.

The student can order multiples of ten ranging from 0-50 in sequential order least to greatest.

The student can identify which numerals (0-10) are “greater than”, “more than”, “less than” or “fewer than” a target numeral.

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

The student can use visual models or objects to depict repeated addition related to a multiplication problem using single digits to 3.

The student can divide objects into two equal sets.

Identify models of halves (1/2, 2/2) and fourths (1/4, 2/4, 3/4, 4/4).

Identify models of thirds (1/3. 2/3, 3/3) and tenths (1/10, 2/10, 3/10, 4/10, 5/10, 6/10, 7/10, 8/10, 9/10, 10/10).

The student can differentiate between halves (1/2, 2/2) and fourths (1/4, 2/4, 3/4, 4/4).

The student can recognize thirds (1/3, 2/3, 3/3) and tenths (1/10, 2/10, 3/10, 4/10, 5/10, 6/10, 7/10, 8/10, 9/10, 10/10) on a model.

The student can differentiate between a whole and one-half.

The student can identify how many equal parts a shape or object are separated into, limited to 1 and 3.

The student can identify one-half and one-fourth in a model.

The student can identify the unit fractions 1/3 and 1/10 when provided with models.

Identify and extend numerical patterns.

The student can create, describe and extend simple number patterns that involve a simple addition or subtraction rule.

The student can extend a simple AB pattern using pictures, objects or familiar symbols.

The student can extend a simple ABAB, ABC or ABBA pattern involving shapes, numbers or objects.