Grade 4 Math Minnesota standards Standards

Data Analysis

Geometry & Measurement

Algebra

Number & Operation

Patterns and Relationships: Represent and connect mathematical patterns and relationships using verbal descriptions, generalizations, tables and graphs. Use representations to generate questions, make predictions and solve mathematical problems.

Equivalence and Relational Thinking: Use concepts and properties of equivalence and relational thinking to represent and compare numerical expressions, proportional relationships, algebraic expressions and equations.

Number Relationships: Describe/Interpret and use quantities, relationships between and representations of quantities and number systems. Describe and relate operations. Use strategies and procedures accurately, efficiently and flexibly. Assess the reasonableness of the results.

Patterns and Relationships

Geometry: Analyze characteristics of geometric shapes to make mathematical arguments and justifications about geometric relationships. Use visualization and geometric modeling to compare, solve problems and communicate ideas.

Measurement: Investigate measurement using a variety of tools, units, systems, processes and techniques in various cultures. Explain and reason with attributes, estimations and formulas to communicate measurement(s) and relationships effectively. Justify decisions and consider the reasonableness of the measurement.

Spatial Reasoning

Chance and Uncertainty: Apply and explain the concepts of probability to interpret data, generate questions, predict and make informed decisions to solve problems and communicate ideas.

Data Sciences: Identify, formulate and investigate statistical questions by collecting data considering cultural perspectives, analyzing and interpreting data and communicating the results.

Data Analysis

Demonstrate mastery of multiplication and division basic facts; multiply multi-digit numbers; solve real-world and mathematical problems using arithmetic.

Demonstrate fluency with multiplication and division facts.

Notice and describe patterns in data-rich situations or two given related data sets that are descriptive and comparative. Ask meaningful statistical questions that can be answered with data. (MP7) ✜

Use an understanding of place value to multiply a number by 10, 100 and 1000.

Collect and organize data to answer a statistical question, analyze variability and address missing, incomplete and bias in data. Represent data in a variety of ways, including technology. (MP1, MP5) #

Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms.

Make predictions and recognize that how the data was collected impacts the reliability of predictions. (MP1, MP8)

Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results.

Critically analyze data visualizations, including tables, double bar graphs, timelines, line plots or spreadsheets to support a claim and solve contextual situations. (MP3, MP7) $ # μ

Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results.

Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction.

Represent and compare fractions and decimals in real-world and mathematical situations; use place value to understand how decimals represent quantities.

Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions.

Classify probability events involving dice, coins, spinners with equal and unequal partitions and blocks in a bag as impossible, certain, likely, unlikely and equally likely. (MP7)

Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions.

Use a number line to connect the values of 0 to impossible, 1/2 to equally likely, and 1 to certain. Approximate locations on the number line where likely and unlikely would occur based on the situation. (MP4)

Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators.

Read and write decimals with words and symbols; use place value to describe decimals in terms of thousands, hundreds, tens, ones, tenths, hundredths and thousandths.

Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks.

Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths.

Round decimals to the nearest tenth.

Use input-output rules, tables and charts to represent patterns and relationships and to solve real-world and mathematical problems.

Create and use input-output rules involving addition, subtraction, multiplication and division to solve problems in various contexts. Record the inputs and outputs in a chart or table.

Use number sentences involving multiplication, division and unknowns to represent and solve real-world and mathematical problems; create real-world situations corresponding to number sentences.

Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences.

Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true.

Classify angles as acute, right and obtuse by estimation, comparison with a right angle and by measurement. (MP6) ✜

Determine lengths to the nearest sixteenth of an inch when measuring with inches and to the nearest tenth of a centimeter when measuring in centimeters. (MP6, MP8)

Measure angles with a protractor. (MP5) ☼

Determine the perimeter and area of two- dimensional figures and label with appropriate units. (MP2, MP6) ✜ ☼

Find the areas of geometric figures that can be decomposed into rectangular shapes using tools like dot or grid paper. Label area measurements using square units. (MP2)

Explain why the area of a rectangle can be calculated by multiplying the length by the width and use the formula 𝐴𝐴 = 𝑙𝑙 𝑥𝑥 𝑤𝑤 to calculate the area of rectangles with whole number side lengths. (MP3)

Make change up to $20 with place values, using $ and ¢ symbols appropriately. (MP7) $

Draw points, lines, line segments, rays, angles and perpendicular and parallel lines. Identify these in two-dimensional figures. (MP5) ☼

Create representations of triangles given the relationships among the sides (scalene, isosceles, equilateral) and the angles (acute, right, obtuse). (MP1, MP6) ☼

Sort and classify quadrilaterals in a hierarchy, including squares, rectangles, trapezoids, rhombuses, parallelograms and kites. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. (MP1, MP6) ✜ μ ☼

Create a representation and describe the front, top and side views of three-dimensional figures composed of cubes and rectangular prisms. (MP5)

Draw the nets of cubes. Recognize nets that will and will not form cubes. (MP1)

Name, describe, classify and sketch polygons.

Describe, classify and sketch triangles, including equilateral, right, obtuse and acute triangles. Recognize triangles in various contexts

Describe, classify and draw quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms and kites. Recognize quadrilaterals in various contexts.

Understand angle and area as measurable attributes of real-world and mathematical objects. Use various tools to measure angles and areas.

Measure angles in geometric figures and real-world objects with a protractor or angle ruler.

Compare angles according to size. Classify angles as acute, right and obtuse.

Understand that the area of a two-dimensional figure can be found by counting the total number of same size square units that cover a shape without gaps or overlaps. Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns.

Find the areas of geometric figures and real-world objects that can be divided into rectangular shapes. Use square units to label area measurements.

Use translations, reflections and rotations to establish congruency and understand symmetries.

Apply translations (slides) to figures.

Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry.

Apply rotations (turns) of 90° clockwise or counterclockwise.

Recognize that translations, reflections and rotations preserve congruency and use them to show that two figures are congruent.

Recognize that in a multi-digit whole number, a digit in one place represents 10 times what it represents in the place to its right. (MP7) $

Read, write, represent and plot on a number line fractional values between 0 and 3, including mixed numbers and fractions greater than 1 with denominators of 2, 3, 4, 5, 6, 8, 10 and 12. Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers. (MP6)

Explain why a fraction is equivalent to the 𝑏𝑏 product 𝑎𝑎 𝑥𝑥 1 using visual models and language. 𝑏𝑏 (MP2)

Explain why a fraction is equivalent to a fraction 𝑏𝑏 𝑛𝑛 𝑥𝑥 𝑎𝑎 by using visual models, with attention to how 𝑛𝑛 𝑥𝑥 𝑏𝑏 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. (MP3)

Compare and order fractions between 0 and 3 and justify reasoning using pictures, position on a number line and selecting, when appropriate, among the strategies such as using a common numerator, referencing a benchmark and using a common denominator. (MP3) μ

Recognize the relationship between decimals and fractions. Read and write decimals and fractions in both decimal and fraction notations using words, symbols and expanded form. Recall the fraction and decimal equivalent forms of one-half, one- quarter and three-quarters. (MP7) $

Compare and order decimal values to the hundredths and justify using place value language, a number line and models such as dimes, pennies, 10 x 10 grids and base 10 blocks. Use place value concepts to name and model equivalent forms of decimal values. (MP4) $

Use visual models to add and subtract fractions with denominators of 2, 4 and 8 with results up to 2. (MP4)

Use the four operations to make financial decisions based on income, spending, saving, credit and charitable giving. (MP1) $

Compare and order whole numbers from 0 to 1,000,000 with place value understanding, number lines and other tools using >, = and < symbols to record the results of comparisons. (MP4) $

Estimate sums and differences, within 1,000,000 using strategies based on place value, approximation and properties of operations. (MP3) ✜ $ ☼

Estimate products and quotients of multi-digit whole numbers by using simple multiplicative relationships, approximation and place value to assess the reasonableness of results. (MP1) $ ☼

Fluently multiply two numbers from 0 to 12 using flexible strategies based on the associative, commutative and distributive properties of multiplication. (MP6, MP7)

Use place value language to describe how to multiply a number by 10, 100 and 1,000. (MP7)

Flexibly decompose numbers into addends or factors to multiply two two-digit numbers with a one-digit number, by and up to a four-digit number. Justify the strategy using equations, rectangular arrays and area models. (MP2, MP7) μ

Solve contextual situations using division with dividends up to the thousands place and using one- digit divisors. Strategies may include using visual models, partial quotients, the commutative, associative and distributive properties and repeated subtraction. (MP7, MP8) $ μ

Solve multi-step contextual situations requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology and the context of the situation to assess the reasonableness of results. (MP4, MP7) $ ✜

Use relational thinking to find a missing value in an open number sentence with multi-digit whole number multiplication and division expressions. Determine if the equation is true or false and justify your reasoning. (MP3) $

Make conjectures and justifications using the distributive property to justify multi-digit multiplication with true/false and open number equations. (MP3) #

Develop an explicit rule that generalizes a visual pattern relating the figure number with the number of items in that figure. Use the rule to find the number of items in figure n. (MP7) μ

Use words to write a rule for multiplicative patterns to solve contextual situations. Compare and contrast pattern rules that are additive and multiplicative, using a variety of strategies including tables, drawings and algebraic equations with a symbol for the unknown number to represent the situation. (MP7, MP8) $ ☼

Generate a number or shape pattern that follows a given descriptive rule. Identify and explain apparent features of the pattern that were not explicit in the rule itself. (MP1, MP3) $ ☼

Collect, organize, display and interpret data, including data collected over a period of time and data represented by fractions and decimals.

Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data.