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How to learn Grade 3: Mathematics

Arkansas academic standards: Mathematics, Grade 3

0 of 32 concepts ready to learn · Markdown, for your AI

1. Grade 3 · Organize and analyze data.

  1. Representing numbers with objects (age 8+): Draw a scaled picture graph and a scaled bar graph to represent a data set; solve one- and two-step comparison, sum, and difference problems using bar charts, pictograms, and tables
  2. Sorting Data into Categories: Organise and represent data with up to three categories by counting objects in each category and sorting categories by quantity

2. Grade 3 · Tell time and solve problems about elapsed time.

  1. Estimating answers (age 7+): Estimate and read time with increasing accuracy to the nearest minute; record and compare time in terms of seconds, minutes, and hours
  2. Telling time to the minute (age 8+): Tell and write time to the nearest minute using analogue and digital clocks

3. Grade 3 · Calculate the area of rectangles and liquid volume.

  1. Measuring Liquids & Masses: Measure and estimate liquid volumes and masses of objects using grams, kilograms, and litres; solve one-step word problems involving mass or volume
  2. Understanding angles (age 8+): Multiply side lengths to find areas of rectangles and represent whole-number products as rectangular areas
  3. Understanding Area: Understand that a unit square has one square unit of area and that the area of a plane figure is the number of unit squares that cover it without gaps or overlaps

4. Grade 3 · Investigate measurement using rulers.

  1. Measuring length (age 7+): Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, metre sticks, and measuring tapes

5. Grade 3 · Analyze attributes of shapes to develop generalizations about their properties.

  1. Understanding angles (age 8+): Understand that shapes in different categories may share attributes defining a larger category; classify quadrilaterals (rhombuses, rectangles, squares) and draw examples of quadrilaterals not in those subcategories
  2. Classifying shapes by line properties: Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or angles of a specified size; recognise right triangles as a category

6. Grade 3 · Develop and apply an understanding of foundational algebraic concepts.

  1. Division as Unknown Factor: Understand division as an unknown-factor problem (e.g. find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8)
  2. Unknown in Multiplication & Division: Determine the unknown whole number in a multiplication or division equation relating three whole numbers (e.g. 8 × ? = 48, ? × 6 = 42)

7. Grade 3 · Solve real-world problems.

  1. Two-Step Equations: Solve two-step word problems using the four operations; represent problems using equations with a letter standing for the unknown quantity
  2. Multiplication and Division Word Problems: Use multiplication and division within 100 to solve word problems involving equal groups, arrays, and measurement quantities

8. Grade 3 · Perform operations using place value understanding and properties of operations.

  1. Shape patterns (age 7+): Look for and use mathematical structure: apply place-value patterns to three-digit operations, use multiplication/division relationships, and exploit shape properties to classify
  2. Mental multiplication and division: Use place value, known and derived facts to multiply and divide mentally, including multiplying by 0 and 1, dividing by 1, and multiplying together three numbers
  3. Properties of Operations: Apply properties of operations (commutative, associative, distributive) as strategies to multiply and divide
  4. Understanding fractions (age 9+): Construct and present logical mathematical arguments involving multiple steps; critique others' reasoning about fractions, angles, or calculations and clearly explain errors or alternative methods
  5. Fluent adding and subtracting within 1000: Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and the relationship between addition and subtraction

9. Grade 3 · Develop and apply equivalent fraction understanding.

  1. Equivalent fractions (age 9+): Explain why a fraction a/b is equivalent to (n×a)/(n×b) using visual models; use this principle to recognise and generate equivalent fractions, including tenths and hundredths

10. Grade 3 · Build a conceptual understanding of fractions.

  1. Fraction Addition Concepts: Understand addition and subtraction of fractions as joining and separating parts; decompose a fraction into a sum of fractions with the same denominator in more than one way
  2. Fractions on a number line: Recognise and use fractions as numbers: place unit fractions and non-unit fractions with small denominators on a number line
  3. Fractions of a whole: Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a/b as a parts of size 1/b
  4. Fractions as parts of shapes: Partition shapes into parts with equal areas and express the area of each part as a unit fraction of the whole
  5. Unit fractions: Recognise, find, and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators

11. Grade 3 · Use place value understanding to compare numbers.

  1. Comparing fractions (age 8+): Compare two fractions with the same numerator or the same denominator by reasoning about size; record comparisons with >, =, or < symbols
  2. Comparing Decimals: Compare two decimals to hundredths (or up to three decimal places) by reasoning about size using place-value understanding; record with >, =, <
  3. Ordering Numbers to 1000: Compare and order numbers up to 1000 using >, =, and < symbols, based on place-value understanding
  4. Comparing Large Numbers: Order and compare numbers beyond 1000

12. Grade 3 · Understand the base ten place value system.

  1. Reading and writing numbers (age 9+): Read, write, order, and compare whole numbers up to at least 1,000,000 using base-ten numerals, number names, expanded form, and place-value understanding
  2. Place value of each digit: Recognise the place value of each digit in a four-digit number (thousands, hundreds, tens, and ones)
  3. Decimal place value (age 9+): Round decimals with two decimal places to the nearest whole number and to one decimal place