How to learn Grade 5: Mathematics

Ohio academic standards: Mathematics, Grade 5

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1. Number and Operations — Fractions · Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. In general, students able to mul

1. Dividing fractions (unit fractions): Interpret and compute division of a unit fraction by a non-zero whole number (e.g. 1/3 ÷ 4 = 1/12); use visual models and the relationship between multiplication and division to explain the result
2. Dividing unit fractions and whole numbers: Solve real-world problems involving division of unit fractions by whole numbers and whole numbers by unit fractions, using visual models and equations

2. Number and Operations — Fractions · Interpret multiplication as scaling (resizing).

1. Multiplication as scaling: Interpret multiplication as scaling (resizing): compare the size of a product to a factor based on the size of the other factor without computing; explain the effect of multiplying by fractions greater than, equal to, or less than 1

3. Number and Operations — Fractions · Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

1. Multiplying fractions (age 10+): Multiply a fraction or whole number by a fraction, including proper fractions by proper fractions; interpret (a/b) × q as a parts of q partitioned into b equal parts; write answers in simplest form
2. Area with Fractions: Find the area of a rectangle with fractional side lengths by tiling with unit-fraction squares; show that the area equals the product of the side lengths
3. 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

4. Measurement and Data · Relate volume to the operations of multiplication and addition and solve real-world and mathematical problems involving volume.

1. Estimating answers (age 10+): Find the volume of right rectangular prisms by packing with unit cubes and show it equals l × w × h (or base area × height); apply V = l × w × h and V = B × h to solve real-world problems; calculate, estimate, and compare volumes of cubes and cuboids in standard units (cm³, m³)
2. Volume as additive: Recognise volume as additive; find volumes of composite solid figures made of two or more non-overlapping right rectangular prisms

5. Measurement and Data · Recognize volume as an attribute of solid figures and understand concepts of volume measurement.

1. Measuring length (age 10+): Recognise volume as an attribute of solid figures; understand that a unit cube (side length 1 unit) has 'one cubic unit' of volume and can be used to measure volume; a solid packed with n unit cubes has volume n cubic units

6. Number and Operations in Base Ten · Solve real-world problems by adding, subtracting, multiplying, and dividing decimals using concrete models or drawings and strategies based on place value, properti

1. Fractions on a number line: Understand and use place value for decimals, measures, and integers of any size; extend the number system to include all positive and negative integers, decimals, and fractions on a single number line

7. Number and Operations in Base Ten · Read, write, and compare decimals to thousandths.

1. Reading and writing numbers (age 10+): Read, write, and compare decimals to thousandths using base-ten numerals, number names, and expanded form; compare using >, =, < based on place-value meaning