How to learn Grade 5: Mathematics

Arizona academic standards: Mathematics, Grade 5

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1. Measurement and Data · Relate volume to the operations of multiplication and addition and solve mathematical problems and problems in real-world contexts 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

2. 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

3. Number and Operations – Fractions · Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.

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

4. Number and Operations – Fractions · Interpret multiplication as scaling (resizing), by:

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

5. Number and Operations – Fractions · Apply and extend previous understandings of multiplication to multiply a fraction by a whole number and a fraction by a fraction.

1. Multiplying fractions: Understand a/b as a multiple of 1/b; multiply proper fractions and mixed numbers by whole numbers, supported by visual models (e.g. 3 × 2/5 = 6/5 = 1 1/5)
2. 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
3. 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
4. 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

6. 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