How to learn Grade 5: Mathematics
Wyoming academic standards: Mathematics, Grade 5
0 of 13 concepts ready to learn · Markdown, for your AI
1. Number And Operations - Fractions · The Proficient student is able to extend the concept of division to divide unit fractions and whole numbers by using visual fraction models and equations.
- 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
- Dividing by Fractions: Interpret and compute division of a whole number by a unit fraction (e.g. 4 ÷ 1/5 = 20); use visual models and the relationship between multiplication and division to explain why the quotient is larger than the dividend
2. Number And Operations - Fractions · Justify the reasonableness of a product when multiplying with fractions.
- 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
- Adding fractions (different denominators): Add and subtract fractions with denominators that are multiples of the same number by finding a common denominator
3. Number And Operations - Fractions · Extend the concept of multiplication to multiply a fraction or whole number by a fraction.
- 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
- Multiplying fractions (age 11+): Interpret fractions and percentages as operators — find a fraction or percentage of an amount by multiplying, understanding that 'of' means multiply (e.g., 3/4 of 200 = 3/4 × 200 = 150)
4. Geometry · May be able to identify the components of a coordinate system with partial success.
- Numbers on a number line: Understand a coordinate system defined by two perpendicular number lines (axes) with an origin at (0,0); know that an ordered pair (x, y) specifies a unique point where the first number gives horizontal distance and the second gives vertical distance from the origin
- Coordinate Transformations: Identify properties of translations, rotations, and reflections; describe and perform these transformations on given figures, and understand that the image is congruent to the original
5. Geometry · Understand a coordinate system.
- Plotting points in the first quadrant: Plot and read ordered pairs in the first quadrant of the coordinate plane; represent real-world and mathematical problems by graphing points and interpreting coordinate values in context
6. Measurement And Data · Relate volume to the operations of multiplication and solve real-world and mathematical problems involving volume.
- 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)
- Volume as additive: Recognise volume as additive; find volumes of composite solid figures made of two or more non-overlapping right rectangular prisms
7. Number And Operations In Base Ten · Read, write, and compare decimals to thousandths.
- 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
8. Operations And Algebraic Thinking · Generate two numerical patterns with each pattern having its own rule. Explain informally the relationship(s) between corresponding terms in the two patterns.
- Number Pattern Relationships: Generate two numerical patterns using two given rules; identify relationships between corresponding terms; form ordered pairs and graph them on a coordinate plane