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    • ▾5th grade
      • ▸Decimal place value
        • •Decimal place value
        • •Hashi puzzles
        • •Decimals to thousandths
        • •Rounding decimals
      • ▸Multi-digit multiplication and division
        • •Multiplying whole numbers by 10, 100, and 1000
        • •Multiplying and dividing decimals by 10, 100, and 1000
        • •Convert fractions to decimals, 10, 100, or 1000 in the denominator
        • •Multiplication, partial products method
        • •Long division
      • ▸Decimal arithmetic
        • •Decimal arithmetic
        • •Dividing whole numbers to get a decimal
      • ▸Add and subtract fractions
        • •Add and subtract fractions, abstract
        • •Adding and subtracting mixed numbers with regrouping
        • •Add and subtract fractions, word problems
      • ▸Multiply fractions
        • •Multiplication as scaling
        • •Areas and perimeters, fractional side lengths
        • •Multiply fractions, abstract
        • •Multiply fractions, word problems
      • ▸Divide fractions
        • •Understanding fractions as division, word problems
        • •Dividing whole numbers by unit fractions
        • •Dividing unit fractions by whole numbers
        • •Dividing mixed numbers
      • ▸Volume
        • •Volume by counting unit cubes
        • •Volume of right rectangular prisms by multiplying
        • •Volume of composite right rectangular prisms
        • •Volume, word problems
      • ▸Coordinate plane
        • •Plot coordinates
        • •Plot coordinates from word problems
      • ▾Algebraic thinking
        • •Intro to parentheses
        • •Distributive property without variables
        • •Convert between words and arithmetic expressions
        • •Linear equations, tables
      • ▸Measurement and data
        • •Unit conversion
        • •Represent and reason with line plots
      • ▸Properties of shapes
        • •Geometric definitions
        • •Classifying shapes
        • •Classifying triangles
        • •Classifying polygons
        • •Symmetries of regular polygons
        • •Quantifiers
     › 5th grade › Algebraic thinking

    Linear equations, tables

    Complete tables involving two variables. Rule can be multiply by a constant or add a constant. For example, to find y, add 2 to x. The problem would be given as follows:
    $$\begin{array}{c|c} x & y \\ \hline 2 & \\ 4 & \\ 6 & \end{array}$$ Graph a given rule as a line, or plot ordered pairs from a table, as directed.

    Watch these Khan Academy videos:

    • Graphing patterns on coordinate plane
    • Graphing sequence relationships
    • Interpreting patterns on coordinate plane
    • Interpreting relationships in ordered pairs

    Do these Khan Academy exercises:

    • Relationships between 2 patterns
    • Tables from rules that relate 2 variables
    • Graphs of rules that relate 2 variables
    • Rules that relate 2 variables

    Next, give your students these challenges:

    • 2019 Math Kangaroo Levels 1-2 Problem #20 by STEM4all
    • Data Shapes by NRICH

    Conclude by leading this investigation:

    Constellations
    by MathPickle

    5.OA.B.3: Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule "Add 3" and the starting number 0, and given the rule "Add 6" and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.

    Lessons and practice problems