Discovering Area Relationships

  • Activities with Rigor and Coherence (ARCs) / Discovering Area Relationships
  • Discovering Area Relationships of Polygons

    6th grade

    Description

    Students discover the area formulas for triangles, parallelograms, and trapezoids. They apply formulas to find areas of irregular shapes.

    Hook

    This can be done as a whole class or with partners. Project (or provide copies) of the "Cork Costs" graphic. Ask students: What do you notice? What do you wonder?

    calculating cork cost from area

    Lessons

    Lesson 1 of 4

    Students develop the area of triangles formula using the area of rectangles and by comparing triangles with equal bases and heights.

    Lesson 2 of 4

    Students use prior knowledge of the area formula for rectangles and triangles to discover the formula for the area of parallelograms.

    Lesson 3 of 4

    Students explore several strategies for calculating the area of a trapezoid while discovering the area formula for trapezoids.

    Lesson 4 of 4

    Students will estimate the area of irregular shapes and use a process of decomposition to calculate the areas of irregular polygons.

    ARC Assessement

    Technology Resources


  • Comments

  • 2 Comments

    • Avatar

      Error- the essential questions and connecting standards on the right hand side of the webpage for discovering area is for a different ARC -

    • Avatar

      Some HOOK suggestions:
      a Which Ones Doesn't Belong activity; "square peg in a round hole" clip from Apollo 13 movie would need an intro to the Apollo 13 story and that "round" is not part of this lesson;
      more» href="https://nrich.maths.org/7019" title="https://nrich.maths.org/7019" class="EkForceWrap" onclick="window.open(this.href); return false;">https://nrich.maths.org/7019«less

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  • ARC Global Essential Question(s)

    How can you build the longest bungee cord for Barbie that keeps her safe?

    Keywords

    Barbie bungee, linear regression, modeling, scatter plot, outlier, line of best fit (least squares regression line), residual, slope, y-intercept, correlation, causation, correlation coefficient, sum of the area of squared residuals, interpolation, extrapolation, prediction

    Vocabulary

    • scatter plot
    • outliers
    • line of best fit (least squares regression line)
    • residual
    • slope
    • y-intercept
    • correlation
    • causation
    • correlation coefficient
    • sum of the area of the squared residuals
    • interpolation
    • extrapolation
    • prediction

    Standards

    CCSS, Content Standards to Domain Level

    • 8.SP.A.1 Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.
    • 8.SP.A.2 Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.
    • 8.SP.A.3 Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept.
    • S-ID.B.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
    • S-ID.B.6.a Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.
    • S-ID.B.6.b Informally assess the fit of a function by plotting and analyzing residuals.
    • S-ID.B.6.c Fit a linear function for a scatter plot that suggests a linear association.
    • S-ID.C.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
    • S-ID.C.8 Compute (using technology) and interpret the correlation coefficient of a linear fit.
    • S-ID.C.9 Distinguish between correlation and causation.
    • F.IF.B.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

    CCSS, Standards for Mathematical Practices

    • SMP 1 Make sense of problems and persevere in solving them.
    • SMP 2 Reason abstractly and quantitatively.
    • SMP 3 Construct viable arguments and critique the reasoning of others.
    • SMP 4 Model with mathematics.
    • SMP 5 Use appropriate tools strategically.

    Effective PtA, highlighted Effective Teaching Practice and/or Guiding Principle CCSS

    • Implement tasks that promote reasoning and problem solving.
    • Use and connect mathematical representations.
    • Facilitate meaningful mathematical discourse.
    • Pose purposeful questions.
    • Elicit and use evidence of student thinking.

    Contributors

    Original author: Samuel E. Zordak
    Illuminations lesson: Barbie Bungee
    CRDT team: Luke Wilcox, Deidra Baker, Jerel Welker, Michelle Greene and Lindsey Gallas