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Engaging Open Tasks for Mathematics Learning: Strategies with Decimals and Fractions

This resource by Lisa Lunney Borden presents innovative open tasks designed for students to explore mathematical concepts creatively. With an emphasis on decimals and fractions, tasks encourage multiple approaches and solutions. Students model decimals using base ten blocks, create unique fraction representations, and investigate geometrical shapes. Collaborative sharing and group discussions enhance learning. The open-ended nature of the tasks fosters inquiry and critical thinking, allowing students to engage deeply with mathematical ideas while developing a variety of problem-solving strategies.

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Engaging Open Tasks for Mathematics Learning: Strategies with Decimals and Fractions

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  1. Designing Tasks for All Students Lisa Lunney Borden MTA 2008

  2. An Open Task: • Open in Process • Many paths to the answer • Open in Product • Many possible answers • Opens up with ‘what if’ variations • Can open up into new explorations

  3. An Open Task: Decimals • Model each decimal with base ten blocks. Make a sketch to record your work. a) O.46 b) 3.04 c) 1.9 d) 1.09 e) 3.35From Math Makes Sense 5, page 118 • Opening it up… • If the flat represents 1, use flats, rods and little cubes to build a robot model. Record a picture of your model and the value as a decimal number. • Repeat two more times. Share with a partner. Share with the group.

  4. An Open Task: Partitioning Numbers • Give students a number of counters (6, 7, 8 or 9) and ask them to build different addition facts and record them.

  5. An Open Task: Partitioning Numbers (continued)

  6. An Open Task: Equivalent Fractions • Think of a fraction. • Model that fraction using your materials at your table. Try to find as many different models as possible. • Record pictures of your model on your page. • Share with your partner. • Share with the whole group.

  7. Example Spaces: Quadrilaterals • Draw a figure that has four sides • Draw another. • Draw one that is really different than the first two.

  8. Example Spaces: Area • Think of a shape with an area of 24 cm2. • Think of another. • Think of one that is really different than the first two.

  9. Verbal: Explain it in Words Concrete: Use Concrete Materials to Build It Contextual: Write a Story Problem Pictorial: Draw a Picture Model Symbolic: Write it in Mathematical Symbols Multiple Representations

  10. Learning Centers: 2-Digit Addition and Subtraction

  11. Learning Centers: Mixed and Improper Fractions • Building Models • Comparing Improper Fractions • Fraction Models • Mixed Number Pictures • Explaining Your Strategy

  12. Learning Centers: Multiplication and Division • Division Stories • Going to the Fair • The Division Debate • Multiplication and Division Word Problems • Paper Clip Chains • Multiplication and Division Arrays • Making My Own Study Cards

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