Year Four - Using Operations Flexibly
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About this Big Idea
In this Big Idea students are asked to choose and justify the mathematical methods and operations that they select. Working with visuals, students use estimation skills in conjunction with operations of their choosing to determine quantities. Students develop an undestadning of the importance of making good estimates and of using estimates in their mathematical thinking.
Understanding Goals:
Students will understand:
- the uses of each operation in mathematics
- the value of making estimates when working mathematically
- mathematical choices they make when problem solving
Background:
By the end of Stage 2, students ask questions and use efficient mental and written strategies with increasing fluency to solve problems. Students use appropriate terminology to describe and link mathematical ideas, check statements for accuracy and explain their reasoning. It is important that students apply and extend their repertoire of mental strategies for the four operations. Comparing their own method of solution with the methods of other students will lead to the identification of efficient mental and written strategies. One problem may have several acceptable methods of solution.
Core Content from the Syllabus:
Working Mathematically
Addition & Subtraction
- apply known single-digit addition and subtraction facts to mental strategies for addition and subtraction of two-, three- and four-digit numbers
- choose and apply efficient strategies for addition and subtraction (Problem Solving)
- discuss and compare different methods of addition and subtraction (Communicating)
- give a reasonable estimate for a problem, explain how the estimate was obtained, and check the solution (Communicating, Reasoning)
Multiplication & Division
- uses mental and informal written strategies for multiplication and division
- find 'multiples' for a given whole number, eg the multiples of 4 are 4, 8, 12, 16
- relate multiplication facts to their inverse division facts
- determine 'factors' for a given whole number, eg the factors of 12 are 1, 2, 3, 4, 6, 12
Language:
- plus, add, addition, minus, the difference between, subtract, subtraction, equals, is equal to, is the same as, number sentence, multiply, multiplied by, multiplication, multiplication facts, double, shared between, divide, divided by, division, equals, strategy.
Connected to:
Mindset Mathematics Learning Activities
Visualise
In this lesson, students estimate the size of crowds from aerial photos. Thinking flexibly about operations means crafting a multistep plan employing whatever operations are useful. Estimating large quantities that cannot be counted gives students a space to make and try such plans. - See page 205
Questions for reflection:
- How did you arrive at your estimates? What methods did you develop?
- How did you decide to use the operations you did? Why did they make sense in your plan?
- Did anyone try something that didn't work?
- What did you try? How did you know it wasn't working? What did you try next?
- How did you keep track of your work? How did you organize your thinking on paper?
- How did you decide what operations to use to come up with your estimates?
Play
Students play the game Target 20, in which players roll four dice and use operations to combine the results to get as close to 20 as they can. Students are challenged to think flexibly about using operations and how choosing different operations can lead to different outcomes. - See page 213
Questions for reflection:
- What strategies did you develop for getting close to 20?
- How did you choose which operations to use? How did you choose what order these operations should go in?
- What was the most creative equation you came up with? What makes you say that?
- What equations did your partner come up with that surprised you? What makes you say that?
- What advice would you offer someone who is learning to play this game?
- What questions do you still have?
Investigate
Students extend their work with multistep problem solving and estimation to figure out how many boxes of pencils the class would use in a school year. - See Page 218
- Does their strategy make sense? Can you follow all the steps?
- Could you explain what they did to someone else?
- Is their method convincing?
- Do you disagree with any part of the process? If so, why?
- Is there something they could have done to make their estimate more accurate? If so, what and why?
Credit:
Boaler, Munson & Williams (2018) - Mindset Mathematics: Visualizing and investigating big ideas Grade 5
NESA - Mathematics K-10 - 2012
