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Addition Strategies
Task
Craig documented Moses' use of a splitting and moving strategies. You can review descriptions of these strategies and other addition strategies here.
Now let's give you a chance to try your hand at documenting addition strategies.
Solve the following problem mentally in as many different ways as you can.
Have a partner document one of the strategies (e.g., with a number line or flow chart) you used to solve this problem.
Switch. You document one of your partner's strategies.
- How would you explain to a colleague (who has not done this activity) the relationship basic facts and place value have with effectively using an addition strategy?
- What are some questions you have about documenting student use of addition strategies?
Watch
Subtraction Strategies
Task
Craig and Moses describe several subtraction strategies that students could use. You can review descriptions of these subtraction strategies here.
Now let's give you a chance to try your hand at documenting subtraction strategies.
Solve the following problem mentally in as many different ways as you can.
Have a partner document one of the strategies (e.g., with a number line or flow chart) you used to solve this problem.
Switch. Now you document one of your partner's strategies.
Discuss:
- How would you explain to a colleague (who has not done this activity) the relationship basic facts, place value and operation sense have with effectively using an subtraction strategy?
- What are some questions you have about documenting student use of addition strategies?
Watch
Algorithms and the Importance of Place Value
Discuss
The "Standard" Algorithms for addition and subtractions are in reality simply organizers to track a mental strategy based on place value. They both start from the right and use "regrouping" when a single place value column cannot accommodate the computation. It is not the "best" or "right" strategy just as it is not a "bad" strategy. It is simply one strategy and, like any other strategy, it is only useful if it is meaningful and efficient. It must be understood to have power.
- In your opinion, what is the place of the standard algorithm in today's math classroom?
- What instructional tips would you offer to the educator who is planning a lesson on the addition and subtraction algorithm?
Record your thoughts and perspectives in a Section 2.3 of the digital handout.
Want to dig deeper?
Read the excellent article on Algorithms and Estimation in The Guide to Effective Instruction in Mathematics, Kindergarten to Grade 6: Volume 5, Teaching Basic Facts and Multidigit Computations (Click here to view pages 52-56).
Wondering what your students might be thinking about Place Value?
Download similar place value tasks to those you saw on the video. Gain some insight into the extent your students are attending to face-value or place-value when they think about numbers.
Remember not to use theses diagnostic tasks for teaching; give the task, analyze the results and plan for instructional next steps using different learning activities. If you do not "poison" the task by teaching students how to get the right answer, you can reuse the task later to measure growth.
Sample Tasks
Watch
(Optional)
Extending Computation Strategies to Fractions
Discuss
Which ideas from Sessions 1 and 2 could you use to help students better understand addition and subtraction with fractions?
What commonalities exist between operating with whole numbers and operating with fractions? How might you make these connections explicit?
What is the role of mental strategies vs standard algorithms when calculating with fractions? How might you help students build computational strategies that are flexible, portable, efficient and accurate to the degree necessary?
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