Fluently add and subtract multi-digit whole numbers using the standard algorithm.
[divider] [/divider] Students are able to…
- Apply previous understanding of work with addition and subtraction models and strategies to current work.
- Utilize an efficient strategy with accurate results.
- Explain the steps in the standard algorithm, showing a place value understanding of why the strategy works.
- Use mental strategies when appropriate.
[divider] [/divider] Students are able to…because teachers:
- Provide a variety of real world problem solving situations for students to interact with.
- Facilitate discussions that allow students to make connections to various strategies and models.
- Pose problems that promote the use of strategies and flexible thinking of numbers.
- Have students explain and record the steps they took to find their solution and check for reasonableness.
[divider] [/divider] Questions to ask students:
- What happens when you don’t have enough (ones, tens, hundreds, etc.) in a number to subtract?
- Sample answer that indicates understanding: You can regroup the number in the next place value (to the left) by taking one away and adding ten to the place value to the right.
- Sample answer that indicates an incomplete understanding or a misconception: You cross it out and add 1 on top.
- Ask students to describe how they know that the sum of 4,789 and 4,216 will be less than 10,000.
- Sample answer that indicates understanding: I know both numbers are less than 5,000 so if you add them together it will be less than 10,000. OR… I estimated 4,789 to 5,000 and 4,216 to 4,000. 5,000+4,000=9,000 and 9.000 is less than 10,000.
- How does your model relate to the problem?
- Sample answer that indicates understanding: Student accurately describes how the model represents the numbers and the actions of subtracting/adding using place value language of ones/tens/hundreds/thousands/etc.
- How does place value play a role in the traditional algorithm of addition or subtraction?
- Sample answer that indicates understanding: Student accurately describes the steps of the traditional algorithm using place value language of: ones/tens/hundreds/thousands/etc.
- Point to a number that has been regrouped and ask, “What is the value of the number placed on the top of the algorithm?”
- Sample answer that indicates understanding: It has a value of 100 because it is a 1s digit in the hundreds place.
- Sample answer that indicates an incomplete understanding or a misconception: It has a value of 1. -or- I carried the one.
[divider] [/divider] FSA Notes
Cognitive Complexity Level: 1 – Recall
Achievement Level Descriptors:
2-adds and subtracts two multi-digit whole numbers using the standard algorithm (not including subtraction across zeros)
3-fluently adds up to three and subtracts two multi-digit whole numbers using the standard algorithm
4-determines the missing digit(s) within the addend in an addition or subtraction problem
5-analyzes and describes an error in a strategy and shows the correct solution
Assessment Limits:
Items may only contain whole number factors and solutions greater than 1,000 and within 1,000,000.
Addition expressions may contain up to three addends.
[divider] [/divider] Additional Resources:
Additional in depth content knowledge:
Blog Post: The struggle can be real when subtracting!
Video: Regrouping Twice – Khan Academy
[divider] [/divider] Sample Formative Assessment Tasks:
Resources/Tasks to Help Your Child at Home:
Using a deck of cards, create two 6-digit numbers. Estimate the sum and difference of the numbers. Then have your child use the place value language of: ones, tens, hundreds, thousands, ten thousands and hundred thousands to describe the steps they will take using the standard algorithm to solve for the actual sum and difference. You could also use a place value chart to focus on lining up the place values of both numbers.
Khan Academy: Relate Place Value to Standard Algorithm for Multi-Digit Addition https://goo.gl/T5X448
Khan Academy: Relate Place Value to Standard Algorithm for Multi-Digit Subtraction https://goo.gl/j13fHf
Khan Academy: Round to Estimate Sums https://goo.gl/c4euBF