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