Topic Three: Use Place Value to Add and Subtract

Pacing (Duration of Unit):

Desired Results

Transfer:
Standards for Mathematical Practices
1. Make sense of problems and persevere in solving them.
2. Reason abstractly quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Established Goals:
3.NBT.2 Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

3.OA.8 Solve two-step word problems using the four operations. Represent these problems using equations with a letter sanding for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

Student I Can Statements:
  • I can add within 1000 by using an algorithm or strategy based on place value.
  • I can subtract within a 1000 by using an algorithm or strategy based on place value.can choose the correct operation to perform the first computation, and choose the correct operation to perform the second computation in order to solve two-step word problems.
  • I can write equations using a letter for the unknown number.
  • I can decide if my answers are reasonable using mental math and estimation strategies including rounding.


Prerequisite Standards:
2.NBT.6 Add up to four two-digit numbers using strategies based on place value and properties of operations.

2.NBT.7 Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in addition or subtracting three-digit numbers, one adds or subtracts hundred and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decomposed tens or hundreds.

2.NBT.8 Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900.

2.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations.
Big Ideas:
Basic Facts and Algorithms
There is more that one algorithm for each of the operations with rational numbers. Some strategies for basic facts and most algorithms for operations with rational numbers, both mental math and paper and pencil, use equivalence to transform calculations into simpler ones.

Properties
For a given set of numbers there are relationships that are always called properties, and these are the rules that govern arithmetic and algebra.

Practices, Processes, and Properties
Mathematics content and practices can be applied to solve problems.
Essential Questions:
  • What are standard procedures for addition and subtracting whole numbers?
  • What strategies can we use to solve problems?
Students will know...
  • The expanded algorithm for adding 3-digit numbers breaks the addition problem into a series of easier problems based on place value. Answers to the simpler problems are added together to determine the final sum.
  • Models and the standard algorithm for adding 3-digit numbers are just an extension to the hundred place of the models an standard algorithm for adding 2-digit numbers.
  • The expanded algorithm for subtracting 3-digit numbers breaks the subtraction problem into a series of easier problems based on place value. Answers to the simpler problems are used to find the final differences.
  • Models and the standard algorithm for subtracting 3-digit numbers are just an extension to the hundreds place of the models and standard algorithm for subtracting 2-digit numbers.
  • Place-value relationships can help simplify subtracting across zero.
  • There are more whole numbers can be grouped and added in any order.
  • Information in a problem can be often be often shown using a problem. Some problems can be solved by writing and completing a number sentence or equation.


Vocabulary: (Review and reinforce vocabulary from previous topic.)
  • addends
  • sum
  • commutative (order) property of addition
  • Associative property of addition
  • Identity property of addition
  • difference
  • fact family
  • round
  • estimate
  • compatible numbers
  • equation
Students will be skilled at...
  • Solve 3-digit addition problems using an expanded algorithm.
  • Add 3-digit numbers using place-value blocks or pictures and record the results using the standard addition algorithm.
  • Add 3-digit numbers using paper-and-pencil methods and use addition to solve problems.
  • Draw a picture to solve a problem.

Assessment Evidence

Performance Assessment:







Other Evidence:
















Exit Tickets



Learning Plan

Learning Activities:

3-1 The expanded algorithm for adding 3-digit numbers breaks the addition problem into a series of easier problems based on place value. Answers to the simpler problems are added together to determine the final sum.

3-2 Models and the standard algorithm for adding 3-digit numbers are just an extension to the hundred place of the models an standard algorithm for adding 2-digit numbers.

3-3 Models and the standard algorithm for adding 3-digit numbers are just an extension to the hundred place of the models an standard algorithm for adding 2-digit numbers.

3-4 There are more whole numbers can be grouped and added in any order.

3-5 Information in a problem can be often be often shown using a problem. Some problems can be solved by writing and completing a number sentence or equation.

3-6 The expanded algorithm for subtracting 3-digit numbers breaks the subtraction problem into a series of easier problems based on place value. Answers to the simpler problems are used to find the final differences.

3-7 Models and the standard algorithm for subtracting 3-digit numbers are just an extension to the hundreds place of the models and standard algorithm for subtracting 2-digit numbers.

3-8 Models and the standard algorithm for subtracting 3-digit numbers are just an extension to the hundreds place of the models and standard algorithm for subtracting 2-digit numbers.

3-9 Place-value relationships can help simplify subtracting across zero.

3-10 Information in a problem can be often be often shown using a problem. Some problems can be solved by writing and completing a number sentence or equation.
Resources:

Centers




Home School Connection:


Multi-Step Problems:



Teacher Online Videos
Persistence In Problem Solving

Mental Math Videos