Unit 1

Place Value, Rounding, and Algorithms for Addition and Subtraction

Math

Description:

In unit 1, students will work with whole numbers less than or equal to 1,000,000.  They will develop their understanding of place value related to multiplying and dividing by multiples of 10.  Students will read and write multi-digit whole numbers in different forms, round and compare two whole numbers using appropriate symbols. Place value charts, number lines and hundreds charts are the tools students will use.  Students will master the standard algorithm for addition and subtraction. Students will create and extend number and shape patterns.

Students should solve multi-step word problems. Students will represent the problems using equations with a variable, and will verify solutions using various estimation strategies and mental computation.   Extending students previous understanding of perimeter of rectangles is one way of developing such understanding (3.MD.D.8).

Louisiana Student Standards for Mathematics (LSSM)

 Number and Operations in Base Ten Generalize place value understanding for multi-digit whole numbers. 4.NBT.1 Recognize that in a multi-digit whole number less than or equal to 1,000,000, a digit in one place represents ten times what it represents in the place to its right. For example, (1) recognize that 700 ÷ 70 = 10; (2) in the number 7,246, the 2 represents 200, but in the number 7,426 the 2 represents 20, recognizing that 200 is ten times as large as 20, by applying concepts of place value and division. 4.NBT.2 Read and write multi-digit whole numbers less than or equal to 1,000,000 using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. 4.NBT.3 Use place value understanding to round multi-digit whole numbers, less than or equal to 1,000,000, to any place. Use place value understanding and properties of operations to perform multi-digit arithmetic. 4.NBT.4 Fluently add and subtract multi-digit whole numbers with sums less than or equal to 1,000,000, using the standard algorithm. Operations and Algebraic Thinking Use the four operations with whole numbers to solve problems. 4.OA.1 Interpret a multiplication equation as a comparison and represent verbal statements of multiplicative comparisons as multiplication equations, e.g., interpret 35 = 5 × 7 as a statement that is 35 is 5 times as many as 7, and 7 times as many as 5. 4.OA.3 Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Example: Twenty-five people are going to the movies. Four people fit in each car. How many cars are needed to get all 25 people to the theater at the same time? Operations and Algebraic Thinking Generate and analyze patterns. 4.OA.5 Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.

Enduring Understandings:

Place value is crucial when operating with numbers.

Estimation helps me see whether or not my answer is reasonable.

Knowing the value of the digits helps me compare numbers.

It is important to understand that the place of a digit represents 10 times the value of what it represents in the place to its right.

Composing and decomposing numbers helps me to add and subtract using a standard algorithm.

Addition and subtraction are inverse operations; one undoes the other.

Knowing when to add and subtract helps me solve one and multi-step problems.

Essential Questions:

·         What type of situations do we add and subtract?

·         How do we round numbers up to the hundred thousand place?

·         How is rounding used in everyday life?

·         How are addition and subtraction alike? How are they different?

·         How do I compose and decompose numbers when using a standard algorithm?

·         How can I use what I know about addition and subtraction to help me solve real world problem?