ALEX Classroom Resource

Students:
When given a variety of two-step word problems involving all four operations,

• Apply understanding of operations to find solutions.
• Use a model to represent the problem situation.
• Write an equation to represent the problem using a symbol for the unknown quantity.
• Explain and justify strategies and solutions.
• Apply understanding of operations and estimation strategies including rounding to evaluate reasonableness of the solution.

Students know:

• Characteristics of addition, subtraction, multiplication, and division.
• Strategies for addition, subtraction, multiplication, and division.
• Strategies for mental computation and estimating sums, differences, products, and quotients.

Students are able to:

• Use a variety of strategies to solve two-step word problems involving all four operations.
• Write an equation to represent the problem context, and use a symbol for the unknown quantity.
• Justify strategy and solutions using mathematical vocabulary.
• Determine and justify reasonableness of solutions using mental computation strategies and estimation strategies.

Students understand that:

• Mathematical problems can be solved using a variety of strategies, models, and representations.
• Contextual situations represented by multiplication and division.
• Reasonableness of solutions can be evaluated by using estimation strategies.

Learning Objectives:
M.3.8.1: Define the identity property of addition and multiplication.
M.3.8.2: Estimating sums and differences using multiple methods, including compatible numbers and rounding, to judge the reasonableness of an answer.
M.3.8.3: Apply commutative, associative, and identity properties for all operations to solve problems.
M.3.8.4: Identify a rule when given a pattern.
M.3.8.5: Solve addition and subtraction problems, including word problems, involving one-and two digit numbers with and without regrouping, using multiple strategies. M 3.8.6: Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
M.3.8.7: Represent multiplication and division with manipulatives.
M.3.8.8: Recall basic addition and subtraction facts.

Students:
When given multi step word problems,

• Solve a variety of multistep word problems involving all four operations on whole numbers including problems where remainders must be interpreted.
• Explain and justify solutions using connections between the problem and related equations involving a single (letter) unknown.
• Evaluate the reasonableness of solutions using estimation strategies.

Note: Multi step problems must have at least 3 steps.

Students know:

• Context situations represented by the four operations.
• How to calculate sums, differences, products, and quotients.
• Estimation strategies to justify solutions as reasonable.

Students are able to:

• Solve multi-step word situations using the four operations.
• Represent quantities and operations physically, pictorially, or symbolically.
• Write equations to represent the word problem and use symbols to represent unknown quantities.
• Use context and reasoning to interpret remainders.
• Use estimation strategies to assess reasonableness of answers by comparing actual answers to estimates.

Students understand that:

• Using problem solving strategies will help them determine which operation to use to solve a problem.
• Remainders must be interpreted based on the context, and remainders are sometimes ignored, rounded up, or partitioned.

Learning Objectives:
M.4.3.1: Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
M.4.3.2: Solve single-step word problems.
M.4.3.3: Recognize key terms to solve word problems.
Examples: in all, how much, how many, in each.
M.4.3.4: Solve division problems without remainders.
M.4.3.5: Recall basic addition, subtraction, and multiplication facts.

Students:

• When given any multi-digit whole number, use place value understanding to round to any place.
• When given a number which is rounded to a place value, identify an unknown number that rounds to that given number.

Example: What are all possible numbers that result in 460 when rounded to the nearest ten? Answer: 455, 456, 457, 458, 459, 460, 461, 462, 463, 464.
• Use rounding in a variety of situations, to include estimating, problem solving, and determining reasonableness of answers.

Note: Expectations are limited to whole numbers less than or equal to 1,000,000.

Students know:

• The relationship among positions of digits in a number and place value. They can use that knowledge to round numbers to nay place.

Students are able to:

• Use place value strategies to round multi-digit whole numbers to any place.

Students understand that:

• rounding multi-digit numbers is an estimation strategy used when writing the original number as the closest multiple of a power of 10.

Learning Objectives:
M.4.9.1: Add and subtract within 1000.
M.4.9.2: Apply signs +, -, and = to actions of joining and separating sets.
M.4.9.3: Add and subtract single-digit numbers.
M.4.9.4: Recall basic addition and subtraction facts.