In this interactive activity, students will be led through steps to estimate numbers by rounding in order to make problems easier to solve. There are teaching activities as well as practice activities available. A handout that reviews the strategies taught during the activity can be printed. After utilizing this resource, the students can complete the short quiz to assess their understanding.

Content Standard(s):

Mathematics MA2019 (2019) Grade: 3

8. Determine and justify solutions for two-step word problems using the four operations and write an equation with a letter standing for the unknown quantity. Determine reasonableness of answers using number sense, context, mental computation, and estimation strategies including rounding.

Unpacked Content

Evidence Of Student Attainment:

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.

Teacher Vocabulary:

Unknown quantity

Mental computation

Estimation

Variable

Reasonableness

Rounding

Expression

Equation

Knowledge:

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.

Skills:

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.

Understanding:

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.

Diverse Learning Needs:

Essential Skills:

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.

Prior Knowledge Skills:

Explain addition and subtraction problems using concrete objects, pictures.

Use multiple strategies to add and subtract including counting on, counting back and using doubles.

Create a number pattern.

Use multiple strategies to add and subtract including counting on, counting back and using doubles.

Recall single-digit subtraction facts.

Recall single-digit addition facts.

Alabama Alternate Achievement Standards

AAS Standard: M.AAS.3.7 Demonstrate fluency of multiplication using skip counting, multiples of numbers, number charts, arrays, etc.

Mathematics MA2019 (2019) Grade: 4

3. Determine and justify solutions for multi-step word problems, including problems where remainders must be interpreted.

a. Write equations to show solutions for multi-step word problems with a letter standing for the unknown quantity.

b. Determine reasonableness of answers for multi-step word problems, using mental computation and estimation strategies including rounding.

Unpacked Content

Evidence Of Student Attainment:

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.

Teacher Vocabulary:

Operation

Multi Step problem

Remainder

Unknown quantity

Equation

Rounding

Mental strategy

Partition

Estimation

Reasonableness

Knowledge:

Students know:

Context situations represented by the four operations.

How to calculate sums, differences, products, and quotients.

Estimation strategies to justify solutions as reasonable.

Skills:

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.

Understanding:

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.

Diverse Learning Needs:

Essential Skills:

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.

Prior Knowledge Skills:

Demonstrate computational understanding of multiplication and division by solving authentic problems with multiple representations using drawings, words, and/or numbers.

Identify key vocabulary words to solve multiplication and division word problems. Examples: times, every, at this rate, each, per, equal/equally, in all, total.

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.

Recall basic multiplication facts.

Add and subtract within 20.

Represent repeated addition, subtraction, and equal groups using manipulatives.

Distinguish between rows and columns.

Use repeated addition to solve problems with multiple addends.

Count forward in multiples from a given number. Examples: 3, 6, 9, 12; 4, 8, 12, 16.

Recall doubles addition facts.

Model written method for composing equations.

Alabama Alternate Achievement Standards

AAS Standard: M.AAS.4.1 Solve one-step word problems involving real-life situations using the four operations within 100 without regrouping and select the appropriate method of computation when problem solving.

Mathematics MA2019 (2019) Grade: 4

9. Round multi-digit whole numbers to any place using place value understanding.

Unpacked Content

Evidence Of Student Attainment:

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.

Teacher Vocabulary:

Round

Place value

Ones

Tens

Hundreds

Thousands

Ten thousands

Approximately

Halfway point

Knowledge:

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.

Skills:

Students are able to:

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

Understanding:

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.

Diverse Learning Needs:

Essential Skills:

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.

Prior Knowledge Skills:

Define the commutative and associative properties of addition and subtraction.

Subtract within 100 using strategies and algorithms based on the relationship between addition and subtraction.

Subtract within 100 using strategies and algorithms based on properties of operations.

Subtract within 100 using strategies and algorithms based on place value.

Add within 100 using strategies and algorithms based on the relationship between addition and subtraction. Add within 100 using strategies and algorithms based on properties of operations.

Add within 100 using strategies and algorithms based on place value.

Recall basic addition and subtraction facts.

Define regrouping, total, sum, difference and solve.

Add and subtract two two-digit numbers with and without regrouping.

Determine the value of the number in the ones, tens, hundreds and thousands place using concrete models or drawings and strategies based on place value.

Match the number in the ones, tens, hundreds and thousands position to a pictorial representation or manipulative of the value.

Alabama Alternate Achievement Standards

AAS Standard: M.AAS.4.9 Round a whole number from 1 to 49 to the nearest ten (using a number line and hundreds chart.)