July 28, 2009

This collection includes lessons on numbers and operations for fifth grade math. All of the lessons are designed using the H.O.P. Centers Framework which is a centers-based system of differentiated instruction. Lessons include student packets, presentations, materials, tips, and answer keys.

- Mathematics > General
- Mathematics > Equations
- Mathematics > Estimation
- Mathematics > Number Sense & Operations
- Mathematics > Problem Solving

- Grade 3
- Grade 4
- Grade 5

Count, read, and write whole numbers to 10,000.

Compare and order whole numbers to 10,000.

Identify the place value for each digit in numbers to 10,000.

Round off numbers to 10,000 to the nearest ten, hundred, and thousand.

Use expanded notation to represent numbers (e.g., 3,206 = 3,000 + 200 + 6).

Find the sum or difference of two whole numbers between 0 and 10,000.

Use the inverse relationship of multiplication and division to compute and check results.

Solve division problems in which a multidigit number is evenly divided by a one-digit number (135 ÷ 5 = __).

Understand the special properties of 0 and 1 in multiplication and division.

Determine the unit cost when given the total cost and number of units.

Solve problems that require two or more of the skills mentioned above.

Compare fractions represented by drawings or concrete materials to show equivalency and to add and subtract simple fractions in context (e.g., 1/2 of a pizza is the same amount as 2/4 of another pizza that is the same size; show that 3/8 is larger than 1/4).

Solve problems involving addition, subtraction, multiplication, and division of money amounts in decimal notation and multiply and divide money amounts in decimal notation by using whole-number multipliers and divisors.

Know and understand that fractions and decimals are two different representations of the same concept (e.g., 50 cents is 1/2 of a dollar, 75 cents is 3/4 of a dollar).

Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns.

Determine when and how to break a problem into simpler parts.

Use estimation to verify the reasonableness of calculated results.

Apply strategies and results from simpler problems to more complex problems.

Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning.

Express the solution clearly and logically by using the appropriate mathematical notation and terms and clear language; support solutions with evidence in both verbal and symbolic work.

Indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy.

Make precise calculations and check the validity of the results from the context of the problem.

Read and write whole numbers in the millions.

Order and compare whole numbers and decimals to two decimal places.

Round whole numbers through the millions to the nearest ten, hundred, thousand, ten thousand, or hundred thousand.

Decide when a rounded solution is called for and explain why such a solution may be appropriate.

Explain different interpretations of fractions, for example, parts of a whole, parts of a set, and division of whole numbers by whole numbers; explain equivalents of fractions (see Standard 4.0).

Write tenths and hundredths in decimal and fraction notations and know the fraction and decimal equivalents for halves and fourths (e.g., 1/2 = 0.5 or .50; 7/4 = 1 3/4 = 1.75).

Write the fraction represented by a drawing of parts of a figure; represent a given fraction by using drawings; and relate a fraction to a simple decimal on a number line.

Use concepts of negative numbers (e.g., on a number line, in counting, in temperature, in "owing").

Identify on a number line the relative position of positive fractions, positive mixed numbers, and positive decimals to two decimal places.

Estimate and compute the sum or difference of whole numbers and positive decimals to two places.

Round two-place decimals to one decimal or the nearest whole number and judge the reasonableness of the rounded answer.

Demonstrate an understanding of, and the ability to use, standard algorithms for the addition and subtraction of multidigit numbers.

Solve problems involving division of multidigit numbers by one-digit numbers.

Understand that many whole numbers break down in different ways (e.g., 12 = 4 x 3 = 2 x 6 = 2 x 2 x 3).

Know that numbers such as 2, 3, 5, 7, and 11 do not have any factors except 1 and themselves and that such numbers are called prime numbers.

Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns.

Determine when and how to break a problem into simpler parts.

Use estimation to verify the reasonableness of calculated results.

Apply strategies and results from simpler problems to more complex problems.

Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning.

Express the solution clearly and logically by using the appropriate mathematical notation and terms and clear language; support solutions with evidence in both verbal and symbolic work.

Indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy.

Make precise calculations and check the validity of the results from the context of the problem.

Estimate, round, and manipulate very large (e.g., millions) and very small (e.g., thousandths) numbers.

Interpret percents as a part of a hundred; find decimal and percent equivalents for common fractions and explain why they represent the same value; compute a given percent of a whole number.

Understand and compute positive integer powers of nonnegative integers; compute examples as repeated multiplication.

Determine the prime factors of all numbers through 50 and write the numbers as the product of their prime factors by using exponents to show multiples of a factor (e.g., 24 = 2 x 2 x 2 x 3 = 2³ x 3).

Identify and represent on a number line decimals, fractions, mixed numbers, and positive and negative integers.

Add, subtract, multiply, and divide with decimals; add with negative integers; subtract positive integers from negative integers; and verify the reasonableness of the results.

Demonstrate proficiency with division, including division with positive decimals and long division with multidigit divisors.

Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns.

Determine when and how to break a problem into simpler parts.

Use estimation to verify the reasonableness of calculated results.

Apply strategies and results from simpler problems to more complex problems.

Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning.

Express the solution clearly and logically by using the appropriate mathematical notation and terms and clear language; support solutions with evidence in both verbal and symbolic work.

Indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy.

Make precise calculations and check the validity of the results from the context of the problem.

names whole numbers combining three-digit numeration (hundreds, tens, ones) and the use of number periods, such as ones, thousands, and millions and associates verbal names, written word names, and standard numerals with whole numbers, commonly used fractions, decimals, and percents.

understands the relative size of whole numbers, commonly used fractions, decimals, and percents.

understands concrete and symbolic representations of whole numbers, fractions, decimals, and percents in real-world situations.

understands that numbers can be represented in a variety of equivalent forms using whole numbers, decimals, fractions, and percents.

uses place-value concepts of grouping based upon powers of ten (thousandths, hundredths, tenths, ones, tens, hundreds, thousands) within the decimal number system.

understands and explains the effects of addition, subtraction, and multiplication on whole numbers, decimals, and fractions, including mixed numbers, and the effects of division on whole numbers, including the inverse relationship of multiplication and division.

selects the appropriate operation to solve specific problems involving addition, subtraction, and multiplication of whole numbers, decimals, and fractions, and division of whole numbers.

adds, subtracts, and multiplies whole numbers, decimals, and fractions, including mixed numbers, and divides whole numbers to solve real-world problems, using appropriate methods of computing, such as mental mathematics, paper and pencil, and calculator.

uses and justifies different estimation strategies in a real-world problem situation and determines the reasonableness of results of calculations in a given problem situation.

understands and applies basic number theory concepts, including primes, composites, factors, and multiples.