Domain:
Number and Operations-Fractions |
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Teacher Notes/Fifth Grade Home
5.NF.A.1 5.NF.A.2 5.NF.B.3 5.NF.B.4 5.NF.B.4.A 5.NF.B.4.B 5.NF.B.5.A 5.NF.B.5.B 5.NF.B.6 5.NF.B.7
Essential Skills and Knowledge | Teacher Resources | Student Resources |
Use equivalent fractions as a strategy to add and subtract fractions. | ||
5.NF.A.1 | ||
Add and subtract fractions with unlike denominators (including mixed
numbers) by replacing given fractions with equivalent fractions in such
a way as to produce an equivalent sum or difference of fractions with
like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) "I Can" Statements I can add and subtract fractions with unlike denominators. I can make equivalent fractions to add and subtract fractions. |
Mondrian and Creating Fractions Arts Intergration Activity focusing on creating equivalent fractions. ![]() ![]() Note: Login to Discovery Streaming Education before selecting links. Running Time: 6:53 minutes ![]() This flow map walks through the steps of find a common denominator. ![]() This notebook walks through the steps of subtracting mixed numbers. ![]() This notebook walks through the steps of adding mixed numbers. ![]() (Login to LearnZillion before selecting the link) ![]() (Login to LearnZillion before selecting the link) ![]() (Login to LearnZillion before selecting the link) ![]() (Login to LearnZillion before selecting the link) ![]() |
Your Turn - Mondrian Activity Arts Integration Activity: Create a Mondrian syle artwork to demonstrate equivalent fractions. ![]() In this game, students will practice adding and subtracting fractions. Subtracting Unlike Fractions Use a model to subtract unlike fractions. Fishy Fractions - Subtracting Unlike Denominators Beware... this is a challenging site. Use your skills to scoop up the correct difference by adding the fractions with unlike denominators. Remember they must be in simplest form. Fishy Fractions - Adding Unlike Denominators Beware... this is a challenging site. Use your skills to scoop up the correct sum by adding the fractions with unlike denominators. Remember they must be in simplest form. Subtracting Mixed Numbers Use a model to rename mixed numbers and subtract. Fishy Fractions - Subtracting Mixed Numbers Beware... this is a challenging site. Use your skills with mixed numbers to beat the clock. Remember they must be in simplest form. Fishy Fractions - Adding Mixed Numbers Beware... this is a challenging site. Use your skills with mixed numbers to beat the clock. Remember they must be in simplest form. Fruit Splat Practice your addition and subtraction of fractions while squishing some fruit! Unique Fraction Game Use your knowledge of addition, subtraction, and equivalent fractions to move your pieces across the board. ![]() ![]() |
5.NF.A.2 | ||
Solve word problems involving addition and subtraction of fractions
referring to the same whole, including cases of unlike denominators,
e.g., by using visual fraction models or equations to represent the
problem. Use benchmark fractions and number sense of fractions to
estimate mentally and assess the reasonableness of answers.
For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. "I Can" Statements I can solve word problems invovling addition and subtraction of fractions using visuals, models, and/or equations. I can use benchmark fractions and my number sense to estimate the reasonableness of answer. |
![]() (Login to LearnZillion before selecting the link) ![]() (Login to LearnZillion before selecting the link) ![]() (Login to LearnZillion before selecting the link) ![]() (Login to LearnZillion before selecting the link) ![]() (Login to LearnZillion before selecting the link) |
Ice Cream Shop Practice your mixed numbers while making ice cream for customers. ![]() ![]() Create a "two" pager in pixie that explains how to solve addition and subtraction of fractions problems. Use word problems and basic computation problems to show your learning! Follow the directions in the pixie. ![]() ![]() Use this pixie to draw visuals for each word problem you solve. Then create your own word problems to model and solve! |
Apply and extend previous understandings of multiplication and division. | ||
5.NF.B.3 | ||
Interpret a fraction as division of the numerator by the denominator (a/b
= a ÷ b). Solve word problems involving division of whole
numbers leading to answers in the form of fractions or mixed numbers,
e.g., by using visual fraction models or equations to represent the
problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? "I Can" Statements I can interpret a fraction as division of the numerator by the denominator. I can sovle word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers. I can use visuals, models, and/or equations to represent a problem involving fractions. |
![]() Note: Login to Discovery Streaming Education before selecting links. Running Time: 2:27 minutes ![]() Identify how fractions relate to whole number, the notebook includes a quiz. ![]() (Login to LearnZillion before selecting the link) ![]() (Login to LearnZillion before selecting the link) ![]() (Login to LearnZillion before selecting the link) ![]() (Login to LearnZillion before selecting the link) |
![]() Model and Solve Word Problems Start by clicking on "Start Modeling". Visualizing Fractions Show the given fraction on the shape by dividing the shape. ![]() ![]() Using this Smart Notebook as a center, answer the following questions through building models and quizzing a partner! |
5.NF.B.4 | ||
Apply and extend previous understandings of multiplication to multiply a
fraction or whole number by a fraction. "I Can" Statements I can multiply a fraction, or whole number, by a fraction by using my understandings of multiplication. |
![]() ![]() This slideshow gives instruction on multiplying a fraction times a whole number and features a quiz as well. Multiplying Fractions Use a model to multiply two fractions. (Note: The visual representation colors and the factor color are opposite.) ![]() Practice multiplying fractions with football situations. ** |
![]() In this millionaire game, you will practice multiplying fracions and writing the answer in simpliest form. Multiplying Fractions Soccer Game Score goals by finding fraction products. Multiplying Fractions Game Practice your multiplying skills with this game. |
5.NF.B.4.A | ||
Interpret the product (a/b) × q as a parts of a
partition of q into b equal parts; equivalently, as the
result of a sequence of operations a × q ÷
b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) "I Can" Statements I can create a story context for equations involving multiplication of fractions by whole numbers. |
How to Multiply Fractions Utilize this resource to introduce multiplying fractions using a visual model. ![]() (Login to LearnZillion before selecting the link) ![]() (Login to LearnZillion before selecting the link) |
Multiplying Fractions with Circle Models - Visual Fractions Use the circle models to determine all parts of the equation. Multiplying Fractions with Rectangle Models - Visual Fractions Use the rectangle models to determine all parts of the equation. |
5.NF.B.4.B | ||
Find the area of a rectangle with fractional side lengths by tiling it
with unit squares of the appropriate unit fraction side lengths, and show
that the area is the same as would be found by multiplying the side
lengths. Multiply fractional side lengths to find areas of rectangles, and
represent fraction products as rectangular areas. "I Can" Statements I can find the area of a rectangle, with fractional side lengths, by tiling it with unit squares. I can find the area of a rectangle by multiplying the side lengths. |
Models for the Multiplication of Fractions Use the following Interactive Activity to model the solution to given problems. Also includes a video. ![]() (Login to LearnZillion before selecting the link) |
Multiplying Fractions using a model Use the model to complete the equation. Multiply Fractions with Models Improve your multiplication of fractions by determining the area of rectangular model. Use Areas Models to Multiply Fractions This tutorial will walk you through the process of using an area model to multiply fractions. You will respond to questions and get feedback quickly. |
5.NF.B.5 Interpret multiplication as scaling (resizing), by: | ||
5.NF.B.5.A | ||
Comparing the size of a product to the size of one factor on the basis of
the size of the other factor, without performing the indicated
multiplication. Understand the relationship between factors and products in order to interpret multiplication as scaling. "I Can" Statements I can compare the size of a product to the size of the factors without performing multiplication. I can analyze the relationship between factors and products in order to interpret multiplication as scaling. |
![]() Using a map scale to determine actual distance. Real world application, but does not include working with fractions. Note: Login to Discovery Streaming Education before selecting links. Running Time: 7:40 minutes Multiplication as Scaling The website gives multiple examples of scenarios that involve multiplication as scaling. Multiplying Fractions Utilize this interactive model to show how the size of one factor effects the size of the product. ![]() (Login to LearnZillion before selecting the link) ![]() (Login to LearnZillion before selecting the link) ![]() ![]() |
![]() Model a particular problem by drawing appropriate models. An example is given to get you started. |
5.NF.B.5.B | ||
Explaining why multiplying a given number by a fraction greater than 1
results in a product greater than the given number (recognizing
multiplication by whole numbers greater than 1 as a familiar case);
explaining why multiplying a given number by a fraction less than 1
results in a product smaller than the given number; and relating the
principle of fraction equivalence a/b = (n × a)/(n
× b) to the effect of multiplying a/b by 1. "I Can" Statements I can explain why multiplying a number by a fraction greater than 1 equals a product greater than the given number. I can explain why multiplying a number by a fraction less than 1 equals a product smaller than the given number. I can explain why multiplying a number by a fraction equal to 1 equals a product equal to the given number. |
![]() (Login to LearnZillion before selecting the link) ![]() (Login to LearnZillion before selecting the link) |
![]() ![]() Sort the expressions in this SmartBoard to determine if its product is greater than 8, less than 8, or equal to 8. Check your answers once you're done for feedback. Good luck! |
5.NF.B.6 | ||
Solve real world problems involving multiplication of fractions and mixed
numbers, e.g., by using visual fraction models or equations to represent
the problem. "I Can" Statements I can solve real world problems involving multiplication of fractions and mixed numbers. I can use visual fraction models or equations to represent the problem. |
![]() (Login to LearnZillion before selecting the link) ![]() (Login to LearnZillion before selecting the link) ![]() Multiple real world problems with models to show the fractions being mutliplied. Each fraction will be a separate picture and can be overlapped with the other to show the product. ** |
Thinking
Blocks The interactive website helps you break apart problems multiplying fractions by whole numbers. |
5.NF.B.7 | ||
Apply and extend previous understanding of division to divide unit
fractions by whole numbers and whole numbers by unit fractions. "I Can" Statements I can apply my understanding of division in order to divide unit fractions by whole numbers. I can apply my understanding of division in order to divided whole numbers by unit fractions. |
![]() Note: Login to Discovery Streaming Education before selecting links. Running Time: 9:00 minutes ![]() (Login to LearnZillion before selecting the link) ![]() (Login to LearnZillion before selecting the link) ![]() (Login to LearnZillion before selecting the link) |
Math Basketball - Dividing Fractions Dividing fractions game is a math basketball activity for young students. The game has 15 division problems and multiple levels and includes a timer. (Some questions are beyond the standard) Soccer Math - Dividing Fractions Solve the division problem, then take your best shot at the goal. Dividing Fractions In this math program you will practicing dividing fractions. (Some problems are beyond the standard.) Dividing Whole Numbers by Unit Fractions This video gives examples with models of multiple situations of dividing a whole number by a unit fraction. |
5.NF.B.7.A | ||
Interpret division of a unit fraction by a non-zero whole number, and
compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. "I Can" Statements I can interpret division of a unit fraction by a non-zero whole number and solve for the quotient. |
![]() Video lesson about diving fractions ![]() (Login to LearnZillion before selecting the link) ![]() (Login to LearnZillion before selecting the link) |
![]() ![]() Use this SmartBoard in order to practice solving for quotients. You'll explore modeling an expression on a number line as well as writing word problems and interpreting word problems of unit fractions by whole numbers. |
5.NF.B.7.B | ||
Interpret division of a whole number by a unit fraction, and compute such
quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. "I Can" Statements I can interpret division of a whole number by a unit fraction and solve for the quotient. |
![]() (Login to LearnZillion before selecting the link) ![]() (Login to LearnZillion before selecting the link) ![]() (Login to LearnZillion before selecting the link) |
![]() ![]() Play Two Truths and A Lie with a variety of problems to test your skills of dividing fractions and whole numbers! |
5.NF.B.7.C | ||
Solve real world problems involving division of unit fractions by
non-zero whole numbers and division of whole numbers by unit fractions,
e.g., by using visual fraction models and equations to represent the
problem. For example, how much chocolate will each person get if 3 people share 1/2 lb. of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? "I Can" Statements I can solve real world problems involving division of unit fractions by non-zero whole numbers. I can sovle real world problems involving division of whole numbers by unit fractions. I can use visual fraction models and equations to represent the problem. |
![]() (Login to LearnZillion before selecting the link) |
![]() ![]() Match each scenario to the correct expression. Once all matches have been made then solve the expression. |
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Number and Operations Fraction Activities | Website/Activity | Content Standards/Technology Standards |
Mondrian and Creating Fractions Your Turn - Mondrian Activity Adding and Subtracting Fractions Game Subtracting Unlike Fractions Fraction Addition and Subtraction Note: If the link does not open, be sure to login to aacps.discoveryeducation.com Add/Subtact Fractions Unlike Denominators Flow Map Adding Mixed Numbers Subtracting Mixed Numbers Subtracting Mixed Numbers Add and subtract fractions and mixed numbers with unlike denominators using fraction bars (Login to LearnZillion before selecting the link) Add and subtract fractions and mixed numbers with unlike denominators using area models (Login to LearnZillion before selecting the link) Add and subtract fractions with unlike denominators (Login to LearnZillion before selecting the link) Add and subtract mixed numbers (Login to LearnZillion before selecting the link) Adding and Subtracting Fractions Game Subtracting Unlike Fractions Fishy Fractions - Subtracting Unlike Denominators Fishy Fractions - Adding Unlike Denominators Subtracting Mixed Numbers Fishy Fractions - Subtracting Mixed Numbers Fishy Fractions - Adding Mixed Numbers Fruit Splat Unique Fraction Game |
Common Core: 5.NF.A.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) | |
Technology Standard: 3.0-Technology for Learning and Collaboration: Students will use a variety of technologies for learning and collaboration. | ||
Ice Cream Shop Assess the reasonableness of answers to word problems involving the addition and subtraction of fractions (Login to LearnZillion before selecting the link) Solve word problems involving the addition and subtraction of fractions with unlike denominators (Login to LearnZillion before selecting the link) Solve word problems involving addition and subtraction of fractions referring to the same whole (2) (Login to LearnZillion before selecting the link) Solve word problems involving addition and subtraction of fractions referring to the same whole (1) (Login to LearnZillion before selecting the link) Add and subtract fractions (Login to LearnZillion before selecting the link) |
Common Core: 5.NF.A.2 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5+ 1/2 = 3/7 by observing that 3/7< 1/2. | |
Technology Standard: 3.0-Technology for Learning and Collaboration: Students will use a variety of technologies for learning and collaboration. | ||
Meaning
of Fractions Thinking Blocks Fractions Visualizing Fractions Interpret a fraction as division and answer division problems using fractions (Login to LearnZillion before selecting the link) Interpreting fractions as division of the numerator by the denominator (Login to LearnZillion before selecting the link) Interpret fractions as division and solving word problems involving division of whole numbers resulting in fraction answers (Login to LearnZillion before selecting the link) Understand fractions as a division of the numerator by the denominator (Login to LearnZillion before selecting the link) |
Common Core: 5.NF.B.3 Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? | |
Technology Standard: 3.0-Technology for Learning and Collaboration: Students will use a variety of technologies for learning and collaboration. | ||
Multiplying
Whole Numbers and Fractions Multiplying Fractions Multiplying Fractions Soccer Game Multiplying Fractions With Football Theme Multiplying Fractions Game |
Common Core: 5.NF.B.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. |
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Technology Standard: 3.0-Technology for Learning and Collaboration: Students will use a variety of technologies for learning and collaboration. | ||
How to Multiply Fractions Multiplying Fractions with Circle Models - Visual Fractions Multiplying Fractions with Rectangle Models - Visual Fractions Interpret the product (a/b) x q as a part of a partition of q into b equal parts (Login to LearnZillion before selecting the link) Multiply fractions (Login to LearnZillion before selecting the link) |
Common Core: 5.NF.B.4.A Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) | |
Technology Standard: 3.0-Technology for Learning and Collaboration: Students will use a variety of technologies for learning and collaboration. | ||
Models for the Multiplication of Fractions Multiplying Fractions using a model Multiply Fractions with Models Multiply fractions (Login to LearnZillion before selecting the link) Thinking Blocks Use Areas Models to Multiply Fractions |
Common Core: 5.NF.B.4.B Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. | |
Technology Standard: 3.0-Technology for Learning and Collaboration: Students will use a variety of technologies for learning and collaboration. | ||
Common Core: 5.NF.B.5 Interpret multiplication as scaling (resizing) by: | ||
Technology Standard: 3.0-Technology for Learning and Collaboration: Students will use a variety of technologies for learning and collaboration. | ||
Maps and Scale Note: If the link does not open, be sure to login to aacps.discoveryeducation.com Multiplying Fractions Interpret multiplication as scaling and predict the outcome of multiplying by fractions less than, greater than, and equal to one (Login to LearnZillion before selecting the link) Interpret multiplication as scaling (Login to LearnZillion before selecting the link) |
Common Core: 5.NF.B.5.A Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. | |
Technology Standard: 3.0-Technology for Learning and Collaboration: Students will use a variety of technologies for learning and collaboration. | ||
Rectangle Multiplication Interpret multiplication as scaling and predict the outcome of multiplying by fractions less than, greater than, and equal to one (Login to LearnZillion before selecting the link) Interpret multiplication as scaling (Login to LearnZillion before selecting the link) |
Common Core: 5.NF.B.5.B Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1. | |
Technology Standard: 3.0-Technology for Learning and Collaboration: Students will use a variety of technologies for learning and collaboration. | ||
Solve
problems involving multiplication of fractions and mixed numbers (Login to LearnZillion before selecting the link) Multiply fractions and mixed numbers (Login to LearnZillion before selecting the link) |
Common Core: 5.NF.5.B.6 Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. |
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Technology Standard: 3.0-Technology for Learning and Collaboration: Students will use a variety of technologies for learning and collaboration. | ||
Maths
Mansion-Show 7- Get Some Fraction Action Note: If the link does not open, be sure to login to aacps.discoveryeducation.com Math Basketball - Dividing Fractions Soccer Math - Dividing Fractions Dividing Fractions Dividing Whole Numbers by Unit Fractions Divide whole numbers by unit fractions and unit fractions by whole numbers (Login to LearnZillion before selecting the link) Solve real world problems involving division of whole numbers by unit fractions (Login to LearnZillion before selecting the link) Divide whole numbers by fractions (Login to LearnZillion before selecting the link) |
Common Core: 5.NF.B.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. | |
Technology Standard: 3.0-Technology for Learning and Collaboration: Students will use a variety of technologies for learning and collaboration. | ||
Dividing Unit Fractions Divide whole numbers by unit fractions and unit fractions by whole numbers (Login to LearnZillion before selecting the link) Divide whole numbers by fractions (Login to LearnZillion before selecting the link) |
Common Core: 5.NF.B.7.A Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. | |
Technology Standard: 3.0-Technology for Learning and Collaboration: Students will use a variety of technologies for learning and collaboration. | ||
Solve
real world problems involving division of whole numbers by unit
fractions (Login to LearnZillion before selecting the link) Interpret and compute division of whole numbers by unit fractions (Login to LearnZillion before selecting the link) Divide whole numbers by fractions (Login to LearnZillion before selecting the link) |
Common Core: 5.NF.B.7.B Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. | |
Technology Standard: 3.0-Technology for Learning and Collaboration: Students will use a variety of technologies for learning and collaboration. | ||
Divide
whole numbers by unit fractions and unit fractions by whole numbers (Login to LearnZillion before selecting the link) Matching Expressions and Scenarios |
Common Core: 5.NF.B.7.C Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? | |
Technology Standard: 3.0-Technology for Learning and Collaboration: Students will use a variety of technologies for learning and collaboration. |
Instructional Technology-August 2016