Match shapes and numbers to earn stars in this fractions game. Challenge yourself on any level you like. Try to collect lots of stars! The main topics of this interactive simulation include fractions, equivalent fractions, and mixed numbers.

Match shapes and numbers to earn stars in this fractions game. Challenge yourself on any level you like. Try to collect lots of stars! The main topics of this interactive simulation include fractions, equivalent fractions, and mixed numbers.

Demonstration/Focus Lesson on how to understand fraction of a set by using manipulatives

Explore fractions while you help yourself to 1/3 of a chocolate cake and wash it down with 1/2 a glass of orange juice! Create your own fractions using fun interactive objects. Match shapes and numbers to earn stars in the fractions games. Challenge yourself on any level you like. Try to collect lots of stars!

Explore fractions while you help yourself to 1/3 of a chocolate cake and wash it down with 1/2 a glass of orange juice! Create your own fractions using fun interactive objects. Match shapes and numbers to earn stars in the fractions games. Challenge yourself on any level you like. Try to collect lots of stars!

Explore fractions while you help yourself to 1 and 1/2 chocolate cakes and wash it down with 1/3 a glass of water! Create your own fractions using fun interactive objects. Match shapes and numbers to earn stars in the mixed number game. Challenge yourself on any level you like. Try to collect lots of stars!

This lesson was designed for ABE math students working on fractions. In this lesson students will make recordings of them solving fraction mathematical problems and review the videos of others.

Compare fractions (halves, quarters, eighths) that make up a whole by drawing toppings on pizzas and cutting the pizzas into slices!

Visit Gabby's pizza shop to help Adi take pizza orders from customers. Viewers learn fractions that make up a whole by drawing pizza toppings in halves and quarters and cutting the pizzas into one eighth slices.

Learning Objective:
To partition objects into equal parts and name the parts, including halves, fourths, and eighths, using words.

In Module 8, the final module of the year, students extend their understanding of part–whole relationships through the lens of geometry.  As students compose and decompose shapes, they begin to develop an understanding of unit fractions as equal parts of a whole.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

In this 35-day Grade 3 module, students extend and deepen second grade practice with "equal shares" to understanding fractions as equal partitions of a whole. Their knowledge becomes more formal as they work with area models and the number line.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

In this 40-day module, students build on their Grade 3 work with unit fractions as they explore fraction equivalence and extend this understanding to mixed numbers.  This leads to the comparison of fractions and mixed numbers and the representation of both in a variety of models.  Benchmark fractions play an important part in students’ ability to generalize and reason about relative fraction and mixed number sizes.  Students then have the opportunity to apply what they know to be true for whole number operations to the new concepts of fraction and mixed number operations.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

This 20-day module gives students their first opportunity to explore decimal numbers via their relationship to decimal fractions, expressing a given quantity in both fraction and decimal forms.  Utilizing the understanding of fractions developed throughout Module 5, students apply the same reasoning to decimal numbers, building a solid foundation for Grade 5 work with decimal operations.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

In Module 3, students' understanding of addition and subtraction of fractions extends from earlier work with fraction equivalence and decimals. This module marks a significant shift away from the elementary grades' centrality of base ten units to the study and use of the full set of fractional units from Grade 5 forward, especially as applied to algebra.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

Grade 5’s Module 4 extends student understanding of fraction operations to multiplication and division of both fractions and decimal fractions.  Work proceeds from interpretation of line plots which include fractional measurements to interpreting fractions as division and reasoning about finding fractions of sets through fraction by whole number multiplication.  The module proceeds to fraction by fraction multiplication in both fraction and decimal forms.  An understanding of multiplication as scaling and multiplication by n/n as multiplication by 1 allows students to reason about products and convert fractions to decimals and vice versa.  Students are introduced to the work of division with fractions and decimal fractions.  Division cases are limited to division of whole numbers by unit fractions and unit fractions by whole numbers.  Decimal fraction divisors are introduced and equivalent fraction and place value thinking allow student to reason about the size of quotients, calculate quotients and sensibly place decimals in quotients.  Throughout the module students are asked to reason about these important concepts by interpreting numerical expressions which include fraction and decimal operations and by persevering in solving real-world, multistep problems which include all fraction operations supported by the use of tape diagrams.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

A higher lift to drag ratio is a major goal of wing design. Can you find the best lift drag ratio for this plane? Adjust the angle of attack and watch the dots of air flow past the airfoil.

This lesson unit is intended to help teachers assess how well students are able to interpret percent increase and decrease, and in particular, to identify and help students who have the following difficulties: translating between percents, decimals, and fractions; representing percent increase and decrease as multiplication; and recognizing the relationship between increases and decreases.

This lesson is regarding the introduction to ratios.  Students will learn what a ratio is, practice finding ratios, and work on making their own ratios. There are YouTube videos, worksheets, and funny images to help students understand ratios.

Fractions and Decimals

Type of Unit: Concept

Prior Knowledge

Students should be able to:

Multiply and divide whole numbers and decimals.
Multiply a fraction by a whole number.
Multiply a fraction by another fraction.
Write fractions in equivalent forms, including converting between improper fractions and mixed numbers.
Understand the meaning and structure of decimal numbers.

Lesson Flow

This unit extends students’ learning from Grade 5 about operations with fractions and decimals.

The first lesson informally introduces the idea of dividing a fraction by a fraction. Students are challenged to figure out how many times a 14-cup measuring cup must be filled to measure the ingredients in a recipe. Students use a variety of methods, including adding 14 repeatedly until the sum is the desired amount, and drawing a model. In Lesson 2, students focus on dividing a fraction by a whole number. They make a model of the fraction—an area model, bar model, number line, or some other model—and then divide the model into whole numbers of groups. Students also work without a model by looking at the inverse relationship between division and multiplication. Students explore methods for dividing a whole number by a fraction in Lesson 3, for dividing a fraction by a unit fraction in Lesson 4, and for dividing a fraction by another fraction in Lesson 6. Students examine several methods and models for solving such problems, and use models to solve similar problems.

Students apply their learning to real-world contexts in Lesson 6 as they solve word problems that require dividing and multiplying mixed numbers. Lesson 7 is a Gallery lesson in which students choose from a number of problems that reinforce their learning from the previous lessons.

Students review the standard long-division algorithm for dividing whole numbers in Lesson 8. They discuss the different ways that an answer to a whole number division problem can be expressed (as a whole number plus a remainder, as a mixed number, or as a decimal). Students then solve a series of real-world problems that require the same whole number division operation, but have different answers because of how the remainder is interpreted.

Students focus on decimal operations in Lessons 9 and 10. In Lesson 9, they review addition, subtraction, multiplication, and division with decimals. They solve decimal problems using mental math, and then work on a card sort activity in which they must match problems with diagram and solution cards. In Lesson 10, students review the algorithms for the four basic decimal operations, and use estimation or other methods to place the decimal points in products and quotients. They solve multistep word problems involving decimal operations.

In Lesson 11, students explore whether multiplication always results in a greater number and whether division always results in a smaller number. They work on a Self Check problem in which they apply what they have learned to a real-world problem. Students consolidate their learning in Lesson 12 by critiquing and improving their work on the Self Check problem from the previous lesson. The unit ends with a second set of Gallery problems that students complete over two lessons.

Students determine how many times they would need to fill a quarter cup to measure the ingredients in a recipe.Key ConceptsThis lesson informally introduces the idea of dividing by a fraction. Students must figure out how many times a quarter cup must be filled to measure the ingredients in a recipe. This involves dividing each amount by 14. Here are some methods students might use:Add 14 repeatedly until the sum is the desired amount. Count the number of 14s that were added.Start with the amount in the recipe. Subtract 14 repeatedly until the difference is 0. Count the 14s that were subtracted.Draw a model (e.g., a bar or a number line model) to represent the amount in the recipe. Divide it into fourths and count the number of fourths.Goals and Learning ObjectivesLearn how to divide by a fraction.

Gallery OverviewAllow students who have a clear understanding of the content in the unit to work on Gallery problems of their choosing. You can use this time to provide additional help to students who need review of the unit's concepts or to assist students who may have fallen behind on work.Gallery DescriptionStew RecipeStudents use fraction operations to help Molly figure out if she has enough potatoes to make stew for all the guests at her party.Multiply or Divide?Students match descriptions of situations to multiplication and division situations.Card SortStudents find the diagram, expression, and answer that match given word problems.Complex FractionsStudents learn about complex fractions and how they are useful for dividing fractions.