Ms. Aprati’s Classroom
Table of Contents
- Models of Rational Numbers
- Rational Numbers on a Numberline
- Ordering Rational Numbers
- Comparing Rational Numbers Using a Number Line
- Fraction Equivalence, Ordering, and Simplifying
- Simplifying Fractions
- Simplifying Fractions تبسيط الكسور
- Copy of Equivalent Fractions
- Comparing Fractions
- Ordering Fractions
- Adding Fractions
- Adding Fractions with an Area Model
- Adding Fractions with Diagrams
- Grade 3 Adding Fractions
- Adding Fractions Scored Practice
- Adding and Subtracting Fractions
- Subtracting Fractions
- Subtracting fractions with number lines
- Subtracting Proper Fractions
- Subtracting Fractions
- Subtracting on Fractions Overview
- Multiplying Fractions
- Multiplying Fractions
- Multiplying Proper Fractions
- Multiplying Fractions
- Multiplying Fractions: Array model activity
- Dividing Fractions
- Dividing Fractions
- Dividing Proper Fractions
- Dividing Fractions
- Dividing Fractions based on patterns
- Dividing Fractions Using Visual Models
- Denseness of Fractions
- Comparing Fractions with Unlike Denominators Using Models
- Adding Fractions with Unlike Denominators
- Fraction Between Two Fractions
- Fractions on a numberline
- Geometry
- Area of Circle
- Circle Area (By Peeling!)
- Triangle Angle Theorems
- Parallelogram: Area
- Surface Area: Intuitive Introduction
- Supplementary Angles (Quick Exploration)
- Volume of cone
- Sphere (Volume + Surface)
- Volume of cylinder
- Volume of rectangular prisms
- Cylinder Volume Word Problems
- Intro to Area Using Unit Squares
- Geometry 2D - Shapes Activity
- 2D shapes
- Discover 2D shapes- NETS!
- Parallel & Perpendicular Lines
- Perpendicular Lines: Quick Intro
- Transversal Intersects Parallel Lines
- Triangle Exterior Angle
- Polygons: Exterior Angles - REVAMPED
- Triangle: Exterior Angles
- Regular Polygons: Perimeter & Area
- Triangle: Area and Perimeter
- Perimeter Practice
- GeoBoard - Arrays, area, perimeter, and representations
- Practice: Using 3.14 to find area and circumference
- Circumference of Circles (New)
- Surface Area & Volume: Right Prism
- Triangle Area Action! (V1)
- Parallel Lines & Related Angles
Rational Numbers on a Numberline
Drag each point to its proper place on the number line. Use your observations in order to answer the questions below the applet.
Plotting Rational Numbers on the number line (guidelines)
[list][*]Divide each unit into the number of parts given by the denominator.[/*][*]Look for the number of tick marks given by the numerator.[/*][/list]
Ranking rational numbers on the number line (guidelines)
[list][*]Find the least common multiple (lcm) of the denominators.[/*][*]Find equivalent fractions to the originals with the same common denominator.[/*][*]Rank from least to highest, according to the new numerators.[/*][/list]
Formative assessment
Use the following applet to practice locating and ranking rational numbers on the number line.
Andre says that [math]\frac{1}{4}[/math] is less than -[math]\frac{3}{4}[/math] because, of the two numbers, [math]\frac{1}{4}[/math] is closer to 0. Do you agree? Explain your reasoning.
Which number is greater?
Which number is farther from 0?
Which number is greater?
Which number is farther from 0?
Is the number that is farther from 0 always the greater number? Explain your reasoning.
Simplifying Fractions
How to use the sliders to help simplify a fraction.
1. Click and drag the blue sliders on the left to the numerator and denominator of the (non-simplified) fraction you are given.[br]2. Find the GCF (greatest common factor of this numerator and denominator. If the GCF is 1, you are done. 3. If the GCF is greater than 1, divide the numerator by the GCF - the result is the "new" numerator. [br]4. Divide the denominator by the GCF - the result is the "new" denominator. [br]5. Click and drag the purple sliders on the right to the new numerator and new denominator.[br]6. Finally, click and drag the handle (the red point) to overlap the two squares to see if they match.
Definition: A fraction is simplified if the numerator and denominator have no common factors.
1. Simplify [math]\frac{9}{15}[/math][br]a) The square on the left illustrates [math]\frac{9}{15}[/math] (9 sections out of 15 are shaded blue).[br]b) Find the GCF of 9 and 15 to simplify [math]\frac{9}{15}[/math]. [br]c) Adjust the purple sliders for the numerator and denominator to create the simplified fraction for [math]\frac{9}{15}[/math].[br]d) Use the handle (red point) to drag the purple square on top of the blue square. If the shaded portions completely overlap, then you have simplified the fraction correctly.
2. Simplify [math]\frac{5}{20}[/math][br]a) Drag the blue sliders to illustrate the fraction [math]\frac{5}{20}[/math]. (5 sections out of 20 should be shaded)[br]b) Find the GCF of 9 and 15 to simplify [math]\frac{5}{20}[/math]. [br]c) Adjust the purple sliders for the numerator and denominator to create the simplified fraction for [math]\frac{5}{20}[/math].[br]d) Use the handle (red point) to drag the purple square on top of the blue square. If the shaded portions completely overlap, then you have simplified the fraction correctly.[br][br][br]3. Simplify [math]\frac{3}{8}[/math][br]a) Move the purple square back to its starting position or click on reset.[br]b) Drag the blue sliders to illustrate the fraction [math]\frac{3}{8}[/math][br]c) Find the GCF of 3 and 8. Can you simplify [math]\frac{3}{8}[/math]?[br]
What is the simplified fraction for [math]\frac{9}{15}[/math]? Use the [math]\pi[/math] button to bring up the math keyboard. Use the division sign to type in your fraction answer. Example: 1 [math]\div[/math] 2 will show [math]\frac{1}{2}[/math].
What is the simplified fraction for [math]\frac{5}{20}[/math]? Use the [math]\pi[/math] button to bring up the math keyboard. Use the division sign to type in your fraction answer. Example: 1 [math]\div[/math] 2 will show as [math]\frac{1}{2}[/math]
Can [math]\frac{3}{8}[/math] be simplified? Explain.
Adding Fractions with an Area Model
Adding fractions with an Area Model
Adding fractions with an Area Model
Use the are model to understand adding fractions.[br][br]Click the RESET arrows to get a new problem. (You might need to do this if the randomly generated problem does not make sense. For example 0/3 + 0/8)
Subtracting fractions with number lines
Use fractions on a number line to develop an understanding for how to subtract fractions.
Multiplying Fractions
TASK: Multiplying Fractions Practice
Dividing Fractions
[url=https://danpearcy.com/2021/11/05/prompt-36-dividing-fractions/]Dan Pearcy Website[br][/url]Inspiration [url=https://danpearcy.com/2021/11/05/prompt-36-dividing-fractions/]https://danpearcy.com/2021/11/05/prompt-36-dividing-fractions/[/url]
Comparing Fractions with Unlike Denominators Using Models
Compare fractions with unlike denominators using visual models in this interactive activity.
Putting It All Together
[i]Answer these open ended questions on your own or with others to form deeper math connections. [/i]
Comparing fractions with the same denominator is easy. For example, comparing [math]\frac{3}{4}[/math] with [math]\frac{1}{4}[/math], we know that 3 parts out of 4 are greater than 1 part out of 4. Using a similar concept and without finding a common denominator, how would you compare fractions with the same numerators?
Area of Circle
In this applet, we consider a circle, and divide the circle into slices of sectors. Then, we visualize the circle's area by rearranging the slices to form a rectangle. [br][br]We know that[br]1. the formula of Area(Rectangle) = Length x Breath[br]2. the formula of Circumference (Circle)=2⋅π⋅r. [br]3. In this rearrangement, [br] (i) area of circle =area of rectangle[br] (ii) the approximate length of the rectangle is half of the circumference.[br][br]Now, [br]Combining these three facts/formula, [br] Area of circle = area of rectangle [br] = ( π⋅r)⋅(r) [br] = π⋅r^2. [br]Conclusion, although we use approximations for the length and breath, the resulting formula for the circle's area is exact, because we can continue the approximation with large number of slices.[br][br]Now, it is teacher's turn to let student to explore the applet by changing the number of sectors using the slider "Make more slices". Then student will notice that as the number of sectors increases.[br][br]Next, student will unfold the sector components using the slider "Unfold the circle".[br][br]Then, students will resemble both semi circle into a rectangle closely using the slider "Move up/Down". This helps to fit the both parts into a single rectangle.