Illustrative Math Alignment: Grade 6 Unit 1

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Topic

Fractions

Description

This image serves as the title card for a series on proper and improper fractions. It displays the text "Proper and Improper Fractions" in a clear, prominent font. The background may include subtle mathematical elements or fraction-related graphics to set the context for the following images in the series.

This introductory image sets the stage for the subsequent images, preparing students for an exploration of the differences between proper and improper fractions. It provides a clear, concise title that immediately informs viewers about the specific fraction concepts they'll be studying.

Topic

Fractions

Description

This image shows 1/4 with labels for numerator and denominator. It displays the fraction 1/4 with the number 1 clearly labeled as the numerator and the number 4 labeled as the denominator.

This representation helps students understand the basic structure of a fraction, identifying the roles of the numerator and denominator. It reinforces the concept that the numerator represents the number of parts being considered, while the denominator represents the total number of equal parts the whole is divided into.

Topic

Fractions

Description

This image provides examples of proper fractions shown as circular fractions: 1/2, 2/4, 3/6, and 4/8. It displays four circles, each divided into the appropriate number of sections with the corresponding number of sections shaded to represent each fraction.

This visual representation helps students see that these fractions, while written differently, all represent proper fractions (less than one whole). It reinforces the concept of proper fractions and introduces the idea of equivalent fractions.

Topic

Fractions

Description

This image is a variation of the previous one, now showing that for a proper fraction, a < b. It displays the fraction a/b again, but with an additional note or visual indicator that the numerator (a) is less than the denominator (b).

This representation introduces the concept of proper fractions, helping students understand that when the numerator is less than the denominator, the fraction represents a part of a whole that is less than one.

Topic

Fractions

Description

This image shows a/b for any whole number a and b, with b not equal to zero. It displays the fraction a/b with labels or explanations indicating that a and b can be any whole numbers, but b cannot be zero.

This representation introduces students to the general form of a fraction and the important rule that the denominator cannot be zero. It helps students understand that fractions can represent a wide range of values and prepares them for working with variables in algebraic fractions.

Topic

Fractions

Description

This image is a variation of the previous one, now showing visual models for 10/10 and 10/9. It displays rectangular visual representations: one divided into 10 parts with all 10 parts shaded, and another pair of rectangles divided into 9 parts with 10 parts shaded.

This representation helps students understand that improper fractions include fractions equal to one whole (like 10/10) as well as those greater than one whole (like 10/9). It reinforces the concept that improper fractions have numerators greater than or equal to their denominators.

Topic

Fractions

Description

This image shows another variation with these fractions: 1/4, 3/8, 5/12, and 15/16, emphasizing that proper fractions are less than 1. It displays visual models for each fraction, clearly showing that the shaded portion is less than the whole in each case.

This representation further reinforces the concept of proper fractions, showing examples with increasingly larger denominators. It helps students understand that even as fractions get closer to 1, they remain proper fractions as long as the numerator is less than the denominator.

Topic

Fractions

Description

This image introduces the concept of improper fractions, stating that a fraction a/b is improper if a is greater than or equal to b. It displays the fraction a/b with a visual or textual explanation indicating that when the numerator is greater than or equal to the denominator, the fraction is improper.

This representation helps students understand the definition of improper fractions and how they differ from proper fractions. It sets the stage for exploring fractions that represent one whole or more than one whole.

Topic

Fractions

Description

This image presents a variation of the previous concept, now using rectangular models to show proper fractions: 1/3, 4/6, 4/9, and 7/12. It displays four rectangles, each divided into the appropriate number of sections with the corresponding number of sections shaded to represent each fraction.

Topic

Fractions

Description

This image provides visual models of improper fractions using rectangular models for 6/5 and 16/12. It shows two rectangles: one divided into 5 parts with 6 parts shaded (extending beyond the original rectangle), and another divided into 12 parts with 16 parts shaded.

This representation helps students visualize improper fractions and understand that they represent more than one whole. It demonstrates how improper fractions can be represented visually, even when they exceed one complete unit.

Topic

Fractions

Description

This image serves as a summary slide showing the four equivalent fractions explored in the previous sequence: 2/3, 4/6, 6/9, and 8/12. It displays all four rectangular models side by side, clearly demonstrating their equivalence.

Topic

Fractions

Description

This image shows the final fraction in the sequence: 8/12. It displays a rectangular model divided into twelve parts with eight parts shaded, representing 8/12. It may also include the numerical process of multiplying both the numerator and denominator of 2/3 by 4 to get 8/12.

Topic

Fractions

Description

This image serves as a summary slide showing the four equivalent fractions explored in the previous sequence: 2/3, 4/6, 6/9, and 8/12. It displays all four rectangular models side by side, clearly demonstrating their equivalence.