Illustrative Math Alignment: Grade 6 Unit 1

Topic

Fractions

Description

Fraction: A number representing part of a whole, usually written as the ratio of a numerator and a non-zero denominator. Examples include 4/16, 3/4, and 7/4, with visuals explaining numerator and denominator. This foundational term establishes the basic structure and meaning of fractions, essential for all subsequent fraction concepts.

Topic

Fractions

Description

Equivalent Fraction: A fraction with the same numerical value as another fraction, but whose numerator and denominator are multiplied by a common factor. Examples show 1/2 = 2/4 and 2/3 = 6/9. This term illustrates how fractions can be rewritten to have different forms while maintaining equality, aiding in operations and comparisons.

Topic

Fractions

Topic

Fractions

Description

The term Numerator represents the part of a fraction that indicates how many parts of the whole are being considered. For example, in 1/4, the numerator is 1, meaning one part out of four. The image uses visual models to illustrate numerators in fractions like 1/4 and 5/12. Understanding the numerator is critical for interpreting the value of a fraction and applying it to real-world problems.

Topic

Fractions

Description

The term Mixed Number describes a number that consists of a whole number and a proper fraction. Examples include 1 1/2, 2 3/4, and 12 2/3. The image explains that the mixed number format combines a whole number with a fractional part. Mixed numbers are a common representation in fractions, linking whole numbers and fractions together in real-world applications.

Topic

Fractions

Description

A ratio is a comparison of two quantities or numbers by division, often written as a fraction. The image defines it as a / b, where b ≠ 0, and provides examples like 1 / 2 and 2 / 3. This term bridges fractions and their use in comparing quantities, which helps learners connect fraction concepts to real-world applications such as proportions and rates.

Topic

Fractions

Topic

Fractions

Description

Comparing Fractions: Determining if one fraction is greater than, less than, or equal to another fraction. Examples demonstrate comparisons like 1/2 < 2/3 and 3/4 > 3/8. This concept reinforces understanding of relative size in fractions, a critical step in working with and manipulating fractions.

Topic

Fractions

Description

Fractional exponents represent rational exponents, where the numerator indicates the power and the denominator indicates the root. Examples include 2(1/2) = √2 and 3(3/4) = (4th root of 33). These are used in advanced mathematical contexts like algebra and calculus. It introduces the connection between fractions and powers, extending the concept of fractions into exponential operations.

Topic

Fractions

Topic

Fractions

Description

Equivalent Fraction: A fraction with the same numerical value as another fraction, but whose numerator and denominator are multiplied by a common factor. Examples show 1/2 = 2/4 and 2/3 = 6/9. This term illustrates how fractions can be rewritten to have different forms while maintaining equality, aiding in operations and comparisons.

Topic

Fractions

Description

Fraction Division: Dividing one fraction by another. Fraction division can be written as a fraction product by using the reciprocal of the divisor. Examples include 1/2 ÷ 1/3 = 1/2 × 3/1 = 3/2. This operation builds on multiplication and introduces reciprocal concepts, expanding fraction operations.

Topic

Fractions

Description

A rational number is defined as a ratio of two integers that can be expressed as a fraction, whole number, or decimal. Examples provided in the image include 0.5, 1 / 4, and 10. The term builds on the concept of ratios and fractions by showing that they can also represent rational numbers, broadening the application of fractions to include whole numbers and decimals.

Topic

Fractions

Description

The term Numerator represents the part of a fraction that indicates how many parts of the whole are being considered. For example, in 1/4, the numerator is 1, meaning one part out of four. The image uses visual models to illustrate numerators in fractions like 1/4 and 5/12. Understanding the numerator is critical for interpreting the value of a fraction and applying it to real-world problems.

Topic

Fractions

Topic

Fractions

Description

Fraction models visually represent fractions and operations. Examples include area models (shaded parts), bar models (partitioned sections), and multiplication models using grids. These provide a concrete way to understand and visualize fraction concepts. This builds on the concept of understanding fractions by providing a visual context, aiding comprehension of abstract fraction operations.

Topic

Fractions

Topic

Fractions

Description

Benchmark Fraction: A known fraction used to compare other fractions that are less than, greater than, or equal to it. The example given uses 1/2 as a benchmark. Fractions like 4/9 and 5/7 are compared to 1/2 on a number line, demonstrating that 4/9 < 1/2 and 5/7 > 1/2. This term helps students understand how to compare fractions using familiar reference points, a foundational skill in fraction concepts.

Topic

Fractions

Description

Benchmark Fraction: A known fraction used to compare other fractions that are less than, greater than, or equal to it. The example given uses 1/2 as a benchmark. Fractions like 4/9 and 5/7 are compared to 1/2 on a number line, demonstrating that 4/9 < 1/2 and 5/7 > 1/2. This term helps students understand how to compare fractions using familiar reference points, a foundational skill in fraction concepts.

Topic

Fractions

Description

The Greatest Common Factor (GCF) is the largest number that divides two numbers evenly, used to simplify fractions. For example, the GCF of 24 and 36 is 12, enabling simplification of 24/36 to 2/3. This ensures fractions are in their simplest form. It supports simplifying fractions and ensures efficient fraction operations.

Topic

Fractions

Description

The term Percent represents a fraction with a denominator of 100, showing a proportion out of 100. Examples include 1% = 1/100, 5% = 5/100, and 25% = 25/100. Percentages are a real-world application of fractions and decimals, often used in data analysis, finance, and everyday calculations.

Topic

Fractions

Description

The term Ordering Fractions refers to arranging a set of fractions in ascending or descending order. The image provides examples of ordering fractions from least to greatest (1/5, 3/8, 1/2, 2/3) and greatest to least (7/8, 3/4, 2/3, 1/3). This term is important for comparing fractions and understanding their relative values, which is a fundamental skill in fraction operations.

Topic

Fractions

Description

The term Numerator represents the part of a fraction that indicates how many parts of the whole are being considered. For example, in 1/4, the numerator is 1, meaning one part out of four. The image uses visual models to illustrate numerators in fractions like 1/4 and 5/12. Understanding the numerator is critical for interpreting the value of a fraction and applying it to real-world problems.

Topic

Fractions

Description

Fraction multiplication involves multiplying numerators and denominators directly. Examples include 1/2 * 1/3 = 1/6 and 3/4 * 4/4 = 3/16. This operation is fundamental for solving problems involving scaling and proportional reasoning. It connects to practical applications of fractions in areas such as ratios, rates, and scaling.

Topic

Fractions

Description

Decimal Fraction: A fraction expressed as a decimal number, typically with a terminating or repeating decimal representation. Examples include 1/2 = 0.5, 3/4 = 0.75, and 1/3 = 0.333... This term bridges fractions and decimals, showing their equivalence and preparing students for broader applications in mathematics.

Topic

Fractions

Topic

Fractions

Description

A unit fraction is a fraction whose numerator is 1 and whose denominator is a whole number. The image provides examples like 1 / 2, 1 / 3, and 1 / 4, and explains that any fraction can be written as the sum of unit fractions. This term highlights the simplicity of unit fractions as building blocks for other fractions, reinforcing the idea that complex fractions can be deconstructed into simpler parts.

Topic

Fractions

Description

Fraction Addition: Combining two or more fractions whose sum is another fraction, mixed number, or whole number. Examples include 1/2 + 1/3 = 5/6 and 1 1/3 + 3/4 = 1 11/12. This operation demonstrates how fractions interact arithmetically, an important skill for problem-solving.

Topic

Fractions

Description

The term Percentage Increase refers to the increase in value expressed as a percentage of the original value. The example shows an increase from 25 to 40, calculated as (40 - 25) / 25 * 100%, which equals 60%. This term reinforces the application of percentages and fractions in scenarios like profit and growth analysis.

Topic

Fractions

Description

Fraction: A number representing part of a whole, usually written as the ratio of a numerator and a non-zero denominator. Examples include 4/16, 3/4, and 7/4, with visuals explaining numerator and denominator. This foundational term establishes the basic structure and meaning of fractions, essential for all subsequent fraction concepts.

Topic

Fractions

Topic

Fractions

Description

The term Ordering Fractions refers to arranging a set of fractions in ascending or descending order. The image provides examples of ordering fractions from least to greatest (1/5, 3/8, 1/2, 2/3) and greatest to least (7/8, 3/4, 2/3, 1/3). This term is important for comparing fractions and understanding their relative values, which is a fundamental skill in fraction operations.

Topic

Fractions

Topic

Fractions

Description

The term Mixed Number describes a number that consists of a whole number and a proper fraction. Examples include 1 1/2, 2 3/4, and 12 2/3. The image explains that the mixed number format combines a whole number with a fractional part. Mixed numbers are a common representation in fractions, linking whole numbers and fractions together in real-world applications.

Topic

Fractions

Description

The term Percent Error describes the difference between an estimated value and the actual value, expressed as a percentage of the actual value. The example provided shows an estimated value of 100 versus an actual value of 107, resulting in a percent error of approximately 6.54%. This concept links fractions, percentages, and error analysis, which are important in measurement and data accuracy.

Topic

Fractions

Description

Fraction: A number representing part of a whole, usually written as the ratio of a numerator and a non-zero denominator. Examples include 4/16, 3/4, and 7/4, with visuals explaining numerator and denominator. This foundational term establishes the basic structure and meaning of fractions, essential for all subsequent fraction concepts.

Topic

Fractions

Topic

Fractions

Description

The term Mixed Number describes a number that consists of a whole number and a proper fraction. Examples include 1 1/2, 2 3/4, and 12 2/3. The image explains that the mixed number format combines a whole number with a fractional part. Mixed numbers are a common representation in fractions, linking whole numbers and fractions together in real-world applications.

Topic

Fractions

Topic

Fractions

Description

Fractions as division represent the numerator divided by the denominator. Examples include 3/2 = 3 ÷ 2 = 1.5 and 4/5 = 4 ÷ 5 = 0.8. This representation helps convert fractions to decimals and understand their equivalence. This illustrates the dual nature of fractions as division, enhancing understanding of fractions in both numerical and decimal contexts.

Topic

Fractions

Description

The term Mixed Number describes a number that consists of a whole number and a proper fraction. Examples include 1 1/2, 2 3/4, and 12 2/3. The image explains that the mixed number format combines a whole number with a fractional part. Mixed numbers are a common representation in fractions, linking whole numbers and fractions together in real-world applications.

Topic

Fractions

Description

The term Ordering Fractions refers to arranging a set of fractions in ascending or descending order. The image provides examples of ordering fractions from least to greatest (1/5, 3/8, 1/2, 2/3) and greatest to least (7/8, 3/4, 2/3, 1/3). This term is important for comparing fractions and understanding their relative values, which is a fundamental skill in fraction operations.

Topic

Fractions

Description

The term Percentage refers to converting fractions and decimals into their equivalent percentages. Examples include 1/2 = 50%, 0.4 = 40%, and 1/3 ≈ 33.3%. This concept connects fractions, decimals, and percentages, emphasizing their equivalence and usage in various contexts.

Topic

Fractions

Description

Comparing Fractions: Determining if one fraction is greater than, less than, or equal to another fraction. Examples demonstrate comparisons like 1/2 < 2/3 and 3/4 > 3/8. This concept reinforces understanding of relative size in fractions, a critical step in working with and manipulating fractions.

Topic

Fractions

Description

A reciprocal is the multiplicative inverse of a number, obtained by swapping the numerator and denominator of a fraction. Examples include the reciprocals 2 / 3 and 3 / 2, as well as 4 / 5 and 5 / 4. This term connects to operations with fractions, especially in division and multiplication, where understanding reciprocals is essential for solving equations and simplifying expressions.

Topic

Fractions

Description

An irrational number cannot be expressed as a fraction and has a non-terminating, non-repeating decimal form. Examples include π = 3.14159... and √2 = 1.41421.... This highlights the contrast between rational and irrational numbers. This connects fractions to the broader number system, emphasizing differences in numerical properties.

Topic

Fractions

Description

Denominator: The part of a fraction that determines the total fractional parts. Visuals show fractions like 3/4 ('three fourths') and 7/12 ('seven twelfths') with denominators highlighted. Understanding the denominator is crucial for interpreting fractions and performing operations like comparison and simplification.

Topic

Fractions

Description

Fraction Bars: A fraction model used to represent fractions, fractions in simplest form, and fraction sums. The visual illustrates 1/2 + 1/3 = 5/6 using colored bars. This visual model aids in conceptual understanding of fraction operations and relationships.

Topic

Fractions

Description

Denominator: The part of a fraction that determines the total fractional parts. Visuals show fractions like 3/4 ('three fourths') and 7/12 ('seven twelfths') with denominators highlighted. Understanding the denominator is crucial for interpreting fractions and performing operations like comparison and simplification.

Topic

Fractions

Description

Denominator: The part of a fraction that determines the total fractional parts. Visuals show fractions like 3/4 ('three fourths') and 7/12 ('seven twelfths') with denominators highlighted. Understanding the denominator is crucial for interpreting fractions and performing operations like comparison and simplification.