Adding and Subtracting Fractions
Students will add and subtract fractions with like denominators, including mixed numbers, by replacing mixed numbers with equivalent fractions, and/or by using properties of operations and the relationship between addition and subtraction.
Key Questions
- Justify why we only add or subtract the numerators and not the denominators when operating on fractions with like denominators.
- Compare the process of adding mixed numbers by converting to improper fractions versus adding whole numbers and fractions separately.
- Explain how number lines can be used to visualize the sum or difference of two fractional points.
Common Core State Standards
About This Topic
Slavery and servitude were foundational to the early economy of many states. This topic examines the lives of enslaved people and indentured servants, focusing on their labor in fields, homes, and trades. Students learn about the system of slavery, where people were treated as property, and indentured servitude, where people worked for a set number of years to pay off a debt. This aligns with standards about economic systems and human rights.
It is essential to handle this topic with great care and sensitivity, focusing on the humanity and resilience of those who were enslaved. Students also explore the ways people resisted these systems. This topic is particularly effective when students use structured discussions to analyze primary sources, such as advertisements or narratives, to understand the harsh realities and the human spirit of the time.
Active Learning Ideas
Inquiry Circle: Analyzing Primary Sources
In small groups, students examine age-appropriate primary sources, such as a runaway slave advertisement or a servant's contract. They use a graphic organizer to identify the challenges these individuals faced and how they might have felt.
Think-Pair-Share: Forms of Resistance
Students learn about different ways enslaved people resisted, from learning to read in secret to escaping. They think about why these acts were brave, pair up to discuss, and share with the class.
Gallery Walk: Contributions of the Enslaved
Post images and text about the skills enslaved people brought with them (e.g., rice farming, blacksmithing, music). Students walk through and note how these skills helped build the state's economy and culture.
Watch Out for These Misconceptions
Common MisconceptionSlavery only happened in the South.
What to Teach Instead
Explain that slavery existed in all thirteen colonies and in many early states, including those in the North. Using a map of early slavery can help students see the widespread nature of the system.
Common MisconceptionEnslaved people were 'happy' or 'well-treated.'
What to Teach Instead
Use primary source narratives to show the reality of life under slavery, which was based on force and the denial of basic human rights. Focus on the constant desire for freedom as evidence of their true feelings.
Suggested Methodologies
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Frequently Asked Questions
What is the difference between an enslaved person and an indentured servant?
How did enslaved people contribute to our state's growth?
How did people resist slavery?
How can active learning help students understand slavery and servitude?
Planning templates for Mathematics
5E Model
The 5E Model structures lessons through five phases (Engage, Explore, Explain, Elaborate, and Evaluate), guiding students from curiosity to deep understanding through inquiry-based learning.
unit plannerMath Unit
Plan a multi-week math unit with conceptual coherence: from building number sense and procedural fluency to applying skills in context and developing mathematical reasoning across a connected sequence of lessons.
rubricMath Rubric
Build a math rubric that assesses problem-solving, mathematical reasoning, and communication alongside procedural accuracy, giving students feedback on how they think, not just whether they got the right answer.
More in Fractions: Equivalence and Operations
Visualizing Fraction Equivalence
Students will explain why fractions are equivalent by using visual fraction models, paying attention to how the number and size of the parts differ even though the fractions themselves are the same size.
2 methodologies
Comparing Fractions with Different Denominators
Students will compare two fractions with different numerators and different denominators by creating common denominators or numerators, or by comparing to a benchmark fraction.
2 methodologies
Decomposing Fractions
Students will understand addition and subtraction of fractions as joining and separating parts referring to the same whole, and decompose a fraction into a sum of fractions with the same denominator.
2 methodologies
Solving Fraction Word Problems
Students will solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators.
2 methodologies
Multiplying Fractions by Whole Numbers
Students will apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
2 methodologies