Students need to determine if fractions are the same as whole numbers by answering several questions and providing evidence and explaining their reasoning.
Thorough explanation of the how and why of text-dependent questions for close, analytic reading. Includes examples.
The Common Core State Standards for reading strongly focus on students gathering evidence, knowledge, and insight from what they read. Indeed, eighty to ninety percent of the Reading Standards in each grade require text dependent analysis; accordingly, aligned curriculum materials should have a similar percentage of text dependent questions.
As the name suggests, a text dependent question specifically asks a question that can only be answered by referring explicitly back to the text being read. It does not rely on any particular background information extraneous to the text nor depend on students having other experiences or knowledge; instead it privileges the text itself and what students can extract from what is before them.
This task shows three equivalent expressions and requires that students understand the structure and purpose of each one. This is a critical aspect of Seeing Structure in Expressions.Â
The primary purpose of this task is to assess students' knowledge of certain aspects of the mathematics described in the High School domain A-SSE: Seeing Structure in Expressions. Specifically, standard A-SSE.3 reads A-SSE.3: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. a. Factor a quadratic expression to reveal the zeros of the function it defines. b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
The Standards avoid the term "simplify" as there isn't always an obvious simplest form. The emphasis instead is on, "purposeful transformation of expressions into equivalent forms that are suitable for the purpose at hand." This task shows three equivalent expressions and requires that students understand the structure and purpose of each one. This is a critical aspect of Seeing Structure in Expressions.Â
Mathematically this task:
â€¢ Prompts students to analyze three equivalent quadratic expressions â€¢ Allows students to focus on the structure of the expressions without focusing on the procedural skill of factoring or expanding the expressions â€¢ Gives a real-world context for students to interpret the properties of quadratic expressions â€¢ Requires students to look for and make use of structure (MP.7)
In the classroom: â€¢ Offers students and teachers an opportunity to see an assessment-type task with two response types â€¢ Allows teachers to target specific student misunderstandings for reteaching â€¢ With follow-up questions, teachers can prompt students to share their thinking about the concepts in this task
Riding at a Constant Speed focuses primarily on application of ratio and rate reasoning to solve problems. The problem presents Lin riding a bike at a constant speed: 20 miles in 150 minutes. The resource uses students' apply their initial understanding of ratios and rates to solve a real-life problem. The task uses friendly numbers so students can easily develop different solution strategies (unit rate, double number line, table, graph) to solve the problem. While the resource does not explicitly mention it, this task has potential to discuss the different representations and have students make connections among them.