Forum Replies Created
-
Posts
-
An answer for this question isn’t determined by the Standards because Standards do not specify a particular standard algorithm for each operation. Moreover, specifying an algorithm doesn’t necessarily specify how it’s notated. That said, one might want students to “fluently extend” zeros because doing so can help with lining up places in quotient and dividend, as can using graph paper.
From Bill’s reply here:
In the Common Core decimals are treated simply as a different way of writing fractions with denominator 10, 100, and so on.
On the better-late-than-never principle . . .
The SBAC question does not have units written in the form units/units. If it did, dollars per pound (the derived unit) would be written using a fraction bar, e.g., dollars/pound or USD/lb. Instead, terminology is as in 6.RP.2.
Jana, I don’t see that the OA Progression says “move away from writing situation equations to writing solution equations,” but rather writing a situation equation, then a solution equation.
The OA Progression says:
Learning where the total is in addition equations . . . students move from a situation equation to a related solution equation. (pp. 13–14)
Grade 6 students continue the K–5 focus on representing a problem situation using an equation (a situation equation) and then . . . writing an equivalent equation that is easier to solve (a solution equation). (pp. 34–35)
See also, pp. 16, 18.
I don’t know if this is part of your concern but note that the front matter for the Progressions says: “Terms used in the Standards and Progressions are not intended as prescriptions for terms that teachers must use in the classroom.”
Generally in the Progressions, a method is more specific than a strategy, e.g., two different methods might use a make-a-ten strategy.
“Notation” vs “written method”: Generally, in mathematics, “notation” is used to mean “any series of signs or symbols used to represent quantities or elements in a specialized system” (the first meaning here: https://www.thefreedictionary.com/notation). A written method might use such notation, or not.
Generally in the Progressions, various things are identified as models in discussions of how they act as models, e.g., in examples of MP4. (See pp. 1–6 of the Modeling Progression.) Some of the same things might be identified as tools in discussions of using appropriate tools strategically (MP5).
That’s discussed here: http://commoncoretools.me/forums/topic/s-ics/
Here’s a quick comment: I don’t think there is any grade in which students are required to know a general definition of unit. However, they see examples of different types of units over the grades as described in the section on units (pp. 10-11) in the draft front matter for the Progressions here: http://ime.math.arizona.edu/progressions/. So, over the grades, their understanding of “unit” expands.
I don’t see anything that constrains the number of equations used to solve a problem in 3.OA.8 to one. Note that 2.OA.1 uses a very similar formulation but goes on to elaborate:
Represent and solve problems involving addition and subtraction.
1. Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
As you note, page 28 of the OA Progression says:
As with two-step problems at Grade 2,2.OA.1, 2.MD.5 which involve only addition and subtraction, the Grade 3 two-step word problems vary greatly in difficulty and ease of representation. More difficult problems may require two steps of representation and solution rather than one.
“Two steps of representation and solution” sounds to me as it includes solutions that involve two (or more) equations or tape diagrams, as in the example in the margin.
It might be that part of the concern is whether students should be able to interpret things like 3 × 10 + 5. That’s discussed here: http://commoncoretools.me/forums/topic/expanded-notation-and-order-of-operations/
Maybe you also want to look at p. 14 of the Ratio and Proportional Relationship Progression, which describes proportional relationships in terms of ratios and begins: A proportional relationship is a collection of pairs of numbers that are in equivalent ratios.
For example, if the relationship in question is given by y = 2x + 1, it has pairs, e.g., (0, 1), (1,3), (2,5), that are not in equivalent ratios. Because of that the relationship between x and y is not a proportional relationship.
The m in y = mx + b is not always a constant of proportionality for the relationship between x and y because y = mx + b does not always represent a proportional relationship between x and y. (On the other hand, one could consider the relationship between the quantities represented by y – b and x.)
Less complicated suggestion: I haven’t read or used them, but you might want to check PTA’s parent’s guides to student success: http://pta.org/parents/content.cfm?ItemNumber=2583
Here’s what the page says:
National PTA® created the guides for grades K-8 and two for grades 9-12 (one for English language arts/literacy and one for mathematics).
The Guide includes:
• Key items that children should be learning in English language arts and mathematics in each grade, once the standards are fully implemented.
• Activities that parents can do at home to support their child’s learning.
• Methods for helping parents build stronger relationships with their child’s teacher.
• Tips for planning for college and career (high school only).
PTAs can play a pivotal role in how the standards are put in place at the state and district levels. PTA® leaders are encouraged to meet with their school, district, and/or state administrators to discuss their plans to implement the standards and how their PTA can support that work. The goal is that PTAs and education administrators will collaborate on how to share the guides with all of the parents and caregivers in their states or communities, once the standards are fully implemented.
Persevering in trying to solve the problem . . . I’m putting short pieces.
Part of what got me into math education from mathematics was the disconnect between the unmathematical beliefs and practices that students often acquire in K–12 and what’s expected in college. (Somewhat related: A large proportion of undergraduates take remedial courses, i.e., courses that repeat topics of high school. See TABLE S.2 and Figure S.2.1 of http://www.ams.org/profession/data/cbms-survey/cbms2010. Over half of the undergraduates in mathematics courses at four-year institutions are taking courses below calculus.)
Order of operations with respect to parentheses is discussed here: http://commoncoretools.me/forums/topic/expanded-notation-and-order-of-operations/, and here: http://commoncoretools.me/forums/topic/5-oa-2/ There’s a discussion of related issues, e.g., the “any order” property in the Expressions and Equations Progression: http://commoncoretools.files.wordpress.com/2011/04/ccss_progression_ee_2011_04_25.pdf.
I think your question is answered here (http://commoncoretools.me/forums/topic/adding-and-subtracting-mixed-numbers-grade-4/#post-1831).
