Connecticut Standards for Mathematics
(CCSS)
Standards for Mathematical Practice
Grade Seven
Adopted from The Arizona Academic Content Standards
Grade Seven Standards for Mathematical PracticeThe K-12 Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. This page gives examples of what the practice standards look like at the specified grade level.
Standards / Explanations and Examples
Students are expected to:
1. Make sense of problems and persevere in solving them. / In grade 7, students solve problems involving ratios and rates and discuss how they solved them. Students solve real world problems through the application of algebraic and geometric concepts. Students seek the meaning of a problem and look for efficient ways to represent and solve it. They may check their thinking by asking themselves, “What is the most efficient way to solve the problem?”, “Does this make sense?”, and “Can I solve the problem in a different way?”
Students are expected to:.
2. Reason abstractly and quantitatively. / In grade 7, students represent a wide variety of real world contexts through the use of real numbers and variables in mathematical expressions, equations, and inequalities. Students contextualize to understand the meaning of the number or variable as related to the problem and decontextualize to manipulate symbolic representations by applying properties of operations.
Students are expected to:
3. Construct viable arguments and critique the reasoning of others. / In grade 7, students construct arguments using verbal or written explanations accompanied by expressions, equations, inequalities, models, and graphs, tables, and other data displays (i.e. box plots, dot plots, histograms, etc.). They further refine their mathematical communication skills through mathematical discussions in which they critically evaluate their own thinking and the thinking of other students. They pose questions like “How did you get that?”, “Why is that true?” “Does that always work?” They explain their thinking to others and respond to others’ thinking.
Students are expected to:
4. Model with mathematics. / In grade 7, students model problem situations symbolically, graphically, tabularly, and contextually. Students form expressions, equations, or inequalities from real world contexts and connect symbolic and graphical representations. Students explore covariance and represent two quantities simultaneously. They use measures of center and variability and data displays (i.e. box plots and histograms) to draw inferences, make comparisons and formulate predictions. Students use experiments or simulations to generate data sets and create probability models. Students need many opportunities to connect and explain the connections between the different representations. They should be able to use all of these representations as appropriate to a problem context.
Students are expected to:
5. Use appropriate tools strategically. / Students consider available tools (including estimation and technology) when solving a mathematical problem and decide when certain tools might be helpful. For instance, students in grade 7 may decide to represent similar data sets using dot plots with the same scale to visually compare the center and variability of the data. Students might use physical objects or applets to generate probability data and use graphing calculators or spreadsheets to manage and represent data in different forms.
Standards / Explanations and Examples
Students are expected to:
6. Attend to precision. / In grade 7, students continue to refine their mathematical communication skills by using clear and precise language in their discussions with others and in their own reasoning. Students define variables, specify units of measure, and label axes accurately. Students use appropriate terminology when referring to rates, ratios, probability models, geometric figures, data displays, and components of expressions, equations or inequalities.
Students are expected to:
7. Look for and make use of structure. / Students routinely seek patterns or structures to model and solve problems. For instance, students recognize patterns that exist in ratio tables making connections between the constant of proportionality in a table with the slope of a graph. Students apply properties to generate equivalent expressions (i.e. 6 + 2x = 3 (2 + x) by distributive property) and solve equations (i.e. 2c + 3 = 15, 2c = 12 by subtraction property of equality), c=6 by division property of equality). Students compose and decompose two- and three-dimensional figures to solve real world problems involving scale drawings, surface area, and volume. Students examine tree diagrams or systematic lists to determine the sample space for compound events and verify that they have listed all possibilities.
Students are expected to:
8. Look for and express regularity in repeated reasoning. / In grade 7, students use repeated reasoning to understand algorithms and make generalizations about patterns. During multiple opportunities to solve and model problems, they may notice that a/b ÷ c/d = ad/bc and construct other examples and models that confirm their generalization. They extend their thinking to include complex fractions and rational numbers. Students formally begin to make connections between covariance, rates, and representations showing the relationships between quantities. They create, explain, evaluate, and modify probability models to describe simple and compound events.
Adopted from The Arizona Academic Content Standards
Grade 7 Pacing Guide
Unit Title / Pacing / Standards1. Operating with Rational Numbers (add/sub) / 4 weeks / 7.NS.1
7.NS.3
2. Operating with Rational Numbers (mult/div) / 3 weeks / 7.NS.2
7.NS.3
7.EE.2
7.EE.3
3. Two and Three Dimensional Geometry / 4 weeks / 7.G.2
7.G.3
7.G.4
7.G.5
7.G.6
4. Proportional Relationships / 5 weeks / 7.RP.1
7.RP.2
7.RP.3
7.G.1
5. Algebraic Reasoning II / 4 weeks / 7.EE.1
7.EE.2
7.EE.4
6. Inferences about Populations / 3 weeks / 7.SP.1
7.SP.2
7.SP.3
7.SP.4
7. Probability / 3 weeks / 7.SP.5
7.SP.6
7.SP.7
7.SP.8
Adopted from The Arizona Academic Content Standards
CT Mathematics Unit Planning Organizers are designed to be a resource for developers of curriculum. The documents feature standards organized in units with key concepts and skills identified, and a suggested pacing guide for the unit. The standards for Mathematical Practice are an integral component of CT Standards (CCSS) and are evident highlighted accordingly in the units.
The information in the unit planning organizers can easily be placed into the curriculum model in used at the local level during the revision process. It is expected that local and/or regional curriculum development teams determine the “Big Ideas” and accompanying “Essential Questions” as they complete the units with critical vocabulary, suggested instructional strategies, activities and resources.
Note that all standards are important and are eligible for inclusion on the large scale assessment to be administered during the 2014-15 school year. The Standards were written to emphasize correlations and connections within mathematics. The priority and supporting standard identification process emphasized that coherence. Standards were identified as priority or supporting based on the critical areas of focus described in the CT Standards, as well as the connections of the content within and across the K-12 domains and conceptual categories. In some instances, a standard identified as priority actually functions as a supporting standard in a particular unit. No stratification or omission of practice or content standards is suggested by the system of organization utilized in the units.
Adopted from The Arizona Academic Content Standards
Connecticut Curriculum Design Unit Planning Organizer
Grade 7 Mathematics
Unit 1 - Operating with Rational Numbers (Addition & Subtraction)
Pacing: 4 weeks (plus 1 week for reteaching/enrichment)
Mathematical PracticesMathematical Practices #1 and #3 describe a classroom environment that encourages thinking mathematically and are critical for quality teaching and learning.
Practices in bold are to be emphasized in the unit.
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Domain and Standards Overview
Number System
· Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
Priority and Supporting CCSS / Explanations and Examples* /
7.NS. 1. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
a. Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.
b. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.
c. Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.
d. Apply properties of operations as strategies to add and subtract rational numbers.
7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.) / 7.NS. 1. Visual representations may be helpful as students begin this work; they become less necessary as students become more fluent with the operations.
Examples:
• Use a number line to illustrate:
o p - q
o p + (- q)
o Is this equation true p – q = p + (-q)
• -3 and 3 are shown to be opposites on the number line because they are equal distance from zero and therefore have the same absolute value and the sum of the number and it’s opposite is zero.
You have $4 and you need to pay a friend $3. What will you have after paying your friend?
4 + (-3) = 1 or (-3) + 4 = 1
7.NS.3. Examples:
• Your cell phone bill is automatically deducting $32 from your bank account every month. How much will the deductions total for the year?
-32 + -32 + -32 + -32 + -32 + -32 + -32 + -32 + -32 + -32 + -32 + -32 = 12 (-32)
• It took a submarine 20 seconds to drop to 100 feet below sea level from the surface. What was the rate of the descent?
Concepts
What Students Need to Know / Skills
What Students Need To Be Able To Do / Bloom’s Taxonomy Levels
Addition and Subtraction of positive and negative numbers (begin with integers and extend to rational number)
o Number Line
· Equivalent Forms
· Opposite Quantities
o Additive Inverses
o Number Line
· Absolute Value
o Number Line
· Properties of Operations
· Mental Computation Strategies
· Estimation Strategies / · Add and Subtract (rational numbers)
· Describe (opposites quantities)
· Understand (positive or negative direction)
· Show (additive inverses)
· Interpret (sums in context)
· Understand (subtraction as additive inverses)
· Show (absolute value)
· Apply (absolute value principle in context)
· Apply (properties of operations as strategies)
· Solve (with and without context)
o Apply (properties of operations to calculate)
o Convert (between equivalent forms)
o Assess (reasonableness of answers)
§ Use (mental computation and estimation strategies) / 3
1
2
1
2
2
2
3
3
3,4
3
2
5
Essential Questions
Corresponding Big Ideas
Standardized Assessment Correlations
(State, College and Career)
Expectations for Learning (in development)
This information will be included as it is developed at the national level. CT is a governing member of the Smarter Balanced Assessment Consortium (SBAC) and has input into the development of the assessment.
Unit Assessments
The items developed for this section can be used during the course of instruction when deemed appropriate by the teacher. /
1. (-10) + (-8) =
Answer: -18
2. (-3) + 12 =
Answer: 9
3. Look at the number line below.
What equation is modeled on the number line?
A) -3 + 3 = 6 B) -3 + 6 = 3* C) -3 + (-6) = 0 D) -3 – 6 = 3
4. -5 – 2 =
Answer: -7
5. 7 – (-6) =
Answer: 13
6. At 8:00 a.m. the temperature outside was -5°C. At 6:00 p.m., the temperature was 25°C. By how many degrees Celsius (°C) did the temperature increase from 8:00 a.m. to 6:00 p.m.?
Answer: 30
7.
Answer:
8. -1.5 – 0.2 =
Answer: -1.7
9. -5 – 3 =
Show or explain how you found your answer. You may use the number line to help you.
Answer: -8 with an explanation that may or may not include using the number line.
Partial Credit: Correct answer,-8, with an incorrect or missing explanation, OR an incorrect answer with an explanation that demonstrates understanding of calculating the answer to a subtraction problem.
No Credit: Incorrect answer with an incorrect or missing explanation.
10. Look at the subtraction problem below.
Write an addition problem that is equivalent to this subtraction problem.
Show or explain how you know your addition problem is equivalent to.
Answer: with an explanation that may include:
· Additive inverse
· Number line movement
· Subtracting is the same as adding the opposite
Partial Credit: Correct answer,, with an incorrect or missing explanation, OR an incorrect answer with an explanation that demonstrates understanding of representing a subtraction problem as an addition problem.
No Credit: Incorrect answer with an incorrect or missing explanation.
11. The temperature at 6:00 a.m. was -5 ºF. At 2:00 p.m. the temperature had increased 14 ºF.
What was the temperature at 2:00 p.m.?
Answer: 9 ºF
12. On July 7, Tim’s bank account balance was -$150. What was the amount of the withdrawal for check #128 that caused this negative balance?
Transaction / Withdrawals (-) / Deposits (+) / Balance
July 5 / Deposit / $45 / $120
July 7 / Check #128 / ? / - $150
Answer: $270
13. The height of Tom’s house from ground level to the top of the roof is feet. The basement floor of his house is feet below ground level. What is the distance, in feet, between the top of the roof and the basement floor?
Answer:
13