Fleming County Schools
7th Grade Mathematics
21st Century Learning: Six principles of learning
1. Being literate is at the heart of learning in all subject areas
2. Learning is a social act
3. Learning establishes a habit of inquiry
4. Assessing progress is part of learning
5. Learning includes turning information into knowledge using multi-media
6. Learning occurs in global context
4 C’s of 21st Century Learning
1. Creativity
2. Collaboration
3. Critical Thinking/Problem Solving
4. Communication
***Information in the explanations and examples found in this document came from Arizona Department of Education and Common Core. Information in resources and assessments came from the Georgia Dept. of Education
Key Instructional Shifts in Mathematics
1. Focus strongly where the Standards focus / Rather than racing to cover everything in today’s mile-wide, inch-deep curriculum, teachers use the power of the eraser and significantly narrow and deepen the way time and energy is spent in the math classroom. They focus deeply on only those concepts that are emphasized in the standards so that students can gain strong foundational conceptual understanding, a high degree of procedural skill and fluency, and the ability to apply the math they know to solve problems inside and outside the math classroom.2. Coherence: think across grades, and link to major topics within grades / Thinking across grades: Instead of treating math in each grade as a series of disconnected topics, principals and teachers carefully connect the learning within and across grades so that, for example, fractions or multiplication develop across grade levels and students can build new understanding onto foundations built in previous years. Teachers can begin to count on deep conceptual understanding of core content and build on it. Each standard is not a new event, but an extension of previous learning.
Linking to major topics: Instead of allowing less important topics to detract from the focus of the grade, these topics are taught in relation to the grade level focus. For example, data displays are not an end in themselves but are always presented along with grade-level word problems.
3. Rigor: require conceptual understanding, procedural skill and fluency, and application with intensity. / Conceptual understanding: Teachers teach more than “how to get the answer” and support students’ ability to access concepts from a number of perspectives so that students are able to see math as more than a set of mnemonics or discrete procedures. Students demonstrate deep conceptual understanding of core math concepts by solving short conceptual problems, applying math in new situations, and speaking about their understanding.
Procedural skill and fluency. Students are expected to have speed and accuracy in calculation. Teachers structure class time and/or homework time for students to practice core functions such as multiplication facts so that students are able to understand and manipulate more complex concepts.
Application: Students are expected to use math and choose the appropriate concept for application even when they are not prompted to do so. Teachers provide opportunities at all grade levels for students to apply math concepts in “real world” situations. Teachers in content areas outside of math, particularly science, ensure that students are using math – at all grade levels – to make meaning of and access content.
PACING and SUGGESTED TIMELINES
Not all of the content in a given grade is emphasized equally in the standards. Some clusters require greater emphasis than the others based on the depth of the ideas, the time that they take to master, and/or their importance to future mathematics or the demands of college and career readiness. In addition, an intense focus on the most critical material at each grade allows depth in learning, which is carried out through the Standards for Mathematical Practice.
To say that some things have greater emphasis is not to say that anything in the standards can safely be neglected in instruction. Neglecting material will leave gaps in student skill and understanding and may leave students unprepared for the challenges of a later grade. The following table identifies the Major Clusters, Additional Clusters, and Supporting Clusters for this grade.
Achieve the Core.org
Major ClusterSupporting Cluster
Additional Cluster
Required Fluencies in the Common Core State Standards for Mathematics
When it comes to measuring the full range of the Standards, usually the first things that come to mind are the mathematical practices, or perhaps the content standards that call for conceptual understanding. However, the Standards also address another aspect of mathematical attainment that is seldom measured at scale either: namely, whether students can perform calculations and solve problems quickly and accurately. At each grade level in the Standards, one or two fluencies are expected.
K / Add/subtract within 51 / Add/subtract within 10
2 / Add/subtract within 20*
Add/subtract within 100 (pencil and paper)
3 / Multiply/divide within 100**
Add/subtract within 1000
4 / Add/subtract within 1,000,000
5.NBT.5 / Multi-digit multiplication
6 / Multi-digit division
Multi-digit decimal operations
7 / Solve px + q = r, p(x + q) = r
8 / Solve simple 2x2 systems by inspection
Fluent in the Standards means “fast and accurate.” It might also help to think of fluency as meaning the same thing as when we say that somebody is fluent in a foreign language: when you’re fluent, you flow. Fluent isn’t halting, stumbling, or reversing oneself. Assessing fluency requires attending to issues of time (and even perhaps rhythm, which could be achieved with technology).
The word fluency was used judiciously in the Standards to mark the endpoints of progressions of learning that begin with solid underpinnings and then pass upward through stages of growing maturity. In fact, the rarity of the word itself might easily lead to fluency becoming invisible in the Standards—one more among 25 things in a grade, easily overlooked. Assessing fluency could remedy this, and at the same time allow data collection that could eventually shed light on whether the progressions toward fluency in the Standards are realistic and appropriate.
*1 By end of year, know from memory all sums of two one‐digit numbers
**2 By end of year, know from memory all products of two one‐digit numbers
***This information is cited from: http://www.engageny.org/sites/default/files/resource/attachments/ccssfluencies.pdf
Learning Targets:
Learning Targets are “I can” statements in student friendly language that guide students’ learning to reach mastery of the intended standard. While they may be formatively assessed, they are not intended to be summatively assessed separately. Teachers need to work with their students to be sure they understand the learning goal. See example below:
Display Intended Standard: (Example from 7th grade)
7.RP.1. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.
Ask students, “What is this asking you to do?”
Student response(s)- “I should be able to find unit rates.”
“We will have to work with fractions, lengths and area.”
Teacher Response: “Do you know what that means?”
Student Response: “No.”
Teacher Response: “Here is an example.” Joe walks ½ mile in ¼ hour. What is Joe’s rate in miles per hour?
Student Response: “I don’t know how to do that.”
Teacher Response: “That is okay. We are going to work on this for a few days. Let’s set a learning target.”
Learning Target: “I can compute unit rates involving fractions, lengths, areas and other quantities in like or different units.
Daily Target: Today, “I know what it means to find the unit rate.”
Grade 7
Grade 7 Overview
Ratios and Proportional Relationships (RP)· Analyze proportional relationships and use them to solve real-world and mathematical problems.
The Number System (NS)
· Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
Expressions and Equations (EE)
· Use properties of operations to generate equivalent expressions.
· Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
Geometry (G)
· Draw, construct and describe geometrical figures and describe the relationships between them.
· Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
Statistics and Probability (SP)
· Use random sampling to draw inferences about a population.
· Draw informal comparative inferences about two populations.
· Investigate chance processes and develop, use, and evaluate probability models. / Mathematical Practices (MP)
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.
In Grade 7, instructional time should focus on four critical areas: (1) developing understanding of and applying proportional relationships; (2) developing understanding of operations with rational numbers and working with expressions and linear equations; (3) solving problems involving scale drawings and informal geometric constructions, and working with two- and three-dimensional shapes to solve problems involving area, surface area, and volume; and (4) drawing inferences about populations based on samples.
(1) Students extend their understanding of ratios and develop understanding of proportionality to solve single- and multi-step problems. Students use their understanding of ratios and proportionality to solve a wide variety of percent problems, including those involving discounts, interest, taxes, tips, and percent increase or decrease. Students solve problems about scale drawings by relating corresponding lengths between the objects or by using the fact that relationships of lengths within an object are preserved in similar objects. Students graph proportional relationships and understand the unit rate informally as a measure of the steepness of the related line, called the slope. They distinguish proportional relationships from other relationships.
(2) Students develop a unified understanding of number, recognizing fractions, decimals (that have a finite or a repeating decimal representation), and percents as different representations of rational numbers. Students extend addition, subtraction, multiplication, and division to all rational numbers, maintaining the properties of operations and the relationships between addition and subtraction, and multiplication and division. By applying these properties, and by viewing negative numbers in terms of everyday contexts (e.g., amounts owed or temperatures below zero), students explain and interpret the rules for adding, subtracting, multiplying, and dividing with negative numbers. They use the arithmetic of rational numbers as they formulate expressions and equations in one variable and use these equations to solve problems.
(3) Students continue their work with area from Grade 6, solving problems involving the area and circumference of a circle and surface area of three-dimensional objects. In preparation for work on congruence and similarity in Grade 8 they reason about relationships among two-dimensional figures using scale drawings and informal geometric constructions, and they gain familiarity with the relationships between angles formed by intersecting lines. Students work with three-dimensional figures, relating them to two-dimensional figures by examining cross-sections. They solve real-world and mathematical problems involving area, surface area, and volume of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes and right prisms.
(4) Students build on their previous work with single data distributions to compare two data distributions and address questions about differences between populations. They begin informal work with random sampling to generate data sets and learn about the importance of representative samples for drawing inferences.
Standards for Mathematical Practice /Standards / Explanations and Examples /
Students are expected to: / Mathematical Practices are listed throughout the grade level document in the 2nd column to reflect the need to connect the mathematical practices to mathematical content in instruction. /
7.MP.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?”.
7.MP.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.
7.MP.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.
7.MP.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.
7.MP.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.