Dekalb County 7^{th} Grade

Sarah Ledford

Main Goal: To develop mathematical understanding by investigating non-traditional open-ended problems.

September | October-November | December | January | March

**Location: Central Office**

**Mathematical Content Goal:** To develop
conceptual understanding of posing questions, collecting, representing, and
analyzing data, and interpreting the results.

**Standards: M7D1. Students will pose questions,
collect data, represent and analyze the data, and interpret results.**

a. Formulate questions and collect data from a census of at least 30 objects and from samples of varying sizes.

b. Construct frequency distributions.

c. Analyze data using measures of central tendency (mean, median, and mode), including recognition of outliers.

d. Analyze data with respect to measures of variation (range, quartiles, interquar- tile range).

e. Compare measures of central tendency and variation from samples to those from a census. Observe that sample statistics are more likely to approximate the population parameters as sample size increases.

f. Analyze data using appropriate graphs, including pictographs, histograms, bar graphs, line graphs, circle graphs, and line plots introduced earlier, and using box-and-whisker plots and scatter plots.

g. Analyze and draw conclusions about data, including a description of the relationship between two variables.

InterMath problems:

**Mean, Median, and Mode****Presenting Data****Predictions from Data****Experiments****Questioning, Collecting, and Reporting data****Pie Charts**

**Location: Central Office**

**Mathematical Content Goal:** To develop
conceptual understanding of computation of rational numbers and simplifying
and evaluating algebraic expressions.

**Standards: M7N1. Students will understand
the meaning of positive and negative rational numbers and use them in computation**.

a. Find the absolute value of a number and understand it as the distance from zero on a number line.

b. Compare and order rational numbers, including repeating decimals.

c. Add, subtract, multiply, and divide positive and negative rational numbers.

d. Solve problems using rational numbers.

**M7A1. Students will represent and evaluate
quantities using algebraic expressions. **

b. Simplify and evaluate algebraic expressions, using commutative, associative, and distributive properties as appropriate.

InterMath Problems:

**Absolute Value****Rational Numbers**- Splitting Fractions in Two
- The Salesman and the Eggs
- Unusual Property
- Increasing by One-Half
- Musical Chairs
- Ordering Fractions
- Where is that Fraction
- Johnny's
Rule

**Simplifying Expressions**- Arranging Toothpicks
- Phone # Problem
**1. Grab a calculator****2. Enter the first 3 digits of your phone # (not the area code)****3. Multiply by 80****4. Add 1****5. Multiply by 250****6. Add last four digits of your phone number****7. Add last four digits of your phone number again****8. Subtract 250****9. Divide by 3**

**Location: Central Office**

**Mathematical Content Goal:** To develop
conceptual understanding of representing
and evaluating quantities using algebraic expressions and applying linear
equations in one variable.

**Standards:**
**M7A1. Students will represent and evaluate quantities using algebraic
expressions.**

a. Translate verbal phrases to algebraic expressions.

b. Simplify and evaluate algebraic expressions, using commutative, associative, and distributive properties as appropriate.

c. Add and subtract linear expressions.

**M7A2. Students will understand and apply linear
equations in one variable.**

a. Given a problem, define a variable, write an equation, solve the equation, and interpret the solution.

b. Use the addition and multiplication properties of equality to solve one- and two-step linear equations.

InterMath Problems:

**Writing Expressions**- Consecutive Odds and Evens
- Theater Seating
- Number Machine
- Number Cruncher - TIM site
- Arranging
Toothpicks

**Simplifying and Generalizing**

**Location: Central Office**

**Mathematical Content Goal:** To develop
conceptual understanding of plane figures, transformations, and point plotting
on the coordinate plane.

**Standards:**
**M7G1. Students will construct plane figures that meet given conditions.**

a. Perform basic constructions using both compass and straight edge, and appropriate technology. Constructions should include copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.

b. Recognize that many constructions are based on the creation of congruent triangles.

M7G2. Students will demonstrate understanding of transformations.

a. Demonstrate understanding of translations, dilations, rotations, reflections, and relate symmetry to appropriate transformations.

b. Given a figure in the coordinate plane, determine the coordinates resulting from a translation, dilation, rotation, or reflection.

**M7A3. Students will understand relationships
between two variables.**

a. Plot points on a coordinate plane.

InterMath Problems:

**Constructions****Transformations**- Transformations from NLVM (translations, rotations, and reflections)
- Rotating Coordinates
- Transformations

**Plotting Points**

**Location: Central Office**

**Mathematical Content Goal:** To develop
conceptual understanding of similar figures, three-dimensional figures, and
relationships between two variables.

**Standards:**
**M7G3. Students will use the properties of similarity and apply these
concepts to geometric figures.**

a. Understand the meaning of similarity, visually compare geometric figures for similarity, and describe similarities by listing corresponding parts.

b. Understand the relationships among scale factors, length ratios, and area ratios between similar figures. Use scale factors, length ratios, and area ratios to determine side lengths and areas of similar geometric figures.

c. Understand congruence of geometric figures as a special case of similarity: The figures have the same size and shape.

M7G4. Students will further develop their understanding of three-dimensional figures.

a. Describe three-dimensional figures formed by translations and rotations of plane figures through space.

b. Sketch, model, and describe cross-sections of cones, cylinders, pyramids, and prisms.

**M7A3. Students will understand relationships
between two variables.**

b. Represent, describe, and analyze relations from tables, graphs, and formulas.

c. Describe how change in one variable affects the other variable.

d. Describe patterns in the graphs of proportional relationships, both direct (y = kx) and inverse (y = k/x).

InterMath Problems:

**Scale factor & Similarity**- SB section 9.4 p. 413
- SB Activity 9T p. 306
- SB Activity 9U p. 308

**3D Figures****Cross Sections**- Cross-section
- SB p. 322 #4 and 5

**Variable Relationships**