**The main focus for this week will be addressing Number Sense ****1.2** one of the Key Standards for the seventh grade as well as several Mathematical Reasoning Key Standards. The extension activities address Number Sense **1.4, 1.5, 2.2**, and **2.3** all Key Standards for the seventh grade as well as several Mathematical Reasoning Key Standards.

**Main Activity**

Square Bowling (ESCOT problem - November 1, 1999)

*This activity presents an interactive problem with a square bowling ball, a bowling alley and two pins. The objective is to type in the scaling factors that will result in the pins being knocked down by the bowling ball.*
Project Mathematics - Similarity - video available for checkout.

*Alignment to CA Mathematics Standards:*

**Number Sense**

**1.2** add, subtract, multiply and divide rational numbers, integers, fractions and decimals and take rational numbers to whole number powers

**Mathematical Reasoning**

**1.1** analyze problems by identifying relationships, discriminating relevant from irrelevant information, identifying missing information, sequencing and prioritizing information, and observing patterns

**2.1** use estimation to verify the reasonableness of calculated results

**2.4** make and test conjectures using both inductive and deductive reasoning

**2.6** express the solution clearly and logically using appropriate mathematical notation and terms and clear language, and support solutions with evidence, in both verbal and symbolic work

**2.8** make precise calculations and check the validity of the results from the context of the problem

**Extensions**

MAC Text

**pp. 154-156** - Fractions and Decimals

**pp. 189-193** - Multiplying Fractions

*Alignment to CA Mathematics Standards:*

**Number Sense**

**1.4** differentiate between rational and irrational numbers

**1.5** know that every fraction is either a terminating or repeating decimal and be able to convert terminating decimals into reduced fractions representations of a decimal

**2.2** add and subtract fractions using factoring to find common denominators numbers

**2.3** multiply, divide, and simplify fractions using exponent rules

**Resources**

**Assessment**
- Students will explain how changing the numerator and denominator changes the size of the bowling ball.
- Students will correctly place fractions on a number line to show relative value.

**The main focus for this week will be addressing Number Sense ****1.2** one of the Key Standards for the seventh grade as well as several Mathematical Reasoning Key Standards. The extension activities address Number Sense **1.4, 1.5, 2.2**, and **2.3** all Key Standards for the seventh grade as well as several Mathematical Reasoning Key Standards.

**Main Activity**

Interactive Mathematics Text

**p. 18** A Square w/ Round Corners

*This activity includes working with rational numbers and products in the setting of circles.*
There will be an **ESCOT Runner** problem on rational vs. irrational numbers. The activity will be written using this Geometer's Sketchpad JAVA applet

Ask Dr. Math: FAQ - Integers, Rational & Irrational Numbers

*Alignment to CA Mathematics Standards:*

**Number Sense**

**1.2** add, subtract, multiply and divide rational numbers, integers, fractions and decimals and take rational numbers to whole number powers

**Mathematical Reasoning**

**1.1** analyze problems by identifying relationships, discriminating relevant from irrelevant information, identifying missing information, sequencing and prioritizing information, and observing patterns

**2.1** use estimation to verify the reasonableness of calculated results

**2.4** make and test conjectures using both inductive and deductive reasoning

**2.6** express the solution clearly and logically using appropriate mathematical notation and terms and clear language, and support solutions with evidence, in both verbal and symbolic work

**2.8** make precise calculations and check the validity of the results from the context of the problem

**Extensions**

MAC Text

**pp. 189-193** - Multiplying Fractions

**pp. 154-156** - Fractions and Decimals

*Alignment to CA Mathematics Standards:*

**Number Sense**

**1.4** differentiate between rational and irrational numbers

**1.5** know that every fraction is either a terminating or repeating decimal and be able to convert terminating decimals into reduced fractions representations of a decimal

**2.2** add and subtract fractions using factoring to find common denominators numbers

**2.3** multiply, divide, and simplify fractions using exponent rules

**Resources**

**Assessment**
- Students will demonstrate ability to multiply fractions.
- Students will demonstrate ability to differentiate between rational and irrational numbers.

**The main focus for this week will be addressing Measurement and Geometry 3.2 and 3.5 as well as several Mathematical Reasoning Key Standards. The extension activities address Measurement and Geometry 2.1, 2.2, 3.1 as well as Measurement and Geometry **** Key Standards 3.4 and 3.6**.

**December 20-31** - Winter Break

**Main Activity**

Interactive Mathematics Text

**p. 8** Pentamino +1 = Hexamino

*This activity includes combinations, symmetry, area, and perimeter of polygons*

Dominoes Activity

Experiment with Volume by Cynthia Lanius

*Alignment to CA Mathematics Standards:*

**Measurement and Geometry**

3.2 understand and use coordinate graphs to plot simple figures, determine lengths and areas related to them, and determine their image under translations and reflections

3.5 construct two-dimensional patterns for three-dimensional models such as cylinders, prisms and cones

**Mathematical Reasoning**

**1.1** analyze problems by identifying relationships, discriminating relevant from irrelevant information, identifying missing information, sequencing and prioritizing information, and observing patterns

**1.2** formulate and justify mathematical conjectures based upon a general description of the mathematical question or problem posed

**2.2** apply strategies and results from simpler problems to more complex problems

**2.4** make and test conjectures using both inductive and deductive reasoning

**2.5** use a variety of methods such as words, numbers, symbols, charts, graphs, tables, diagrams and models to explain mathematical reasoning

**3.3** develop generalizations of the results obtained and the strategies used and extend them to new problem situations.

**Extensions**

MAC Text

**p. 324-326** - Translations

**p. 327-329** - Reflections

**p. 378-380** - Drawing Three-Dimensional Figures

**p. 381-382** - Making a Model

**p. 383-386** - Surface Area of Prisms

**p. 387-391** - Surface Area of Cylinders

**p. 301-302** - Constructing Perpendicular Lines

**p. 311-312** - Bisecting Angles and Segments

*Alignment to CA Mathematics Standards:*

**Measurement and Geometry**

2.1 routinely use formulas for finding the perimeter and areas of basic two-dimensional figures and for the surface area and volume of basic three-dimensional figures, including rectangles, parallelograms, trapezoids, squares, triangles, circles, prisms, and circular cylinders

2.2 estimate and compute the area of more complex or irregular two- and three-dimensional figures by breaking them up into more basic geometric objects

3.1 identify and construct basic elements of geometric figures, (e.g., altitudes, midpoints, diagonals, angle bisectors and perpendicular bisectors; and central angles, radii, diameters and chords of circles) using compass and straight-edge

**3.4** demonstrate an understanding of when two geometrical figures are congruent and what congruence means about the relationships between the sides and angles of the two figures

**3.6** identify elements of three-dimensional geometric objects (e.g., diagonals of rectangular solids) and how two or more objects are related in space (e.g., skew lines, the possible ways three planes could intersect)

**Problem of the Week** - pp. 108-114 - Unit 9 - perimeter and area

*On the first Wednesday of the month students will have a reading activity in class. They will read the different POWs in their text and select one to work on for that week.*

*Alignment to CA Mathematics Standards:*

**Mathematical Reasoning**

**1.1** analyze problems by identifying relationships, discriminating relevant from irrelevant information, identifying missing information, sequencing and prioritizing information and observing patterns.

**1.2** formulate and justify mathematical conjectures based upon a general description of the mathematical question or problem posed.

**1.3** determine when and how to break a problem into simpler parts.

**2.4** make and test conjectures using both inductive and deductive reasoning

**2.5** use a variety of methods such as words, numbers, symbols, charts, graphs, tables, diagrams and models to explain mathematical reasoning.

**2.6** express the solution clearly and logically using appropriate mathematical notation and terms and clear language, and support solutions with evidence, in both verbal and symbolic work.

**3.1** evaluate the reasonableness of the solution in the context of the original situation

**3.2** note method of deriving the solution and demonstrate conceptual understanding of the derivation by solving similar problems.

**Resources**

**Assessment**
- Students will explain how many different arrangements can be made using 6 tiles considering reflections and rotations.
- Students will demonstrate understanding of going from a two-dimensional net to a three-dimensional solid figure by noting which hexaminoes can be folded to create a cube.