**The main focus for these weeks will be addressing several Mathematical Reasoning Key Standards. **

**January 17** - Martin L. King, Jr. Day

**Main Activity**

Rock, Scissors, Paper

*This activity includes determining the probability of winning at Rock, Scissors, Paper using both the real-life simulation and a computer simulation.*

This will be available as an **ESCOT Runner** problem (POW January 1, 2000).

*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

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

**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

**2.6** 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

**Extensions**

MAC Text

**pp. 495-496** - Fair and Unfair Games

**pp. 500-502** - Theoretical and Experimental Probability

**pp. 503-505** - Act It Out

*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

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

**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

**2.6** 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

**Resources**

**Assessment**
- Given a set of circumstances students will explain and justify their explanation of whether a game is fair or unfair.

**Problem of the Week** - pp. 148-154 - Unit 10 - probability

*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.

**The main focus for these weeks will be addressing Number Sense ****1.2** and Measurement and Geometry **3.4** both Key Standards for the seventh grade as well as several Mathematical Reasoning Key Standards. The extension activities address Measurement and Geometry 2.1 and 2.2 **Key Standard 3.6** as well as several Mathematical Reasoning Key Standards.

**Main Activity**

Paper Folding Problem

*This activity includes folding a sheet of paper once to
obtain three similar triangles.*
This will be available as an **ESCOT Runner** problem. The activity is called The Paper Folding Problem.

*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

**Measurement and Geometry**

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

**Mathematical Reasoning**

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

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

2.4 make and test conjectures using both inductive and deductive reasoning

**Extensions**

MAC Text

**p. 297-300** - Angles (including congruent angles)

**p. 307-310** - Triangles and Quadrilaterals

**p. 241-242** - Area Activity

**p. 243-245** - Triangles and Quadrilaterals

**p. 351-353** - Area of Irregular Figures

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

*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

**3.6** 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)

**Mathematical Reasoning**

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

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

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

**Resources**

**Assessment**
- Students will demonstrate understanding of congruence and similarity.
- Students will use formulas to find the perimeter and area of two-dimensional figures.
- Students will estimate and compute the area of irregular two-dimensional figures.
- Students will identify elements of three-dimensional objects.