**The main focus for this week will be addressing Algebra and Functions ****1.3** one of the Key Standards for the seventh grade as well as several Mathematical Reasoning Key Standards. In addition, the first Problem of the Week will be assigned.

**Main Activity**

Interactive Mathematics Text

**p. 16** Fruit for Thought Activity

*This activity includes algebraic reasoning, mathematical reasoning, and properties of numbers.*
Variable Dilemma Activity

Variable Dilemma Rubric

POW (similar problem)

*Alignment to CA Mathematics Standards:*

**Algebra and Functions**

**1.3** simplify numerical expressions by applying properties of rational numbers (identity, inverse, distributive, associative, commutative), and justify the process used

1.4 use algebraic terminology correctly (e.g., variable, equation, term, coefficient, inequality, expression, constant)

**Mathematical Reasoning**

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

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

**2.3** estimate unknown quantities graphically and solve for them using logical reasoning, and arithmetic and algebraic techniques

**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

**p. 276 #11** - similar problem (homework)

**pp. 204-206** - Properties of Numbers

**pp. 225-229** - Properties of Numbers

*Alignment to CA Mathematics Standards:*

**Algebra and Functions**

**1.3** simplify numerical expressions by applying properties of rational numbers (identity, inverse, distributive, associative, commutative), and justify the process used

**Problem of the Week** - pp. 26-32 - Unit 7 - problem solving

*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 to match the fruit (or the letters) to the digits 0 through 9 using what they know about the properties of numbers and mathematical reasoning.

**The main focus for the two weeks will be addressing Algebra and Functions 1.5 and also ****3.4** which is one of the Key Standards for the seventh grade as well as several Mathematical Reasoning Key Standards.

**Main Activity**

Leonardo da Vinci Activity

*Is the ratio of our arm span to our height really equal to ***1**?
Interactive Mathematics Text

**p. 256** Data Bank: Human Proportions

*Alignment to CA Mathematics Standards:*

**Algebra and Functions**

**1.5** Represent quantitative relationships graphically and interpret the meaning of a specific part of a graph in terms of the situation represented by the graph.

**3.4** plot values of the quantities whose ratio is always the same (cost vs. number of an item, feet vs. inches, circumference vs. diameter of a circle). Fit a line
to the plot and understand that the slope of the line equals the quantities.

**Mathematical Reasoning**

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

**2.3** estimate unknown quantities graphically and solve for them using logical reasoning, and arithmetic and algebraic techniques

**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

**p. 410-413** - ratios

**Resources**

**Assessment**
- Students will explain the conclusion to the question - Is your arm span equal to your height?

- Students will generalize using the class data

- Students will plot values of the quantities of a ratio using graph paper and a spreadsheet program.

**The main focus for this week will be addressing Mathematical Reasoning Key Standards for the seventh grade.**

**Main Activity**

Interactive Mathematics Text

**p. 7** Nutty Excursion Activity

*This activity includes volume equivalency, problem solving,and written expression.*
This will be available as an **ESCOT Runner** problem. The activity is called The Pirate Diamond Problem

*Alignment to CA Mathematics Standards:*

**Measurement and Geometry**

1.1 compare weights, capacities, geometric measures, times and temperatures within and between measurement systems (e.g., miles per hour and feet per second, cubic inches to cubic centimeters)

**Mathematical Reasoning**

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

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

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

**Extensions**

MAC Text

**p. 239-240** - capacity

**Resources**

**Assessment**
- Students will explain each step of how to measure 8 cubic units using a 6 and a 10 cubic unit container.