TITLE: What Comes Next? Chapters 1-4

CONTENT AREAS (What areas of mathematics does this lesson cover?): Number sense: patterns, estimation, addition and multiplication, percents

GRADE LEVEL: 8th

MATERIALS NEEDED: Calculators, handouts, graphs, cards with forecasting situations, butcher paper, markers, meter sticks

KEY CONCEPTS: Forecasting techniques allow us to predict future growth. Addition and multiplication growth numbers create different patterns.

EALR'S and GLE'S (Make the connections clear and specific)
Component 1.1: Understand and apply concepts and procedures from number sense.

Number and numeration

1.1.4 Apply ratio, percent, and direct proportion in situations. W

Solve problems involving percentages (e.g., percent increase/decrease, tax, commission, discount). [SP, MC]

Computation

1.1.7 Understand and apply strategies and tools to complete tasks involving computation on rational numbers.

Describe strategies for mentally solving problems involving integers and exponents. [CU]

Use calculators to compute with whole number powers beyond the cubed numbers.

Estimation

1.1.8 Apply estimation strategies to predict or determine the reasonableness of answers in situations involving computation on rational numbers in any form including whole number powers and square roots of square numbers. W

Describe various strategies used during estimation involving integers. [CU]

Use estimation to predict or to verify the reasonableness of calculated results. [RL]

Statistics

1.4.5 Understand and apply data techniques to interpret bivariate data. W

Make predictions about real-world situations (e.g., population trends, socio-economic)

Examine data in a two-column table to interpolate or extrapolate additional values. [RL]

GOALS (Remember the difference between goals and objectives):

- Students will be able to find addition and multiplication growth numbers using guess-and- check strategies and calculators.

- Students will be able to grow a number from start to target in four steps.

- Students will be able to recognize and describe the differences between multiplication and addition growth patterns.

OBJECTIVES

- Students will practice making forecasts about world population growth.

- Students will build growth sequences using addition and multiplication models.

- Students will create a visual representation of the two growth models with spirals.

PROCEDURES

Each group moves over to analyze the spiral made by their neighboring group. They figure out what the growth number is, determine if it is an addition or a multiplication spiral, and calculate what the length of the thirtieth segment would be if the spiral continued. Would the spiral still fit in our classroom? How many centimeters, meters or kilometers long would it be?

The whole class goes from spiral to spiral. How can we tell an addition spiral from a multiplication spiral? Notice the astounding growth on the multiplication spirals that start with very small growth numbers under 3.

POST-ASSESSMENT
Assign homework from book that gives students more practice in finding growth numbers with both models and extending forecasting concepts to include the past.

TEACHER REFLECTION

I felt like I had to rush my students to get them through four chapters in a one-hour class! This made it impossible to build the concepts as thoroughly as I would have liked. The math was more difficult for the class than I anticipated. I was really pleased by the discussions I heard in the small groups as I walked around the room, not only about math strategies but about socio-economic trends. This topic of forecasting really integrates social studies and math in a way that I find engaging and relevant to current issues (exactly why I chose this unit!). The book suggested having students draw the spirals individually on graph paper but I think the larger format where each group made a different spiral was more successful in this case, giving us a very colorful, visual way to compare the two growth models.