Discovering Pi and Solving Proportions Ratios, Proportions, and Stats across Multiple CCSS by Joe Shim and Veronica Smith Diamond Point Elementary School, Diamond Bar Emerson Middle School, Pomona

Fractions, ratios, proportions, and stats? How are all these related? Can we make connections between them? How do students feel about these standards? How do we as teachers feel about these standards? How can these be fun?

All fractions are ratios but not all ratios are fractions... Ratios compare two events. Skills are common between ratios and fractions. Ratios are less threatening to learn for students. Ratios can be fun...

A Ratio Activity Investigation of Circles In groups you will measure the diameter and circumference of as many circles as possible. You will then chart your measurements. After charting you will perform operations with those measurements. – +, -, x, / the numbers with each other – use calculators Measure as many lids as possible.

Discovering Pi

Engaging

Benefits of this project... perseverance attending to precision collaboration communication critical thinking building vocabulary measuring skills generalizing kinesthetic learning engaging concrete real life connections

21st Century Skills Bloom’s

Extension use string to see if the relationship is real by seeing if it is about 3x the diameter use string and chalk to measure out larger circles – draw out a large circle using chalk and string to keep consistent radius – measure the diameter with string or measuring wheel – compare that measurement with the larger circle

Important Foundational Skills Fluency in multiplication and division develop into powerful forms of ratio and proportional reasoning. The idea of relationships between quantities become explicit The gradual development of data representations over the prior years leads to statistics

6.SP.5 - Statistical Investigation 3. Analyze the data with appropriate methods 4. Interpret results and draw valid conclusions from the data that relate to the questions posed. 1.Formulate questions that can be answered with data (anticipating variability in responses) 2.Design and use a plan to collect relevant data

Grasshopper Jump Name your grasshopper. Practice your jumps. In your groups make your grasshopper jump and measure results. After completing the jumps fill out the requested information.

Making Connections “Standards are not to be checked off a list during isolated units of instructions, but rather content to be developed throughout the school year through rich instructional experiences.”* *The Mathematics Framework, CA SBE 11/6/13 Q.How can we relate topics of study throughout the curriculum? A. Look for opportunities to reinforce major standards.

Extensions and Rigor Extending the concept to other standards. 6.SP.5.d - Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. New Question: If you could jump like a grasshopper how far would you jump?

Student Engagement!

Literature Connection Circumference series of books If You Hopped Like a Frog Jim and the Beanstalk

Skittles Experiment According to Skittles there is an even distribution of colors… Let’s see how accurate they are… Investigation Open and sort the Skittles by color into the circle. Redistribute them to make a chart. Calculate the fractional amount for each color.

Poster Project

M & M simulation Engages students by using familiar materials. Reinforces the ideas of connecting abstract concepts with concrete examples.

According to M&Ms % colorPlainPeanutCrispyMinisPeanut Butter Almond Brown13%12%17%13%10% Yellow14%15%17%13%20% Red13%12%17%12%10% Green16%15%16%12%20% Blue24%23%17%25%20% Orange20%23%16%25%20%

Closure Review and Reflections: How can simulations and activities help you in engaging and motivating students in the classroom? (think-ink-pair-share)