October 2016

• ## Classroom Resource Collaboration Center

NCTM is excited to offer a featured resource in your grade band this month to help you make the most of your NCTM membership. As we launch our new Classroom Resource Collaboration Center, we'll keep members informed through Summing Up and social media. Check out the #NCTM_CRCC hashtag on Twitter to follow along as we share and discuss these and other NCTM classroom resources.

## Kindergarten-Grade 2

Young mathematicians love to count and compare, especially when they can compare things about themselves to their classmates. The How Many Letters Are in your Name lesson from NCTM's Illuminations starts out perfectly for kindergartners just learning to print their names, count to ten, and recognize their friends' names.

The lesson can be extended for first and second grade to include tasks such as students' representing the letters in their full names using multiple 10-frames, subtracting to find out how many more letters one student has compared to another, or graphing the number of letters in each name in their group of 3 or 4.

## Grades 3-5

Students' work with fractions in elementary school is built on an understanding of unit fraction. The French Fry Tasks in the article Unit Fraction Knowledge and the French Fry Tasks from Teaching Children Mathematics provide a useful set of tasks, questions, and games to help students build up their intuition about concepts like the relative size of different unit fractions and the whole being made up of repeated copies of unit fractions. These tasks can be used as a whole class exploration of unit fractions, and are also appropriate tasks for small groups or stations when students need extra practice with fraction estimation and understanding of unit fractions. The key is to focus with students on developing the iteration strategy for guessing and testing how long each unit fraction of the french fry will be.

## Grades 6-8

Middle-school mathematicians benefit from having many opportunities to engage in algebraic reasoning, both formal and informal. Tasks like the Math Forum Problem of the Week Ostrich Llama Count (PDF) gives students a chance to compare and make connections across numeric, verbal, graphical, visual, and algebraic descriptions of the same situation. The Teacher Packet (PDF) has sample student solutions that can be used in a lesson focused on comparing representations that is outlined in a California Math Council ComMuniCator Article about Ostrich Llama Count. Adjust for different grade levels by choosing just the appropriate representations from the activity.

## Algebra 1

Gathering real-world data is a great way to help novice algebraists make meaning of slope, x-intercepts, and y-intercepts. But it can be challenging to find real-world data with negative slopes and interesting x-intercepts. Walk the Plank from NCTM's Illuminations has students exploring the linear relationship between distance from a scale and weight.

Teaching Tip Because weight can be a sensitive topic, consider using heavy items like bowling balls, dumbbells, and sandbags that can be placed on the plank and moved back and forth, rather than students' weights.

## Geometry

Problems with multiple solutions paths are great for seeing structure and making connections among different concepts. The Broken Pottery (PDF) Math Forum Problem of the Week allows students to tackle a geometry problem about the relationships between arc length, angles, radii, and chord length, and explore how different solutions to the same problem make use of similar relationships. This problem can be used as a non-routine challenge problem for students to apply their learning, or to launch an investigation about arcs or chords. It can also be used as a lesson on finding the center of a circle given just arcs or chords, by inviting students to Notice and WonderTM (PDF) about solutions their classmates came up with, or ones you found in the Teacher Packet (PDF).

## Algebra II/Pre-Calculus

As part of NCTM's Focus on Reasoning and Sense-Making in High School, a collection of tasks was created that promote the mathematical practices and conceptual understanding in high school. Horseshoes in Flight (PDF) is one task that focuses on helping students see and make use of structure in quadratic expressions as they connect different pieces of expressions to the parabolic path of a horseshoe in flight.

## Probability and Statistics

Novice statisticians need time to grapple with the important concepts underlying hypothesis testing. The article Statistical Literacy: Simulations with Dolphins from Mathematics Teacher builds from students initial intuitions, through carefully designed simulations, to give students a chance to grapple with and make sense of foundational ideas in statistics.

Be sure to also check out these additional resources and tools for your classroom.

## Math Forum - Problems of the Week

Get your weekly dose of math problems and puzzles from the Math Forum. You will also find more math resources and tools, as well as a Math Forum: Problems of the Week Blog, furthering discussion.

## Brain Teasers

Want quick ideas for great back-to-school icebreaker classroom activities? We've got you covered. Challenge your new students and mathematics enthusiasts alike with these staff-picked puzzles. In need of more? Browse the entire Illuminations library and discover what's in store in this amazing resource.