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• "CCSS.Math.Content.4.OA.C.5"
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## Readers Exchange: Grossman and McCoid talk back

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## Back Talk: Fifth graders' thinking about numerical and spatial patterns

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## Problem Solvers: Problem And Problem Solvers: Solutions

The classic question of mixing water and wine (Ball 1896, p. 27) is the basis of the May problem, which can be solved without using computation.

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## Questions to Elicit Students' Mathematical Ideas

Create opportunities for students to engage in the Standards for Mathematical Practice and support them in further explaining and justifying their ideas.

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## Fostering optimization ideas in early grades

iSTEM: Integrating Science, Technology, and Engineering in Mathematics authors share ideas and activities that stimulate student interest in the integrated fields of science, technology, engineering, and mathematics (STEM) in K-grade 6 classrooms. This article describes how optimization ideas can be fostered in early grades through a game-based activity called Avoiding Invasion from Aliens

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## Problem: Pattern Blocks

This month's problem capitalizes on children's natural enthusiam to explore patterns to help them solve problems that might be too difficult or time-consuming to model directly.

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## A Fibonacci Simple Ecosystem: Prey and Predator

Predators and prey in the population of an ecosystem can be evaluated and investigated with mathematical explorations. Intermediate elementary students explore Fibonacci sequences in relation to prey and discuss models to maintain a balance between the species through mathematics by modifying variables. iSTEM (Integrating Science, Technology, and Engineering in Mathematics) authors share ideas and activities that stimulate student interest in the integrated fields of science, technology, engineering, and mathematics (STEM) in K-grade 6 classroom.

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## Solutions: Which is the Better Deal?

Third-grade students from Coronation Public School in Cambridge, Ontario, Canada, were given a chance to examine two different allowance plans and decide which plan would provide them with more money after twelve weeks.

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## A second grader's algebraic reasoning

A talkative second grader helps her teacher describe, extend, and generalize about growing patterns.

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## How Many Dogs? How Many Chickens?

Students say some amazing things. Back Talk highlights the learning of one or two students and their approach to solving a math problem. Each article includes the prompt used to initiate the discussion, a portion of dialogue, student work samples (when applicable), and teacher insights into the mathematical thinking of students. This article describes the thought processes of two third-grade students who were given a problem involving finding the number of dogs and chickens on a farm when they know only the total number of legs. Their solution strategies include standard mathematical operations as well as pictorial representations.