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## Postscript: Knock 'em down

This simple dice game supports students' development of flexibility with numbers, the properties of the four operations (+, −, ×, ÷), and the order of operations. It requires only dice and a game board for each player.

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## Technology-Powered Assessments for Learning

Making student thinking visible improves the feedback loop for the learner, the teacher, and the entire class.

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## What my thinking looks like

Challenge your students to create a visual representation of their thinking that can be captured in a single photograph. First, pose a task based on a real-world situation that is familiar to your students.

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## Build those numbers

Students are challenged to use numbers rolled on three dice to write expressions for values 1–12, using as few rolls as possible. Postscript items are designed as rich grab-and-go resources that teachers can quickly incorporate into their classroom repertoire with little effort and maximum impact.

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Several detours prompted me to find time in an overcrowded school day to incorporate important, powerful, daily, whole-class application of fact strategies.

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## Arithmogons

Easy-to-design puzzles that encourage mathematical reasoning and promote numerical fluency, arithmogon puzzles are simple: Add the numbers in two circles to get the number in the square. Every month, this final page of the journal highlights a quick game, puzzle, activity, or instructional strategy and suggestions for teachers of different grade bands to use the idea in the classroom.

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## Digital Date Equations

This article shares ideas for using the calendar date to increase students' mental mathematics and problem-solving skills. Postscript items are designed as rich grab-and-go resources that any teacher could quickly incorporate into his or her classroom repertoire with little effort and maximum impact.

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## Oki-Doku: Number Puzzles

Consider using these problems to help students develop number and operation sense in a simple and fun way.

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## Strengthening Discussions

Teachers can foster strategy sharing by attending to the cognitive demands that students experience while talking, listening, and making mistakes.

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## Developing Quantitative Mental Imagery

Use these descriptions of diagnostic and instructional tools to help young learners move beyond reliance on physical materials to negotiate arithmetic tasks.