# Sketch Pad Canonical: https://manipulatives.org/manipulatives/sketch-pad/ An open drawing space for turning a math idea into a picture, revising it, and explaining your thinking. ![A reusable drawing board showing twelve dots in four rows of three, with a blue marker](https://manipulatives.org/_astro/sketch-pad.DMKfcKBd.svg) Published: 2026-10-10 Reviewed: 2026-10-10 Topics: teaching-strategies, operations, geometry ## What they teach ### Visual models Represent quantities, groups, or shapes with marks whose meaning you can explain. ### Connections Match a drawing to a situation and an equation, identifying what each part represents. ### Reasoning and revision Change a model when it does not fit the question, then explain why the new version works. ## How to use them 1. **Choose a question.** Start with a small situation, such as four plates with three crackers on each. Decide what one mark will represent. 2. **Draw a useful model.** Draw four groups of three marks. Keep the groups visible so someone else can see how the quantity is organized. 3. **Explain and revise.** Describe the drawing and write a matching expression. Rearrange the marks into an array and explain why the total stays twelve. ## Try an activity: Twelve, two ways Draw twelve dots as four rows of three. Draw the same total as two rows of six. Compare 4 × 3 and 2 × 6: what changed, and what stayed the same? Use labels or colors to make the groups easy to see. ## Draw the relationship you want to see A sketch pad does not supply a fixed mathematical model. The learner chooses what the marks represent. That makes it useful for moving from a story to a diagram: dots can stand for objects, a line can show distance, and rectangles can show groups or parts of a whole. Before calculating, ask what each mark means. In a drawing of four groups of three, a group might represent one plate and a dot one cracker. The same twelve dots could represent a different situation, so the explanation matters as much as the picture. ## Keep the drawing simple enough to discuss Use a few clear marks rather than spending the lesson on decoration. Color can distinguish two parts of a total, but labels should make the meaning understandable without relying on color alone. Draw an arrow, circle a group, or add a short note when it helps someone follow the reasoning. A rough sketch may show a relationship without preserving exact lengths or angles. If a question depends on measurement, use an agreed scale or a more structured tool, such as a [number line](https://manipulatives.org/manipulatives/number-lines/), [math bars](https://manipulatives.org/manipulatives/math-bars/), or [geometric pieces](https://manipulatives.org/manipulatives/geometric-shapes/). Paper, a small whiteboard, and a digital sketch pad all offer ways to make and revise a model. Keep useful work long enough to discuss it before erasing. The goal is a picture that supports an explanation, not a polished drawing. ## Choose your toolkit Paper you already have may be enough. Choose pages large enough for a model and explanation, and check which drawing materials suit the paper. The selected option is a four-pack of paper sketch pads. For a reusable alternative, a whiteboard you already own can work. A grid is helpful for arrays, but blank pages support a wider range of drawings. - [Melissa & Doug Mini Sketch Pads (4-Pack)](https://www.amazon.com/dp/B01HQLYMUE) — Four 6 × 9-inch spiral-bound sketch pads with 200 pages total for drawing math models and keeping explanations to revisit. The heavyweight paper suits pencils, crayons, and markers. ### Manipulatives app Use the drawing space to sketch a model and explain what its marks represent. Dots, bars, arrows, and short labels are often enough. Paper or a whiteboard can support the same conversation. [Explore the app](https://apps.apple.com/us/app/manipulatives-hands-on-math/id6780701668) ## Related tools - [Math Bars](https://manipulatives.org/manipulatives/math-bars/) - [Number Lines](https://manipulatives.org/manipulatives/number-lines/) - [Geometric Shapes](https://manipulatives.org/manipulatives/geometric-shapes/) - [Ten Frames](https://manipulatives.org/manipulatives/ten-frames/) ## Sources - [Melissa & Doug 6x9 Spiral Bound Mini-Sketch Pad 4-Pack](https://www.amazon.com/dp/B01HQLYMUE) — The selected paper option contains four 6 × 9-inch spiral-bound sketch pads with 200 pages total and heavyweight white paper for drawing.