Step 1: Start with playful exploration of materials prior to formally using them for conceptual lessons/development in Math Tubs with minimal or no expectation or guidance provided.  This is a great opportunity for 'pre-assessment' to observe what students already notice and know. For examples,  let students build with base 10 blocks, 2D/3D shapes/blocks, geoboards, balance scales, connecting cubes, string,  etc. Watch what they do, what they understand, and which creations will help move your learning objectives forward.

Step 2: Choose 2-3 creations that target concepts/ideas that you want all students to explore and move toward in your future lessons that will help stretch student thinking (example: analysis of shapes, symmetry). Allow 5-10 minutes for whole class group math talk around these creations. Ask questions such as, "What math do you see?" "How do you know?" "Does anyone see something different?" "If we think about (quantity, measurement, shapes), what do you notice?"

Step 3: If possible, allow all students to record their thinking and work (for example, using a quick digital online portfolio or google drive). It's amazing how important this is to students, especially if their design was not selected to showcase that day. Documented work also becomes a great conversation piece for students to have with their parents on an ongoing basis.

Read a story such as The Paper Bag Princess (R. Munsch) or The Three Little Pigs. Then create provocations such as "Help the princess rebuild her castle. Make sure your castle has a bridge and 2 towers." "Build all 3 piggy houses before the wolf blew them down. What different materials will you choose to represent each house?"

Note: Research shows that children demonstrate significant gains in building performance when narratives are added and specific building goals are provided rather than free, unguided block play or just specific building goals being given (example: build a wall that could be used to contain animals). (Davis, Spatial Reasoning in the Early Years, pg. 37)

"It seems that in this case, some children needed the promise of a challenge to spark their interest and creativity."

Students can use books as an inspiration to find MATH (shapes, quantity, patterns, attributes) in the outside natural world. They can represent their ideas using pastels, construction paper, etc. to recreate what they are noticing. Have students record thinking in some way (write/someone scribe, discussion, video record). 

How many different kinds of patterns can you put into one design? This provocation comes after weeks of pattern development, discussion, and play.

Students explore recording what they are seeing using paint as well as sharpie markers to create fine details before or after. Focus could be on representing an entire plant/tree OR using the magnifying glasses to explore closely a detail to represent. Words can be added to their pages to show what they are noticing (shapes, attributes, etc).

Students use the materials to explore measuring and comparing things around the classroom, including: natural materials (such as log table, rocks), man made things, AND shapes (example: can they figure out that some of the pattern block shapes have the same/different length of sides?).

Materials are set out for students to explore this provocation that facilitate shape discussions. Examples: building blocks, pattern blocks, shape attribute blocks, pentominoes, base 10 blocks, link cubes.

This provocation comes after free exploration and a build up of concept development through past provocations. See "Math Tubs" Coding for a sample sequence. 

A clear plastic table cloth with Sharpie paint pen shapes drawn on it invites children to use different materials to compose different shapes. Children will use spatial thinking to flip, rotate, and/or reflect shapes to ensure the pieces fit inside the shapes.

Students can choose the number(s) they investigate.

Offers student choice in the materials and the numbers they choose.

More ideas and details at https://blogs.sd38.bc.ca/sd38mathandscience/2017/06/11/the-studio-at-grauer/

More ideas and details at https://blogs.sd38.bc.ca/sd38mathandscience/2017/06/11/the-studio-at-grauer/