tions are possible. Here are a few good books with good ques- tions to spark simple graph explorations with children: Which Would You Rather Be? by William Steig, Whose Shoes? by Stephen R. Swinburne, and Anno’s Flea Market by Mitsumasa Anno. The eighth topic area is spatial relationships . Learners de- velop the processes of generating, maintaining and manipulat- ing mental images of two- and three-dimensional objects, in- cluding moving, matching and combining them. It is a critical math topic. Spatial Relationships begin at birth. Most learners start to learn by reaching for and grasping objects that are dan- gled in front of them. Next, the learners are cruising around to negotiate a path through a room. Lastly, the learner can locate items or decide how best to get from here to there, which have begun to represent space. Learners will learn the relationships between different positions in space (includes maps and coor- dinates). The key concepts embedded in these activities that make them mathematical are their relational nature. Here are some activities or tools to try: Do games like Simon Says and allow learners take turns as the leader to give directions. Puzzles involve spatial sense. Have multi-piece puzzles, pattern blocks, and tanagrams should be available with different levels of sup- port and age appropriateness. The last topic is shapes , everything in the material world has a shape. Learners need to go beyond the use of superficial shape labels to recognizing and specifying the defining attri- butes of shapes. As learners sort shapes with others, they be- come aware of rules about shapes. Learners will also discover, while exploring three-dimensional solids, that the faces of solids look like circles, rectangles, triangles and other common two-di- mensional shapes. When learners are given the chance to com- bine, rotate and compare shapes this will help learners develop understanding of part/whole relationships within and among shapes. Learners can learn to identify structures within embed- ded figures (finding "hidden shapes" within more complex dia- grams). Here are some activities or tools to try: Using the web- site Illuminations website allows students to manipulate shapes. If a student struggles with fine motor skills, this site allows the use of a snap together tool. This tool snap shapes together once they are close. Educators can also purchase wooden shapes that have velcro on them, which allows the learners to connect real wooden shapes together. Busy Shapes app for iOS and Android has 150 incremental levels. In conclusion, it is vital for us to make sure that our learners have the foundational skills in mathematics before we move onto more complex concepts. Math concepts are around us in every aspect of our lives and filter into other content areas. The number sense, counting, comparing and composing numbers, sets and attributes, and patterns are the foundational building blocks to the other three topic areas which are measurement, shapes and data analysis. When we are designing our lessons we need to make sure that we are designing for all of our learn- ers’ needs.
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