Hands-on math is considered to be a space that moves learning from a passive process to an engaging one through "the creation, expression, and presentation of ideas" (DeGeorge & Santoro, 2004, p. 1). In Arvind Gupta's book, *Hands-On Math: Stories & Activities*, he provides several different activities to teach math by "doing" and through a hands-on approach.

In this resource, these activities are helpful because I find that each one can be easily related to the curriculum, in addition to being aligned, scaffold-based, and rigorous. Furthermore, each of the activities is low-cost in nature, which is important for teachers who do not have the same access as teachers in public and private schools here in Ontario. Although I have not used any of these particular activities, I know that student engagement increases when students are presented with a math activity that is challenging and rich in nature. For example, the number dots for teaching patterns, pushes students to think about patterns outside the basic ways of writing patterns (e.g. 2, 4, 6, and 8). As such, these activities move students from simply “thinking” to “doing” in math.

However, the activities are randomly dispersed, so it requires time to match it to an expectation. For example, the number patterns with dots fits well with the expectation around repeating, growing, and shrinking patterns, but I had to think about that on my own. Unfortunately, Gupta (2009) does not mention what expectation the activity covers. It also requires time to extend the activity because Gupta (2009) only provides one or two examples for each one, so if anyone wants to use the activity for a full lesson then it would mean coming up with more examples.

In this resource, these activities are helpful because I find that each one can be easily related to the curriculum, in addition to being aligned, scaffold-based, and rigorous. Furthermore, each of the activities is low-cost in nature, which is important for teachers who do not have the same access as teachers in public and private schools here in Ontario. Although I have not used any of these particular activities, I know that student engagement increases when students are presented with a math activity that is challenging and rich in nature. For example, the number dots for teaching patterns, pushes students to think about patterns outside the basic ways of writing patterns (e.g. 2, 4, 6, and 8). As such, these activities move students from simply “thinking” to “doing” in math.

However, the activities are randomly dispersed, so it requires time to match it to an expectation. For example, the number patterns with dots fits well with the expectation around repeating, growing, and shrinking patterns, but I had to think about that on my own. Unfortunately, Gupta (2009) does not mention what expectation the activity covers. It also requires time to extend the activity because Gupta (2009) only provides one or two examples for each one, so if anyone wants to use the activity for a full lesson then it would mean coming up with more examples.

Fielder (1989) suggests teachers believed “that their students learned mathematical concepts best when given opportunities for concrete manipulative activities” (p. 16). Similarly, (DeGeorge & Santoro, 2004) suggest that manipulatives " such as counting with beans or coins, or more sophisticated manipulatives (e.g., geo-boards, tangrams, and pattern blocks), hands-on learning helps students to more readily understand concepts and boosts their self confidence" (p. 1).

- DeGeorge, B. & Santoro, A.M. (2004). Manipulatives: a hands-on approach to math. National Association of Elementary School Principals.
- Fielder, D.R. (1989). Project hands-on math: making a difference in K-2 classrooms.
*The Arithmetic Teacher*, 36(8), 14-16. National Council of Teachers of Mathematics. - Gupta, A. (2015).
*Hands-on maths: stories & activities*. Scholastic India. Gurgaon, India.