My new school is looking for ways that related arts (music, art, and PE) can integrate math into their lessons easily. Any ideas or research that you’ve found that helps this work? We are doing this Kinder through 5th grade.

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I bet you could incorporate a Walk to Read or intervention type approach but include math in its place!
This approach includes all hands on deck and students can be broken into leveled or mixed groups for instruction or intervention run for 20-30 mins.

My school was exceptional with this. First, the specials must meet regularly with the grade-level teachers to learn the curriculum. In art, they studied and created shapes and studied abstract artists/art. PE had an entire curriculum based on balance and focus. In music, they created rhythms and songs to learn about historical facts and to memorize information.