Research shows that students learn math concepts best using a 3-step framework called the concrete-representational-abstract (CRA) approach. During the initial stage of introducing a new skill, students use concrete objects to physically model the concept. Once there is a solid understanding of why and how the concept works, students move into the representational stage where they turn the concrete models into pictures. Finally, in the abstract stage, students learn the algorithm that symbolizes the concept using numbers and mathematical symbols. Entering the abstract stage too soon prevents students from developing a deep understanding of the mathematical process. As we begin our multiplication unit, we are moving slowly using the CRA approach so that students' brains can make connections between what they already know about numbers (skip counting, making equal groups, doubles) and the new concepts they're learning. There's more to multiplication than just memorizing the facts!
Day 1: Last week we began to think about how arrays represent multiplication. We started off by solving the "Arranging Chairs" problem. The students worked with a partner to put chairs into equal rows and columns. Every partnership had a different number of chairs. They used colored tiles to build a model of all the different ways they came up with. Then they used graph paper to make a pictorial representation of all of their arrangements.
Day 2: Students worked in groups and used the arrays they created from the Arranging Chairs problem to show the total number of chairs in each arrangement. Most groups used skip counting strategies or repeated addition. Some connected the repeated addition to multiplication as they remembered a strategy used when playing Circles and Stars.
Day 3: We went on an array hunt around Westchester to look for every day arrays in the real world. The students discovered arrays in many different places and in many different forms. Students used iPads to take pictures of the arrays they found, cropped and edited the photos, and uploaded them into a Google Slides presentation. All 23 students shared one Google Slides document, so using collaboration skills to build our presentation was a must. Enjoy our final product! And stay tuned as we dive deeper into multiplication this week.