Using whiteboards, students begin by drawing models of multiplication facts using groups and items inside of a group, such as a dot or tally mark, or creating arrays with rows and columns. I review the structure of a multiplication sentence of groups x items inside of a group = product.
I also review at this time reversing the order of the multiplication sentences to the format of
32 = 4 x 8
I practice to be certain students have a thorough understanding of the structure of the multiplication sentences.
Students will be solving math facts as fast as possible creating area models on graph paper to record the facts solved during this lesson. They are to solve from memory or skip count, but they are asked to avoid counting each square individually. I model this on the document camera for students.
Practicing their math facts becomes a game when using dice and presenting the challenge to fill the graph paper edge to edge and top to bottom. In this activity students are given the task of using dice to create arrays for multiplication facts to 100. In this task, the zero on the dice is valued at zero. Other items that can be used if dice are not available are playing cards or number cards with digits. You can substitute a set of face cards to represent zero.
Students work independently, and I ask them to start looking for patterns, related facts, and also ways to break the area models into parts with twos or fives, for faster solving. This includes using friendlier numbers of 5 and 2 whenever possible. For example, multiplication with 8 can be changed into 5 and 3, and seven can be decomposed to 5 and 2. This is the beginning of the using the distributive property that is part of the Common Core Standards.
Students use 10-sided dice and graph paper to create area models and arrays to solve facts to practice fluency and develop the ability to quickly recall facts. Because students are recording the arrays on the graph paper, they use these diagrams for related facts.
One of the students is challenged by 6 x 9, trying to figure out how to solve without counting. This provides the opportunity to show her how to decompose the array into 5 x 9 and 1 x 9.
I ask the students to record on their whiteboard three ways to solve the equation
8 x 3 = _____
This quick check for understanding allows me to see which model is favored by students. Some students write 8 x 3 = 24, arrays, groups, tallies, and one student skip counted by threes to get to 24. The model used most frequently was the array.