This lesson asks students to use the math skills they are learning and applying them by creating word problems for their peers to solve. Objectives —Select one more more math operations to use in a word problem; —Produce multi-step word problems that their classmates can solve; —Solve word problems created by their classmates. Represent these problems using equations with a letter standing for the unknown quantity.
Arrays, multiplication and division Jennie Pennant, with the help of Jenni Way and Mike Askew, explores how the array can be used as a thinking tool to help children develop an in-depth understanding of multiplication and division.
Using Arrays to Explore Numbers Arrays are useful models for multiplication which can be used in a variety of ways, ranging from highly structured lessons to games and open investigations.
An array is formed by arranging a set of objects into rows and columns. Each column must contain the same number of objects as the other columns, and each row must have the same number as the other rows.
Building Multiplication Facts and Tables Arrays can be used for building multiplication facts in a meaningful way. Before drilling and memorising tables, children must understand how these facts are derived.
For example, by progressively adding another column of three objects, children can build the three-times tables for themselves. This representation not only assists in understanding the process, but provides a visual image for children to draw upon as they begin to use and memorise the basic number facts.
Using arrays to explore larger numbers Arrays can be helpfully used to explore calculations such as 13 x 5 where the array can be split into useful chunks such as 10 and 3. This means that children can use their known number facts to work out calculations. After a while drawing all the dots can get very tedious!
The blank array then becomes a very useful tool for helping children model their thinking and work out how to do more complex multiplications in an informal way. Here's a child using the blank array, as a thinking tool, to help them work out 15 x The blank array helps children to use other strategies, such as compensating, when carrying out multiplication.
Here, to work out 34 x 9, the child has decided to do 34 x 10 and then take off the 34 x 1. Beyond the blank array this 'dividing the multiplication into easy parts' strategy can be formalised into the grid method.
The children can see how the 'abstract' grid method overlays the array and formalises the blank array into a standard form. Division as the Inverse Operation of Multiplication Of the four operations, division is the most troublesome for young students.
Full understanding of division tends to lag well behind the other operations. For many children opportunities to explore the concept with concrete materials are curtailed well before they perceive the relationships between division and the other four operations.
One such relationship, the inverse relationship between division and multiplication, can be effectively illustrated using arrays. Language clearly plays an important role in being able to express the mathematical relationships and the physical array supports this aspect of understanding by giving the children a concrete image to talk about.
Placing the mathematics into a real-life context through word problems can facilitate both understanding of the relationship and its expression through words.
For example, "The gardener planted 3 rows of 5 seeds. How many seeds did she plant? How many seeds in each row?Have the student write story contexts for multiplication of whole numbers and then substitute fractions for the whole numbers.
Encourage the student to consider if the context still makes sense and, if so, ask the student to create a visual fraction model to show the product. Create multiplication stories where one factor is 6 or 7, and play a multiplication game. Grade 4 supplement set a5 Number & Operations: Multi-digit Multiplication Includes sketching 2-digit by 1-digit multiplication combinations to using the standard algorithm to multiply up to 3-digit by b Write a story problem to match the multiplication problem you just solved.
Use multiplication and division within to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
The largest and most comprehensive K math worksheets site aligned directly to the core curriculum. In this lesson you will learn how multiplication is a comparison by using number sentences.
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