A key way to teach multiplication is via multiplication sentences. Unlike a traditional sentence, multiplication sentences use numbers and symbols to express a statement. By learning multiplication sentences, fourth graders learn how multiplication and addition relate to each other.

They will not necessarily recognise the links between multiplication and division. Students can feel overwhelmed by how many multiplication and division facts there are to learn, unless they see the links between them.

A good command of basic facts is required for carrying out multiplication and division algorithms.

Three different stages Students pass through three stages: If they know the answer to one, then they know the answer to the other. Students can use the known fact to solve missing numbers tasks. Students recognise the relationship between multiplication and division. Illustration 2 Examples of types of tasks that would be illustrative of using multiplication facts to solve multiplication problems, aligned from the Mathematics Online Interview: Question 28 - Sharing teddies on the mat Question 29 - Tennis balls task Question 30 - Dot array task Question 31 - Teddies at the movies Teaching strategies Understanding about fact families builds connections in mathematics and reduces the amount of material that students need to learn.

The key teaching strategy is to emphasise that there are related facts that belong together. Once a student knows one fact, they can use this to solve related number sentences with missing numbers. Fact families from arrays uses real objects, counters and squared paper as representations of number facts.

Students generate fact families themselves. Recognising different fact families encourages students to group facts into families.

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Fact family fortune is a simple game designed to highlight which combinations of three numbers are in the fact family and which ones are not. Fact family bonanza encourages students to extend the notion of fact family creatively.

Fact families from arrays Arrays in common objects Many objects found at home are arranged in arrays, for example, egg cartons, muffin trays, trays for organising nails and screws, and boxes of chocolates.

As well as using real objects, a digital camera can be used to bring pictures into the classroom. Ask the students to choose an object or picture and write down as many multiplication and division number sentences as they can about their array.

For example, consider a muffin tray which is a four by three array. They should also write a sentence or story about these facts e. Inventive students might write compound sentences, although this is not the primary aim of this activity e. Rearrangement does not change the relationship between the three numbers.

Give students some counters and get them to write other number sentences, also explained in words. Extend to larger numbers by drawing rectangles on squared paper e. This extends the models students have for multiplication from equal groups, to arrays, to area of a rectangle.

Link to the multiplication tables that the students are currently learning. Recognising different fact families Give students a set of numbers e. Ask students to group all the number sentences from the same family together.

For example, here are eight number sentences from one fact family there are two more fact families possible with the numbers provided:Jun 02, · Familiarize yourself with arrays and practice using them to write multiplication sentences in this worksheet/5(19). Students can write related multiplication sentences and solve them.

Students can also be given a multiplication sentence with an unknown variable and then write the related division sentence.

Once that is completed, have students write a related word problem and solve it. Write a division problem. Write the multiplication sentence that helps you solve the division problem. Draw an array of the multiplication sentence.

Find the quotient to the division problem. This is a sample of student work: Student Work - Exit Ticket for Relating Multiplication and Division. In this exit ticket, you can see how the student related the multiplication to the division by drawing an array model of the .

Write ÷3 below the x 5 in 3 x 5 = Ask: How many counters are in each row? (5) Write5 below the 15 in 3 x 5 = Say: Read the division sentence aloud. (Fifteen divided by three is equal to five.) Say: The product in a multiplication sentence is the dividend in a division sentence.

The . Write a related multiplication sentence for the division problem. Think: Use the divisor as a factor and the dividend as the product. The quotient will be the unknown factor.

52 ÷ 4 = 4 × = 52 STEP 3 Find the sum of the unknown factors of the smaller areas. _ + _ = _ STEP 4 Write the multiplication sentence with the unknown factor that you found. Jun 02, · Who knew that multiplication and addition were so closely related? This valuable worksheet explores the concept, giving your fourth grader a slew of images, and asking her to write both multiplication and addition facts that relate/5(19).

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Division as repeated subtraction - a complete lesson for third grade