Part of the “10 Minutes a Day: Times Tables Worksheets” series
This is the fourth post, with an attached worksheet to download for your class, on the teaching of times tables.
Free Worksheet 4x Tables Worksheet A: 4X Facts – Double Double
(click thumbnail to download now)
How to use the worksheet: This worksheet is one in a set of 40 worksheets that is used to reinforce a times table strategy or group of facts. Teach the strategy, then set the class up with a timer. Say “Go!”, and have the children race to the end of the worksheet. As each student finishes they call out, “Finished!” The timer or the clock will give them their time to write at the top of the page.
Worksheet format:The facts are repeated throughout the worksheet with each fact appearing about 8 times. There are some addition and subtraction facts at the bottom to help students to remember those too.
4x Times Tables – Based on doubling, twice
This article is from the 10-article series “Times Tables Strategies”. Times tables strategies are taught in the following order: 2x; 5x & 10x; 3x; 4x; 1x, 0x, 11x, & squares; 9x, 6x, 8x, 7x, 12x.
The 4x facts are based on the skill of doubling, and build on the previously learned 2x (doubles) facts. These facts are in the easier half of all multiplication facts to be learned, and are quite readily visualized by students.
Teaching 4x Facts
Introduce 4x facts by reminding students of doubling and the doubles facts they learned at the start of this sequence. Remind them that doubling is a skill that is used often in mathematics, and knowing how to quickly double a number will be a very useful skill for them to learn.
Learning a 4x fact is accomplished via the following sequence:
[Fact example: 8×4]
- First, double 8: Double 8 = 16
- Next, double the result: Double 16 = 32
- This is the answer to the question 8×4: Double double 8 = Double 16 = 32
For children to double a two-digit number such as 16, they need to understand place value and be able to double each digit correctly and combine the result. Double 16 is found by doubling 10, doubling 6, and adding the two results. Double 10 is a straightforward place value idea: double 10 is two tens, or twenty. Double 6 is a multiplication fact already learned before tackling the 4x facts.
Help children by taking these processes slowly, taking sufficient time that the children can provide the intermediate answers themselves, and can understand each step on their own. Taking the “double 16” example, you could ask the following sequence of questions to lead children through the thinking required to work out this double:
- What is 16 made up of? – A ten plus 6 ones
- Let’s double each part. What is double 10, or two tens? – Twenty
- Now, what is double 6, or two times six? – Twelve
- Now, add the two answers together. What is twenty plus twelve? – Twenty is two tens, twelve is ten plus two. That is three tens and two – thirty-two.
Don’t expect children to be able to hold all these numbers in their heads. For those who can, the above verbal sequence may be enough for them to learn how to double 16. However, many children will benefit from having physical manipulatives in front of them as they work through this process, such as base ten blocks or ten frames and counters.
By grouping students in groups of four, they can collaborate in modeling the four times facts. You could provide each student with a single ten frame and counters, then each student displays the same amount. If the fact is 8×4, then each student would put out 8 counters on the ten frame. Then each pair display double 8 by combining their ten frames and counters; two counters are moved to the left-hand ten frame to show 16 as 10 plus 6. Then the two pairs of students combine all their ten frames and counters, carefully moving the two tens next to each other and the two sixes being combined to show ten and two.
Virtual on-screen manipulatives (such as those at http://www.glencoe.com/sites/common_assets/mathematics/ebook_assets/vmf/VMF-Interface.html) would be very useful, if you have a data projector and especially with an interactive whiteboard. These manipulatives avoid the “messiness” of physical materials, and show the results of mathematical processes very cleanly and clearly.
The next article in this series is “Times Tables Strategy 1x, 0x, 11x, & Squares – Special Cases”.
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