{"id":22919,"date":"2016-01-04T17:50:15","date_gmt":"2016-01-04T17:50:15","guid":{"rendered":"http:\/\/thomasjpitts.co.uk\/wordpress\/?p=22919"},"modified":"2016-01-04T17:20:54","modified_gmt":"2016-01-04T17:20:54","slug":"4-what-is-the-singapore-bar","status":"publish","type":"post","link":"https:\/\/thomasjpitts.co.uk\/wordpress\/2016\/01\/04\/4-what-is-the-singapore-bar\/","title":{"rendered":"4: What is the Singapore Bar?"},"content":{"rendered":"

Today I was reunited with the mathematical phenomenon known as the Singapore Bar.<\/p>\n

I have always been a firm believer in using pictures and representations to aid mathematical thinking and the bar is a prime example of this. To be honest, it’s nothing Earth shattering\u00a0 – if you’ve ever used a number line to explore your thinking, it’s much the same.<\/p>\n

Take this problem for example:<\/p>\n

Jake is 3 years older than Lucy and 2 years younger than Pete.<\/em><\/p>\n

The total of their ages is 41 years old.<\/em><\/p>\n

Find Jake\u2019s age.\u00a0What else can you find?<\/em><\/p><\/blockquote>\n

My brain leaped immediately to creating an algebraic equation. The bar is a step between a trial and error approach and the leap to sticking letters inside numbers.<\/p>\n

Let me show you.<\/p>\n

\"Singapore<\/p>\n

From this diagram, you can see that the common link is Lucy’s age. Rewording the question is essentially the key, but creating the image in stages helps a lot too.<\/p>\n

Removing the additional years (shown as squares above), gives us 41-8, which is 33. From that point, it isn’t a great leap to get to 33\u00a0\u00f7 3 = 11, so Lucy is 11, Jake is 14 and Pete is 16.<\/p>\n

Adding their\u00a0ages up is a final additional stage to ensure your answer makes sense, of course.<\/p>\n

When I was presented with the question, I did this:<\/p>\n

L = J-3;\u00a0P = J+2;\u00a0J = J<\/em><\/p>\n

41 = 3J-3+2<\/em><\/p>\n

41 = 3J-1<\/em><\/p>\n

42 = 3J<\/em><\/p>\n

42\u00a0\u00f7 3 = J<\/em><\/p>\n

J = 14<\/em><\/p><\/blockquote>\n

I did miss a few steps out by doing them in my head though.<\/p>\n

If you want to try a further example, I’ll leave this one here for you:<\/p>\n

Abe, Ben and Ceri scored a total of 4,665 points playing a computer game.<\/em><\/p>\n

Ben scored 311 points fewer than Abe. Ben scored 3 times as many points as Ceri.<\/em><\/p>\n

How many points did Ceri score?<\/em><\/p><\/blockquote>\n

To be honest, thinking like this is far from natural, but I can see how it would close the gap and potentially, once children are comfortable with it, reduce the fear of algebra for children.<\/p>\n

The other major revelation was more a confirmation of one of my long held beliefs. I was told today, by two separate people, that we should be spending a lot longer on breaking down our teaching mathematical topics than we currently are. Finally, I don’t feel like a lone voice…<\/p>\n

If we, as a profession, can continue to think like this, then maybe, just maybe, some good changes are ahead of us.<\/p>\n","protected":false},"excerpt":{"rendered":"

Today I was reunited with the mathematical phenomenon known as the Singapore Bar. I have always been a firm believer in using pictures and representations to aid mathematical thinking and the bar is a prime example of this. To be honest, it’s nothing Earth shattering\u00a0 – if you’ve ever used a number line to explore […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0,"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[3355,18],"tags":[3366,3367,3365],"class_list":["post-22919","post","type-post","status-publish","format-standard","hentry","category-3355","category-maths","tag-mathematical-mastery","tag-puzzles","tag-singapore-bar","has-post-title","has-post-date","has-post-category","has-post-tag","has-post-comment","has-post-author",""],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p6OeSW-5XF","jetpack-related-posts":[],"builder_content":"","_links":{"self":[{"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/posts\/22919","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/comments?post=22919"}],"version-history":[{"count":5,"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/posts\/22919\/revisions"}],"predecessor-version":[{"id":22925,"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/posts\/22919\/revisions\/22925"}],"wp:attachment":[{"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/media?parent=22919"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/categories?post=22919"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/tags?post=22919"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}