{"id":5185,"date":"2019-01-29T08:32:59","date_gmt":"2019-01-29T08:32:59","guid":{"rendered":"http:\/\/www.eastkent-tutors.co.uk\/wordpress\/?p=5185"},"modified":"2019-01-29T08:32:59","modified_gmt":"2019-01-29T08:32:59","slug":"exchanging","status":"publish","type":"post","link":"https:\/\/www.eastkent-tutors.co.uk\/wordpress\/2019\/01\/29\/exchanging\/","title":{"rendered":"Exchanging"},"content":{"rendered":"

Recently a number of parents have told me how strange they find some of the methods their children use in maths. Two of the big queries are ‘chunking’ – more about that one later- and ‘exchanging’.<\/p>\n

Some of our tutors are available for daytime sessions to help parents learn these different methods, but below is a whistle-stop explanation of how we ‘exchange’.<\/p>\n

 <\/p>\n

Imagine I have 32 children in my class and I decide to buy them all a mars bar. Unfortunately, my local shop only stocks packs of 10 so I buy 4 packs.<\/span><\/p>\n

When I give the mars bars out, I have to open the packs of 10 so I have individual bars.<\/span><\/p>\n

That\u2019s what decomposition, or \u2018exchanging\u2019 (the method your child uses for subtraction) does \u2013 it breaks tens in more useful units.<\/span><\/p>\n

To take 5 away from 21 I’d lay the calculation out like this:<\/p>\n

\u00a0 <\/span>\u00a0 \u00a0 <\/span>\u00a0<\/span><\/p>\n

\u00a0 T\u00a0\u00a0 U<\/span><\/p>\n

2\u00a0\u00a0\u00a0\u00a0\u00a0 1-\u00a0\u00a0<\/span><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 5 \u00a0<\/span> \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0<\/span><\/p>\n

You can see I don\u2019t have enough in the units column to take 5 away, so I exchange the 10 for ten units \u2013 in other words I break open one of the packs of 10 to make 10 units and I put them in the unit column. Now I have 11 in the units column \u00a0but I only have 1 pack of 10 left in the tens column :<\/span><\/p>\n

\u00a0 \u00a0 \u00a0 T\u00a0\u00a0 U<\/span><\/p>\n

\u00a0 \u00a0 1<\/sup> 2<\/span>\u00a0 1 <\/sup>1-<\/span><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 5<\/u><\/span><\/p>\n

\u00a0 \u00a0 \u00a0 1\u00a0\u00a0 6\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n

 <\/p>\n

Let\u2019s look at another example.\u00a0\u00a0\u00a0 <\/span><\/p>\n

\u00a0T\u00a0\u00a0 U\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/span><\/p>\n

6<\/sup>7<\/span>\u00a0\u00a0 1<\/sup>2<\/span><\/p>\n

\u00a03 \u00a0 \u00a0 7<\/span><\/span><\/p>\n

\u00a03\u00a0\u00a0\u00a0 5\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n

Sometimes we might need to exchange more than once.<\/span><\/p>\n

Let\u2019s take a look at how we can do that.\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0<\/span>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n

H\u00a0 \u00a0T\u00a0\u00a0 U<\/span><\/p>\n

2\u00a0 \u00a00\u00a0\u00a0 1 \u2013<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0 2\u00a0\u00a0 5<\/u>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n

 <\/p>\n

We don\u2019t have anything to exchange in the 10s column so we need to go to the 100s column and exchange 1 pack of 100 for 10 lots of 10:<\/span><\/p>\n

H\u00a0 \u00a0T\u00a0\u00a0 U<\/span><\/p>\n

1<\/sup><\/span>2<\/span>\u00a0 1<\/sup> 0\u00a0\u00a0 1 \u2013<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0 \u00a02\u00a0\u00a0 5<\/u>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n

 <\/p>\n

Now we can exchange from the 10s column:<\/span><\/p>\n

H\u00a0 \u00a0T\u00a0\u00a0 U<\/span><\/p>\n

1<\/sup><\/span>2<\/span>\u00a0 9<\/sub><\/strong> 1<\/sup> 0<\/span>\u00a0\u00a0 1<\/sup>1 \u2013<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a02\u00a0 \u00a0\u00a05<\/u><\/span><\/p>\n

1\u00a0\u00a0\u00a0\u00a0\u00a0 7\u00a0\u00a0\u00a0\u00a0 6\u00a0<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

Recently a number of parents have told me how strange they find some of the methods their children use in maths. Two of the big queries are ‘chunking’ – more about that one later- and ‘exchanging’. Some of our tutors are available for daytime sessions to help parents learn these different methods, but below is […]<\/p>\n","protected":false},"author":8,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-5185","post","type-post","status-publish","format-standard","hentry","category-uncategorised"],"_links":{"self":[{"href":"https:\/\/www.eastkent-tutors.co.uk\/wordpress\/wp-json\/wp\/v2\/posts\/5185","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.eastkent-tutors.co.uk\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.eastkent-tutors.co.uk\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.eastkent-tutors.co.uk\/wordpress\/wp-json\/wp\/v2\/users\/8"}],"replies":[{"embeddable":true,"href":"https:\/\/www.eastkent-tutors.co.uk\/wordpress\/wp-json\/wp\/v2\/comments?post=5185"}],"version-history":[{"count":2,"href":"https:\/\/www.eastkent-tutors.co.uk\/wordpress\/wp-json\/wp\/v2\/posts\/5185\/revisions"}],"predecessor-version":[{"id":5187,"href":"https:\/\/www.eastkent-tutors.co.uk\/wordpress\/wp-json\/wp\/v2\/posts\/5185\/revisions\/5187"}],"wp:attachment":[{"href":"https:\/\/www.eastkent-tutors.co.uk\/wordpress\/wp-json\/wp\/v2\/media?parent=5185"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.eastkent-tutors.co.uk\/wordpress\/wp-json\/wp\/v2\/categories?post=5185"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.eastkent-tutors.co.uk\/wordpress\/wp-json\/wp\/v2\/tags?post=5185"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}