Heartsjoy Posted February 18, 2014 Share Posted February 18, 2014 I have the answers. I'm looking for drawn bardiagrams Singapore style as these are from Challenging Word Problems bk 6, the older edition. p. 50 #20 1/2 lb. of fish costs twice as much as 4/5 lb of vegetables. If 7/10 lb. of fish and 1/2 lb. of vegetables cost $13.70 altogether, how much more does each lb. of fish cost than each lb of vegetables? p. 50 #21 Roland had five times as many postcards as Patrick. After Roland gave 1/4 of his postcards to Patrick, Patrick gave 1/6 of his postcards to Roland. If Roland had 90 more postcards than Patrick in the end, how many postcards did Roalnd have at first? Quote Link to comment Share on other sites More sharing options...
kateingr Posted February 18, 2014 Share Posted February 18, 2014 For the second one, I'd think of it as three different bar diagrams. (I have no idea how to "draw" these, but so let me know if the explanation makes sense.) 1st Diagram Roland needs 5 units, Patrick needs 1 unit. R _ _ _ _ _ P _ 2nd Diagram (showing that Roland gives 1/4 of the postcards to Patrick). Roland's units need to be divisible by 4, so I'm going to subdivide every unit in the diagram into 4 pieces. Now, Roland has 20 units, Patrick has 4 units. Cross out 5 of Roland's pieces and give them to Patrick. New totals: Roland 15, Patrick 9. Third Diagram (showing that Patrick gives 1/6 of the cards to Roland). Now, Roland's units need to be divisible by 6. So, I'm going to further subdivide every unit in the diagram into 2 pieces. New count is Roland 30, Patrick 18. Cross out 3 of Patrick's units and give them to Roland. Final count: Roland 33, Patrick 15. The difference between Roland and Patrick is 18 units. 90/18 = 5, so each of the current units equals 5 postcards. Roland started with 5 units, but each of those units contained 8 of the current units (since it was divided by 4, and then by 2). So, 5 original units times 8 of the new units times 5 postcards per new unit equals 200 postcards. Whew! Does this match the answer book? Quote Link to comment Share on other sites More sharing options...
kateingr Posted February 18, 2014 Share Posted February 18, 2014 Okay, now I'm looking at the first problem. You must be in a crazy subdividing section! This one looks like it needs to be subdivided twice, too, but I don't have time right now to figure out what the denominators have to be. I'll try to take another look later tonight. Quote Link to comment Share on other sites More sharing options...
Heartsjoy Posted February 18, 2014 Author Share Posted February 18, 2014 Yes 200 postcards. [-----------------------------200 postcards at 5 postcards per each unit (--)--------------------------------------------------] [----------------------------40 units of (--)----------------------------------------------------------------------------------------------] Roland [{--l--}{--l--}{--l--}{--l--}][{--l--}{--l--}{--l--}{--l--}][{--l--}{--l--}{--l--}{--l--}][{--l--}{--l--}{--l--}{--l--}][{--l--}{--l--}{--l--}{--l--}] Patrick [{--l--}{--l--}{--l--}{--l--}] Roland [{--l--}{--l--}{--l--}{--l--}][{--l--}{--l--}{--l--}{--l--}][{--l--}{--l--}{--l--}{--l--}][{--l--}{--l--}{--l--} Patrick [{--l--}{--l--}{--l--}{--l--}][{--l--}{--l--}{--l--}{--l--}][{--l--} [-----------33 units of (--)-------------------------------------------------------------------------------------] Roland [{--l--}{--l--}{--l--}{--l--}][{--l--}{--l--}{--l--}{--l--}][{--l--}{--l--}{--l--}{--l--}][{--l--}{--l--}{--l--}{--l--}{--l Patrick [{--l--}{--l--}{--l--}{--l--}][{--l--}{--l--}{--l--}{--l [----------15 units of (--)----------------------][----18 units of (--)-----------------------------------------] [---------90 postcards-------------------------------------] [{--} [5postcards Many Thanks, I'm seeing the pattern of subdividing to a common denominator. Quote Link to comment Share on other sites More sharing options...
Heartsjoy Posted February 18, 2014 Author Share Posted February 18, 2014 I'm still stumped on the first one. Quote Link to comment Share on other sites More sharing options...
lorisuewho Posted February 19, 2014 Share Posted February 19, 2014 I am now entirely scared out of my mind about CWP 6!!! We are only at level 2 and already I have been stumped by one or two ( on how to draw the bars). Quote Link to comment Share on other sites More sharing options...
Heartsjoy Posted February 19, 2014 Author Share Posted February 19, 2014 Just keep asking for help. My kids have a great algebraic understanding I never had. I've asked for help here. On the 1800 Singapore forum, and on the Singapore math forum. Sometimes it takes me a week or two. Quote Link to comment Share on other sites More sharing options...
kateingr Posted February 19, 2014 Share Posted February 19, 2014 Okay, I finally got the first one! The clue for me was seeing that the answer is the *difference* between a whole pound of fish and a whole pound of vegetables. That suggested that starting with a whole pound of fish and a whole pound of vegetables in the initial bar diagram would be helpful. We know from the question that 1/4 of a pound of fish costs the same as 4/5 of a pound of vegetables, so these bars should be equal. F 1 unit (to stand for 1 fourth) V 4 units (to stand for the 4 fifths) Next, I extended each bar to show a whole pound of the fish or vegetables. F 4 units (4 fourths) V 5 units (5 fifths) I then subdivided the Fish bar to match the units in the Vegetable bar. (Each fourth was divided into four pieces.) F 16 units V 5 units I drew a brace in the space showing the difference between the two bars and labeled it with a question mark. Now, on to finding the right number of subdivisions. Since we will need to work with half a pound of vegetables, I subdivided all of the units in half so I could easily see 5 tenths of a pound of fish. F 32 units V 10 units But now we need to be able to work with tenths of a pound of fish. The first common multiple for 32 and 10 is 160 (32 x 5). So, I subdivided all the units 5 times. F 160 units V 50 units 7/10 F + 1/2 V = 13.70 7/10 of 160 = 112 1/2 of 50 = 25 112u + 25 u = $13.70 137 u = $13.70 u = $.10 There is a difference of 110 units between the final two bars, so the difference between a pound of each is $11.00! Quote Link to comment Share on other sites More sharing options...
kateingr Posted February 19, 2014 Share Posted February 19, 2014 Problems like this just wow me--I find it so amazing that Singapore gives kids the tools to do this kind of deep thinking. My son just started 2A, so this is still far off for us. I'm currently taking a middle school bar modeling course on ed2go.com to keep up my teachers certificate, so I've enjoyed seeing these problems and knowing that this class may eventually help me teach my kids better! Quote Link to comment Share on other sites More sharing options...
Heartsjoy Posted February 19, 2014 Author Share Posted February 19, 2014 Wow!! It is so helpful to draw this out and see that cost units can be equal while fractions of pounds of fish and veg are not. My brain needs to see it just like singapore draws it. The whole thinking key of singapore is teaching yourself to find the unit that is staying constant and keep it equal as you manipulate it to the size you need in order to compare it. Never learned this in school only now getting glimmers. Thanks for the input; it's keeping us going. Thanks to singapore my non mathy brain and kid's brains are dabbling in AOPS and I'm not afraid to send my kids farther than I went. They truly have a desire to think math. Quote Link to comment Share on other sites More sharing options...
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