IM 7.4.4 Lesson: Half as Much Again

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[/img][br]What do you notice? What do you wonder?
Complete the table to show the total distance walked in each case.
[list][*]Jada’s pet turtle walked 10 feet, and then half that length again.[/*][*]Jada’s baby brother walked 3 feet, and then half that length again.[/*][*]Jada’s hamster walked 4.5 feet, and then half that length again.[/*][*]Jada’s robot walked 1 foot, and then half that length again.[/*][*]A person walked feet and then half that length again.[/*][/list]
Explain how you computed the total distance in each case.
Two students each wrote an equation to represent the relationship between the initial distance walked ([math]x[/math]) and the total distance walked ([math]y[/math]).[br][list][*]Mai wrote [math]y=x+\frac{1}{2}\cdot x[/math].[/*][*]Kiran wrote [math]y=\frac{3}{2}\cdot x[/math].[br][/*][/list]Do you agree with either of them? Explain your reasoning.
[size=150]Zeno jumped 8 meters. Then he jumped half as far again (4 meters). Then he jumped half as far again (2 meters). So after 3 jumps, he was [math]8+4+2=14[/math] meters from his starting place.[/size][br][br]Zeno kept jumping half as far again. How far would he be after 4 jumps? 5 jumps? 6 jumps?
Before he started jumping, Zeno put a mark on the floor that was exactly 16 meters from his starting place. How close can Zeno get to the mark if he keeps jumping half as far again?
If you enjoyed thinking about this problem, consider researching Zeno's Paradox.
Match each situation with a diagram. A diagram may not have a match.
For each diagram, write an equation that represents the relationship between x and y.
Write a story for the diagram that doesn't have a match in the above activity.
In the applet below, there is a set of cards that have proportional relationships represented three different ways: as descriptions, equations, and tables. [br][br][list=1][*]Take turns with a partner to match a description with an equation and a table.[br][list=1][*]For each match you find, explain to your partner how you know it’s a match.[/*][*]For each match your partner finds, listen carefully to their explanation, and if you disagree, explain your thinking.[/*][/list][/*][*]When you agree on all of the matches, check your answers with the answer key. If there are any errors, discuss why and revise your matches.[/*][/list]

IM 7.4.4 Practice: Half as Much Again

Match each diagram with a situation.
[img]data:image/png;base64,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[/img]
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[/img]
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eUrVuDNJUt0SoOItAHaP7f8orcPZuGYVcCz/85gAB06dkSF5GSUjorSKQ0i0gZo/527dDHxGoPp2loFPEfoczduRGp6OsqUKxeRBa1KTpU8bYD2X6tOHby9Zk1Q0YWtA35Dbi5SUlMN7Gdf1Aa97n/EqrPHqAmo2SjbpD+uYiX0HD3ZqvR3uf1upNaui7LR0UjPPBuX3XqXVenvdueDqFrvHJSLK4+Mug1w2W2jrEo/7f2sC1ua9NeoVQurVq+OHOBbXtsHD7+TZ9U57s2NaNyhqwE+KTUdE5ZttSr9dz27FLWzLkTZ6BhkNr0IIxYssSr99y9+H3QUMQkJqNusFUb+2670096b9+iNmIRERBzwbXoPxMxN31h1PrR6O7I7dzPAV0jLwNR3d1mV/nsXvoPMpi0QFRNjgLnnpdVWpX/i8o9wTsv2Bpj6LS7B6Jfftir9tHc6utjEJAFvA/wCPrwVtIC36AElB+0K9uHl4UMPjzx86DX/qyOTh7eoWS8PH15g5OHl4UPahxPwAv6vHjvY/+Xh5eFDVmmpSR/eCouVg4AX8AI+QBtQk15N+pDBwtpZTfrwekgBL+AFfIDekRWWmvThrbDUpA/CWClWuE95+PCWgTy8PHxIKwEBL+BP1elo0M4BnjvQQhTwAj5QW/F1n4AX8CFrpagPH94Ki5WAgBfwAj5AG1AfXn34kMHC2llN+vB6SAEv4AV8gN6RFZaa9OGtsNSkD8JYKVa4T3n48JaBPLw8fEgrAQEv4E/V6WjQzgGeO9BCFPACPlBb8XWfgBfwIWulqA8f3gqLlYCAF/ACPkAbUB9effiQwcLaWU368HpIAS/gBXyA3pEVlpr04a2w1KQPwlgpVrhPefjwloE8vDx8SCsBAS/gT9XpaNDOAZ470EIU8AI+UFvxdZ+AF/Aha6WoDx/eCouVgIAX8AI+QBtQH159+JDBwtpZTfrwekgBL+AFfIDekRWWmvThrbDUpA/CWClWuE95+PCWgTy8PHxIKwEBL+BP1elo0M4BnjvQQhTwAj5QW/F1n4AX8CFrpagPH94Ki5WAgBfwAj5AG1Af3uI+fJMuV2PUCyusOoc++Rrqt2iL0lFRiE9OwYh/vWlV+gfNWoCqZ5+LstHRqNEwCwMefcqq9N8xbyHqZDdDdPl41GzcBANnzrcq/bT38ztdadJfo1YtrFq9GkePHg2Y4tMCvtMBNx4/fhwbN21CSmqqASYpNR01Gp5v1VmtfiMkpFQx6afRVT+nsVXpT8ush4SUyihTrhzKV0pGemY9q9LPyiquQkWUjY5BfKUUpNWxK/2096QqaYiKiUHN2rXx9po17gX+l19+wc5du1CvQQNUqlwZFZKTdUqDiLQB2v952dnYsmUL6AgDPazy8MzUsWPHMGfOHAwYNAg33nyzTmkQkTbQb8AAzMrJAZ3gb7/9FijvsA54Zu7QoUM4ePAg9h84oFMaRKQN0P7JQTCws1awDviAqzLdKAWkgIcCAt5DEl2QAu5VQMC7t2yVMyngoYCA95BEF6SAexUQ8O4tW+VMCngoIOA9JNEFKeBeBQS8e8tWOZMCHgoIeA9JdEEKuFcBAe/eslXOpICHAgLeQxJdkALuVUDAu7dslTMp4KGAgPeQRBekgHsVEPDuLVvlTAp4KCDgPSTRBSngXgUEvHvLVjmTAh4KCHgPSXRBCrhXAQHv3rJVzqSAhwIC3kMSXZAC7lVAwLu3bJUzKeChgID3kEQXpIB7FRDw7i1b5UwKeCgg4D0k0QUp4F4FBLx7y1Y5kwIeCgh4D0l0QQq4VwHrgOe2OitXrcL8BQvw5FNPWXu+8OKL2LZtG06cOOFe61LOHKeAVcD/+uuv2LdvH7KaNEH5xESzISN3YbXxTMvIwG1/+1tQGwE6znqUIOsUsAp4evcNubknd4+1EfT8NMclJKBl69Y4fPiwdUajBNurgNXAd+1wHl56fLBF5y3ImXgDGp9bEwT+4latBLy97FiZcquBH3RjW3z/0d+tOnPfHIO2FzcQ8FbiYn+irQb+9j7tcDwvx6rzo+UPoEPrcwW8/exYmQMBH+IKQ8BbyYlrEi3gBbxrjFkZKVwBAS/gC7cS3eEaBSIe+AObp2PPe5Px5fsP4cdtj+LYZ77HBA5vn4lvN03DzrUT8eX7U8z9wY4hqEnvGnaszEhEA0+4lz07DCMGXorRt1+Gzf83Fkc/ne1zEPCL9ZMxfczVGHh9S0wedRU+WzPB572+KgIBbyUnrkl0hAM/G0//vQ+qp1dE9YyKWDCjH+jFvcF67LPZeP6xgchITcIZZ5yOIX0vMZ7e273+rgl417BjZUYiHvgl/xqCszPTUDk5AePvvAI/fTLDK/D05v2ua4GY6LI4s2olfLD4Xp/3CngrWYiIREc48DlY/+poNMuqiQoJsbildysc+tgTeHr3xx/qjVrVU1AhMdY0//dueNhrxeAPdr4nDx8RXDk2kxENPAGk5760VQPExkSha7uGHgNx7NPvWjsRndqcg4Ty0WhYryq2LB1bJO8u4B3LQcQkLOKBP7jlEVzTNRtly5QyMHOqbkEvTY8/b+pNphlf5Y9mf8H3g30tDx8xbDkyoxEPPIEddH0rlCldCqkpifhm41SwCc/r/Pv1hofRpFENRJUtjU6tz8GO1eP/VCEIeEfatRLlQwEBn5eDB4Z1RVJ8DFIqxWPD62NONtf35U5Fzvhept+enpqEaWN6eO3jBwO9PLwPS9TlkCgg4PNyzIBcRmoFVEqKwytzb8V3Wx7B0U9ngSvbmp1fC+WiyqBH5yx8+Nb9p+TdWTEI+JDYtX7EhwICPi8HrzxxK+rWTkVSQgxmjrvOzKajd589vheiy5VB5eR4PJ8zwCzDDcabe7tXwPuwRF0OiQICPi8H7y26Bxc0rmFG4R8ccQW+/mAKVjw3HM2yapm++3VXNMEnq8adsneXhw+JTetH/Cgg4PNysG35A+jeKQvlY8vhb/9zCfLWTDD9ej6GY79+5fMjPB7XefPegVyTh/djjXqrxBUQ8Hk5+HzdJNx2UxvExUSZefKcfdeuxdmmTz+gV0twkk3+yH0gUPu7R8CXuE3rB/woIODzcnDgw+mYfHc3xEaXRc8u2RjWvz2qpVdE/cw007T3NvvOH9T+3hPwfqxRb5W4AgI+LwdHdszCvx7ta4C/5KJ64CM4DtRxqu3h7bOKpe+eXwkI+BK3af2AHwUE/B8BMBY9cauZT58YH43Spc5AqwsysfY/o4oVdkIv4P1Yo94qcQUE/B/AL392OOrUqIzSpUuZ0fpxwy83z+PzPXNx/RXwJW7T+gE/Cgh4M4U2x4zEZ9asYta6t2hS23j34hqoK1hZCHg/1qi3SlwBAZ+Xg/2bp+GxidejYmKcmWLLpbD7Nk4t9ua8mvQlbs/6gUIUiHjg6cXfXTgKbZvXNVNo+TiuuCbZFPTs+a/l4QuxSL1dogpEPPDfb/27CVdVPjYKFRNj8czMfuYxXT6gxf1XwJeoPevLC1EgYoFnYAvC/r+Tb0DtM1NQMSkW116ebabV8jFdcYOe/30CvhCL1NslqkDEAM+mO0NRvzBnkAlW+eT0mzHq1k6oWT0ZFZPi0PKCTKx8boR5Jp8PZ0n8FfAlas/68kIUiBjg6bW53JV99PQqSaiSkoDYmLKmGc8AF/95fLDPiLXFCb6AL8Qi9XaJKhAxwHN9+ycrx+HKSxsbyOPjyiGzZmUMvrE11rx8V0hgZ8Uh4EvUnvXlhSgQMcATNsac50KY3e9OMoEpP39vsglpxbny/nackYcvxIr0tjUKRBTwxQluUb9LHt4aNlyZUAGvzSRdadjKlHcFBLyA924ZuupKBQS8gHelYStT3hWwGvirOmfjrX8Ps+pcMLM/shrVRFxCAi5u1QqHDx/2XjK6KgVKQAGrgP/555+xcdMmVE5LQ+moKCQnJ6HeWVWtOmvWSEViUjzKJyaiddu2Ar4EjFpf6VsBq4A/ceIE9nzxBZo2a4aMatVQJS3NyjM1PR116tbFoMGDcfToUd+lo3ekQDErYBXwzPvx48ex6NVXMea++3DH0KFWnkOHD8fUadOQm5sLVmI6pECoFLAO+FAJo9+RAm5UQMC7sVSVJyngQwEB70MYXZYCblRAwLuxVJUnKeBDgf8HdRGn3B22d98AAAAASUVORK5CYII=[/img]
Elena walked 12 miles. Then she walked [math]\frac{1}{4}[/math] that distance.  How far did she walk all together?  Select [b]all [/b]that apply.
Write a story that can be represented by the equation [math]y=x+\frac{1}{4}x[/math].
Select [b]all [/b]ratios that are equivalent to [math]4:5[/math].
Jada is making circular birthday invitations for her friends. The diameter of the circle is 12 cm. She bought 180 cm of ribbon to glue around the edge of each invitation. How many invitations can she make?

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