IM 6.5.3 Lesson: Adding and Subtracting Decimals with Few Non-Zero Digits
Evaluate mentally:
[math]1.009+0.391=[/math]
Decide if each equation is true or false.
[math]34.56000=34.56[/math]
Explain your reasoning.
[math]25=25.0[/math]
Explain your reasoning.
[math]2.405=2.45[/math]
Explain your reasoning.
[size=150]Andre and Jada drew base-ten diagrams to represent [math]0.007+0.004[/math]. Andre drew 11 small rectangles. Jada drew only two figures: a square and a small rectangle.[/size][br][img]data:image/png;base64,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[/img][br]If both students represented the sum correctly, what value does each small rectangle represent?[br]
What value does each square represent?
Describe a diagram that could represent the sum [math]0.008+0.07[/math], OR draw it in the applet below.
Draw a diagram that could represent the sum 0.008 + 0.07
[size=150]Here are two calculations of [math]0.2+0.05[/math][/size]. 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[/img][br][br][size=100]Which is correct? Explain why one is correct and the other is incorrect.[/size]
Compute each sum. If you get stuck, consider drawing base-ten diagrams on the applet below to help you.
[img]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJQAAABECAYAAABnAhz7AAAP50lEQVR4Ae1dB1RURxdeOoI0AQvNgoKCgIAlVmyoWBITu7/GrrES1PgrRKMx/r8mJho1tqjYohhrjoqigoAlv10DKEVEBdQoCipWyvefO2QR1sfsLm9X3XPeO2fPe2/unftm7nw7M+/OfXdkkA5JAxrUgEyDsiRRkgags4B6+vQpMjMzcevWLdy7e++DaMrCwiLcunkTWZmZKC4q0miZ7t65g/T0dDx5/FijcjUtTPcAVVyM9et+Ra/uPeDuWh+1nZzh5+WDKRMn40R8vKb1o5a8SRMmoqFrA3Rq3wG5jx6plZfHfPrUKfg29oZzLQeEr9/AY33vNJ0CVG7eY3Tt1BkGMhnsbaqhU0AH9OzeHf4+vjAzNoFMJnsvCs/JeQh/nyYwNzGBnZU1fBp74dHDhxpp3GVLlsLWypr9TA2NsHL5Co3I1ZYQnQJUi2bNGGhaNW+BvLzccjo5uP8A6rrUZmDb+fvOcjRt3mzetAk17ezYcz/u0RP1XGqjaRM/0T3Us/x8BHbsyOrbuGEjBHXpClMDQ6xZuUqb1REtW2cAdenSZabcBnXqIjk5WbDiv23Zyho2oHUb5D3OE+TRVOLrggKMGTUaVlXMYCTTx9rVaxATHc2GJf8mvqIAdeRwFFo0LfnzUF1u376Fwf0HQF8mkwClqQYcMmgQ+4dOnzqVK7KOswusLSwRGRnJ5RNLTE1LYwCv7eiEw4dKnnUkKgo1qtlCDKAKCgowavhwJnt6SAiePctnRe3Qth37s0g9lNiWA3D7diaa+fmzedOeXbu5EseMGAk9mQyjR4zk8mmCGLFtO64lXS0VFXnwoGhAkbDbmZlYpTC0tZcAVapn0Rdnz54B9QR1nJxx/tw5rrw1q1fDUKaH5v7+XD5tECMjNQMoobJJPZSQViqZdnD/ftSwtYOfTxPcyLjBlXI4MgpVjIxhYWrK5dMGUQIUdMOwuXXzZvbaHNCmDe7fv8/FQlJSUqkJgcuoBaIEKB0BVPiGDahmaYWOAe3xUIl9JyEhEeb/2KS0gBmuSAlQugKo8HDYEqDaqQYouZHzyeMnXABomigBSkcAtXHDRlSzskaHdu2Qk5PDxUFiYpLUQ3E1pF2iThg2I7Ztg52VDdq2bIl7d+9yNXLuzFlUkYY8ro60SdQJQMXHxcGhRk00rN8ANOnmHb9H7ICJgSFqOzry2LRCk4Y8HRny0tOvw8fTC7Xs7HHs6FEuGGbPCoORnj5bOOYyaoEoAUpHAFVYVIigwK6wNDfH6lX8xdFO7duzZYvZoWFagAxfpAQoHQEUNSMt/JJ7SlDnLnj16pVgy15Pvw4LUzNmVVdmUS8roKioSOlkvyx/RdcSoHQIUNSIZA4w1jfAimXCPkHDhn7OVuQH9++PwoKCitq9XHphYSG+Dg1F40YeWLL4x3I0dW8kQOkYoGKiY2BZxYyt1U39MgTkFkvH8ehodApoz1bjXRydkJKcojIW/rpyBXbWNrCxsISLgyMybmSonFeR8VBkJFsiauor3h9KUXaHdgGs3msVFo0V+d73vU685ZVV0pVLl9G6xUdMuTQEyn8Eiq6BXZCbW97xrmxeoevz584zMDnWqIma9tVx7eob7wEhfl7a3j17GKjJ0S/nwQMeq9q0Jl7erK5ie1G1H6xmBp0DFNWvuLgY1Hg/fP89FsyfjyU//oSzZ86wdDXrj/yn+ej3WR82lE6cMEHd7OX4r169innffouflyzB82fPytHE3tDLyIwZM/DnqdNiRWk1v04CStMaefHiBdLS0kDzKekQpwEJUOL0J+VW0IAEKAWFSLfiNCABSpz+pNwKGpAApaAQ6VacBiRAidOflFtBAxKgFBQi3YrTgAQocfqTcitoQAKUgkKkW3EakAAlTn9SbgUNSIBSUIh0K04DEqDE6U/KraABnQUURWCJi41FdHQ0/jx9Go80GOBLQUdKbynARUJCAqKPHUP00aO4ePEinj9/rjSfKgzktRAfH89cdGKPH2dR+1TJJ8RDOos6dBixMTEgWUK/Y0eO4NKlS0LZVUrTOUCdPXsWA/v2hbmxaanrCrmweDRwx1fTpqlUaU0y/bZ1Kzq2C2BuK3JXGjq3+agl/rtgQaUflZuXh8EDBsC1Tt1y9axhY4tRw0cg/Xq62rKHDx1aTlbZ8pa9buLtrbZseQadAlTM8RjUdnBkSundoxcoyBg53a1ZtQoN6tZj6Z990htFRe/Ga+CHRYvYF83UGNOCQ/7558dixrTpsLW0ZuVZvGiRXNcqn7Ozs1lYRZLrVs8VO7ZtY7Gndmzfgc4dSnzmvRt54sYNfpwHxQf26f0ZLM3METxlCuhLoqjDUW/9Dh44oDQgiaLcsvc6BShSMLkAh86cWbYO7DovLw89ugWxUD5fv4MPFOhzLipP9Wq22L3z7RBDNLx4NWrEfNx37VQ9oh4FMhs2dCjr8fp80lvQfz4kOBhGMhma+vq+pQdeQgv/psyZcMf27Tw2UTRBQF27eg3Bk6fgm9lzRAnXZOYN69ezBmzfpi2ev3ghKDohMRFmhsZoWN8NadfTBHk0lThk4CDmvz5u9OgKRW4K38jK3CuoO/LzSwKHVcj8DyEtNZXF6SSwPswRjtOZ//QpKCwk8VAPrerh7dmYuSgf2L9f1Sxq8wkCKvZ4HPPdpoi2H8Lx+nUBunfpCgszM/ywcCG3SBTAlcL5rF+7jssnhpiVlY16zi6ws6kGZb0PNToF+khNSVXpkfPnfct6WQ+3hlz+2WFhDNAD+vXn8smJ9JLg6eYOp5q1cPLESXmyxs+CgDp18iT7Utffx0fjD6yMwJSUZPZVSi376jiq5EPPOaFhrEF69ehZmUeplGfP7p1sqGtQzxV3srO5eZr5+rGe5MfFi7l8cqKvtzcDyn/mfydPEjz/sXcv621c66jmv34zI4NN8Os6uyAxIUFQpiYSdQJQcXGxoI8I3Oq6stdzXsW3bf0Nxnr6cHetx2MTRVu+dCkszczYsKNM0KhhIxhABvbrp4yV0a3MzWGib4BDB/kxQi9euMAi+rk4OOD06VNKZSclJoLA5OZaX+MfUJR9uE4Aau/uPSy+JkXGpd0TeMfJk6dgZmTMJrU8PjG0uXO+YcPqwL7KQbJg3nwYklnDnT+EUXloQm5hWoX1fjRK8I6srCwW+J+G3QgVJtn0VudYoxa8PT1x584dHIk6jH1794F6un2794D86jVxCALqwvnzcKpRC838/DTxDNEySgOOqRAfiv6J8vhQoh9cgYCpwV/CVN8AE8Z9UQHHm+Q1K1cycNtb2bxJrOCKvjM0MzRiPc/lixcr4CpJpi06PN0bwqaqJdauWs3lJeKe3bthZV4VdpZW7E2P5nZlf2RO8PFsDDIbiDlkYTNDMfGL8QieNBnBkyZhWkgIhg8Zyuw9FO0k9N8zWXoJfTJGjxyFTRve7fYQGzeEl0SwaxegUgQ7OaAKC7RgjyouBgGKIryMH6scUDRpp6jENDFXdty7c5f1fLUdnXH5onJrtbdHY1hXtcCqlSuVicazZ8+wYvkKfDV1Gvv8bEdEBChMEp2XL10GijJMPTuB7PuF6tvO5AWQGerplUOqHLUUdbemnb0grUe3bvL87+QcHq56SMTEhDc91EsNLX+Uq6QcUPoGGD9ufDmS0M2OiB1sDlXNwlKIXC6tFFBOygFF8Ri85ID6RTmgyj1I4Obx48cInTULNlUtWGjsypoWBIe8lJQUODs4olWz5gKPfvdJmzduYkFb6V+Uk8P/IjfhrwStD3nTQ6ayHmrc6DFKlbH856XsK+eatvZKee///TfrJVxqOYAm3bzj0cMcNHJzZ8PXurVreaxq0UZ+PgzGMn1079KtUuuRgoCSmw38PhCzwb69e9lElV7BaTsz3hEbG4cqhkYwMTTksYmizZ83D2ZGJuj76adK5cybM5dNyn28vZTyFhUXMcu6vbWN0p21bt+6zZZlyFK/Uw1LvLJC0ByKRilvD09kZ/FNIkKyuID6UOxQ9Pk1GeRcXWrjypUrQvUoTdu0IZy9dtPanraOFcuWwaKKGZqpsPQxdPAQNikfoKLZwLKKOeM/eOAgt/i0SE5zLWdmNtDc5+npaekMULR13K2b/D+vUAF1AlD3HzxAQKvWsLWygbKdpoYPG8YaZPCAgUL11Uja2f+dYZsE0V59Vy5f5sqsbmvHJuXr1/7K5ZMThwwczBp07Bj+cLp+3TrYWFigUX03NuGW5xd7pvpQD9W4YUO2kaS68gQBRRsZ2tvYwsvDU115WuMf0KcvaL+47+bN5z6jiZcXjA0MsHLFL1w+MUSKPUU9IIUA2rJ5C1cUNQ7ZlpKSErl8cqI8sBoZcnlH2MxZLPTjx0HdeWxq0yjwCJWZtgJ58kT9sNyCgKK1nvp16qL1Ry3VLpC2MlxNSmQVpbH973vCW8IeO3qMrcJ7uLnj5s2bKheFFJeamqpWsIyfFi9m5enb+1MUFQpvBztv7lzGQ7uP0mu7KgdFOaYNHKlRL14QtkWRewtNyIknJkb1xWFlzyc7WOsWLWFhYoZfVixXxi5IFwTUy1cv8ejhI+TlanfPOcEScRK7dg5kSuzdq9dbq/cn40/A28ODvVGpY0fJzc1DUx9fJjeoi3rmEJpnmOgZIGzWTBQXvyk47Te8ZfNmONVyYH5RUVFRb4gqXK1dvRrmJqbw9fLGOYXNkmjjyW6BgWxYD+zQUQVpYD0NzfuiDh2q0LP1RPyJUh+soG7dKr23sSCgVCrle2DKzMoCRXKjf2bL5i0wZeIkZmQcOWw4i6tJ6WSUffnypcqlo1ic9tbVmHXaoXoNpXOisoJPnohnex7Tc8kXa9qXIcww3Ltnr1LHu3Vr1H+lp7BCX02dyupJUfXGjRkL8oGaMHYc6M2bnkdvvMnXhDeiLFtGuiZfsbYtW7G5HI065G8VMiWYGbPp/K+Bg5hZhuQSiHMe8jcXUJRf9l6nAEUFf/3qNcjFg5YdyCJOW5nRrpq0bceqShj4yK2Eot/RW1tdJ2c8UDPy3PXr1zFuzBi413NlvQbth0wGYfIcVfamVrYhhK5XLFuOTu0DQG9+Rnp6zLmQgDQ77Gu1dyz9Y98+9O/Tl+0USkswFHqbnBXpTNMbsjvt3rVLrWFfqMw6Byh5JZ7m54Pil6cmJyNDTVdYuYySczF+XbMGXTsFYt/ePeVJatzR9CD52jWkXEtGdnaWGjmVs964kYHUlBSQwfn169fKM3A4KH9GRok8cuYjmbmP1AsjyRGvG9ub8Sog0T4sDehsD/VhqVEqjVwDEqDkmpDOGtGABCiNqFESIteABCi5JqSzRjQgAUojapSEyDUgAUquCemsEQ3IQmfMwOzQUNB2YNJP0kFlMDAnLAwhU6YgLi6OrPgy5gBGFlPpJ+mgMhgw1jNgy0ELFyyAjJYsugV2kX6SDiqNgaAuXdHczx+/R0Tg/yDxSu4JFWEQAAAAAElFTkSuQmCC[/img]
[math]0.209+0.01[/math]
[math]10.2+1.1456[/math]
The applet has tools that create each of the base-ten blocks. This time you need to decide the value of each block before you begin.
[list][*]Select a Block tool, and then click on the screen to place it.[/*][*]Click on the Move tool (the arrow) when you are done choosing blocks.[/*][*]Subtract by deleting with the delete tool (the trash can), not by crossing out.[/*][/list]
To represent 0.4 - 0.03, Diego and Noah drew different diagrams. Each rectangle represented 0.1. Each square represented 0.01.
Diego started by drawing 4 rectangles to represent 0.4. He then replaced 1 rectangle with 10 squares and crossed out 3 squares to represent subtraction of 0.03, leaving 3 rectangles and 7 squares in his diagram.[br][img]data:image/png;base64,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[/img][br][br][br][size=100]Noah started by drawing 4 rectangles to represent 0.4. He then crossed out 3 of rectangles to represent the subtraction, leaving 1 rectangle in his diagram.[/size][br][img]data:image/png;base64,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[/img][br][br]Do you agree that either diagram correctly represents [math]0.4-0.03[/math]? Discuss your reasoning with a partner.
To represent 0.4 - 0.03, Elena drew another diagram.
[size=150][size=100]She also started by drawing 4 rectangles. She then replaced all 4 rectangles with 40 squares and crossed out 3 squares to represent subtraction of 0.03, leaving 37 squares in her diagram.[/size] 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[/img][br][br]Is her diagram correct? Discuss your reasoning with a partner.
Find each difference. If you get stuck, you can use the applet below to represent each expression and find its value.
[math]0.3-0.05[/math][br][br]Explain how you got your answer.
[math]2.1-0.4[/math][br][br]Explain how you got your answer.
[math]1.03-0.06[/math][br][br]Explain how you got your answer.
[math]0.02-0.007[/math][br][br]Explain how you got your answer.
The applet has tools that create each of the base-ten blocks. This time you need to decide the value of each block before you begin.
[list][*][size=150]Select a Block tool, and then click on the screen to place it.[/size][/*][size=150][*]Click on the Move tool (the arrow) when you are done choosing blocks.[/*][*]Subtract by deleting with the delete tool (the trash can), not by crossing out.[/*][/size][/list]
A distant, magical land uses jewels for their bartering system. The jewels are valued and ranked in order of their rarity.
[size=150][size=100]Each jewel is worth 3 times the jewel immediately below it in the ranking. The ranking is red, orange, yellow, green, blue, indigo, and violet. So a red jewel is worth 3 orange jewels, a green jewel is worth 3 blue jewels, and so on.[br][br]At the Auld Shoppe, a shopper buys items that are worth 2 yellow jewels, 2 green jewels, 2 blue jewels, and 1 indigo jewel. If they came into the store with 1 red jewel, 1 yellow jewel, 2 green jewels, 1 blue jewel, and 2 violet jewels, what jewels do they leave with? Assume the shopkeeper gives them their change using as few jewels as possible. You may use the applet below to keep track of your work.[/size][/size]
IM 6.5.3 Practice: Adding and Subtraction Decimals with Few Non-Zero Digits
Here is a base-ten diagram that represents 1.13. Use the diagram to find 1.13 - 0.46.
Compute the following sums. If you get stuck, consider drawing base-ten diagrams on the applet below.
[math]0.027+0.004[/math]
[math]0.203+0.01[/math]
[math]1.2+0.145[/math]
If you get stuck, consider drawing base-ten diagrams.
A student said we cannot subtract 1.97 from 20 because 1.97 has two decimal digits and 20 has none. Do you agree with him? Explain or show your reasoning in the applet below.
[size=150]Decide which calculation shows the correct way to find [math]0.3-0.006[/math].[/size]
Explain your reasoning.
Complete the calculations so that each shows the correct difference by typing in the empty boxes.
The school store sells pencils for $0.30 each, hats for $14.50 each, and binders for $3.20 each. Elena would like to buy 3 pencils, a hat, and 2 binders. She estimated that the cost will be less than $20.
Do you agree with her estimate? Explain your reasoning.
Estimate the number of pencils could she buy with $5. Explain or show your reasoning.
[size=150]A rectangular prism measures [math]7\frac{1}{2}[/math] cm by 12 cm by [math]15\frac{1}{2}[/math] cm.[/size][br][br]Calculate the number of cubes with edge length [math]\frac{1}{2}[/math] cm that fit in this prism.
What is the volume of the prism in[math]cm^3[/math][b][sup][/sup][/b]? If you are stuck, think about how many cubes with [math]\frac{1}{2}[/math]-cm edge lengths fit into [math]1\text{ cm}^3[/math].
Show your reasoning.
At a constant speed, a car travels 75 miles in 60 minutes. How far does the car travel in 18 minutes?
If you get stuck, consider using the table.