IM 6.6.1 Lesson: Tape Diagrams and Equations

Label the length of the diagram.
Which equation is represented by the diagram above?
Label the length of the diagram.
Which equation is represented by the diagram above?
Draw a diagram to represent the equation 4 + 3 = 7.
Draw a diagram that represents the equation 4 ∙ 3 = 12.
Here is a tape diagram. Which equations match this diagram?[br][br][img]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAQkAAABYCAYAAADmzQKCAAAL1ElEQVR4Ae2d+VcUVxbH+z+J0N2AGDHGEHHBJVFR1ERFByLue0SDGoO4ZFQW9y0uQQEFAY1HzRkVFdT5QcWIo3IMLqMIOk7cQFBUEFTQO+e+M92HpUWo6uruevV957zTRXW95X5u1ZfXVa/uM/1+8CDNmzOHZs2caajMNnOeHRVlKLuN5mej2zsveg6lpqTQu3fvSGkyBXb+nKxe3tSxvT8F+HcQn7wta7bZaG3nRZyNYres/oRdjq9VPs8587XduWMAPa+sVKoRZPo8oBP16/sVVVRU0PPnzw2RKyrKKbh7d+rVvQeVlZUZwmaj+BZ2Nr6GB/UfQHyNqxKJLp0+o0EDQhSrjF4L9gkOpr7Bvej9+/d6NQH9BoGPEvh2yBDniMTA/gOorq7uow3KckBd3Vvq3bMn9ekZTK9fv5bFLNgBAs0IDA0NhUg0o9KKHRCJVkDCIVIQgEgodCNEQiE4FNMdAYiEQpdBJBSCQzHdEZBKJB4+fEi5OTlUUlysuSMgEpojRgMeQkAakaipqaHQASHkb/WhtavXaI4XIqE5YjTgIQSkEYmfFy0myyftqL3FShvXb9AcL0RCc8RowEMISCESR7OzxaywrZu3UKcOn9K6NWs1xwuR0ByxvYHsw0doT2YmvX371r6PN0pLS2lnSiqdyM1ttB9/OJeA7kWi9PFj6uDrJ96fePLkCVm8vGj92nXOpeSgNoiEAyga7eKfjzxCPJeXZ2+B5+SEh40kH28znT19xr4fG84noGuR4JmO4SNHidFDVVUVPXzwgCztvGjDuvXOJ9WkRohEEyAa/snTpD/1a09TJ022t/Lz4sXka7bQsexs+z5saENA1yKxZfNm8vU206mTJwWd4tu3IRLanCdurzV+eZzwbeWzSjp86JAQiO3bfnV7v4zQAd2KRMHly2KoyTcsbQkiYSMh3+e9/9yj9lYfmjR+ghCIH+fOlc9ID7VIlyLx8uVL6t2jJ33dpy/xo09bgkjYSMj5GRsTI+5NsFDwzz0k1xDQnUhw4AsOgtHRz5948lTD9KSsTAxJk1wwDMU9iYbktd+urq6iYUO/IT+zhbZt2aJ9g2jBTkB3IpF//jz5ma0U0q8/pe9Ko+TtO+x5RUKCEImxoyMpZUeypo/GIBL2c8glG1MnTaLOAZ2EUAQFfkk8mkRyDQEdikQ+DQ0dTPxqeo+goEa5a5cvyPxJO/G0I7hbd4qNWaAZRYiEZmibVbwiIVHcfzr/xx90tbBQ3KzOSE9vdhx2aENAdyLREoa7d++IkcSmDRtbOswp30EknILxo5X8tmev+InR8LF2yNf9RUSwunrjxC/5KCgND5BKJO6UlAiRwLRsDc8YF1Z9IidHPMmYNmVqo1YP7N8vbmAePHCg0X78oQ0BqUTi1s2b4qRKiIvXhlaDWjGSaABDg80XL16IG9SzZ0ZRZZMArLU1NTRj2nSXTL/XwDTdVSmVSJSXl9PKxEQ6c/q05o6ASGiLGHFDteXbltqlEom2GK72WIiEWoIorxcCEAmFnoJIKASHYrojAJFQ6DKIhEJwKKY7AhAJhS6DSCgEh2K6IwCRUOgyiIRCcCimOwJOFQk1C4rqjdy7d/X2xXmaRkzSmy3oLwi0RMApIsHrBIaGDGypHSm/sy3zJ6VxMAoE/k+Al/lzyoLBfhYrTRw7TrzvP3HceJI586vKbCuvtsx5wpixNHnCRKltltmfsM3x9crnOWd/H18hEpXPnikWTtPCBQuoW2CgeLGKlyrnYLQyZ5uNPboGEWe21bZPZrthm9zndVP/8jnNOeiLQJo5fTrVNQlE3BbFMPHBHIeQX99FBgOcA3KdA3xt16tcDFyIRFtUBceCAAgYiwBEwlj+hrUg0GYCJg4jx6HjkEAABOQjwC9O/vfePVWGmbb88gul7dypqhIUBgEQ8EwCHLdj8cKFqjpnyty9m1gokEAABOQjsCcrixLi4lQZZjp86B+qK1HVAxQGARDQjMDmTZtUDwJMHKD0h6hZmnUSFYMACLiPwOLYhbQnM0tVB0z3//qLxo4e3WzVZ1W1ojAIgIBHEJg2aTJdyM9X1RdTfX09RUZ8R7eLilRVhMIgAAKeRaCsrIxGjQgjjjmqJol5ErzK8/akJDX1oCwIgICHEdi/b59TbiUIkbh08SKNGjGCjPS6uIf5E90BAacT4NXwTuTmqq7XPuOSl2LL2L1bdYWoAARAwP0Ejh87Rn8LCyO+naA22UWC70l81as3lRQXq60T5UEABNxIoKy0lPr16UsXLlxwSi/sIsG18ewsrvzmv286pXJUAgIg4FoC9+/fp8EhAyk1JcVpDTcSCa6Vl2HjVb+3/5okXiF3WkuoCARAQDMCr6qrKX1XGoX060c7U1Od2k4zkeDa+ScHL9EWNmw4LVoQS8nbd9DerCzKyswUmad6Hj96lE6eOCFujPDNEWT3Mzh18iQVFhbSMxVRiDiexLWrV4nrgk/d71ObD/ha48xPLDIzMsR1yNdkanKyeDdj5PDhNG3yFPrzyhWnCgRX5lAkbK3w22P79v5Ga1atosT4eFqRkCCW4otbtoxif4qhhTELkD2EAYt5zPz5ImQZz3uZGx1NPJu2telqYSHFxsTQmO++E6H85s+dJ/5BwMeec46zj/k65OUw+Vrk7dUrV1JWRoam9xJbFInWnmA4zrMIPH70mHanpYuRIIcnrK2t/WAH+bE3i/6Ib4dRyo5k1a8Vf7AhfKFbAhAJ3bru4x2vqakRo4vI8AiqqqpqVoCXE+AgwFEzZtDzJqt/NzsYOwxLACJhANcvX7qUpk+Z2szSn36cT9GzZjfbjx0g0JAARKIhDYm3R4dHiJvPNhNzjh+nYUOG4sU+GxB8fpAAROKDaOT64vq1a0IUal69EoaFDR9O586elctIWKMJAYiEJlg9s9KZ02cQjyAKr/xJ4yLHeGYn0SuPIwCR8DiXaNehw4cO0ZJFi8QjtF2piGuqHWm5aoZIyOXPFq0pLS2l8FGjxKPRolu3WjwWX4KAjQBEwkbCIJ8chISn7r5588YgFsNMtQQgEmoJ6qx81Pffi4lTOus2uutGAhAJN8J3R9N/X7KEpkyY6I6m0aZOCUAkdOo4pd3mG5ccHBUJBFpLACLRWlKSHHc0O1uEA5DEHJjhAgIQCRdARhMgoGcCEAk9ew99BwEXEIBIuAAymgABPROASOjZey30Pf/8eZoz+wfKPnKkhaOI8vLyKG7ZcuLw65y3bd1KHCcRCQRsBCASNhISfXJIM0s7L/KzWCkxPsGhZRzs+JvBQ8jq5U2hISHilXGeQ9E5oBMF+PvTP0+dclgOO41HACIhkc8fPXpM0bNmkY+XN82LnkO+ZgutXrXKoYXXr18XyzueOX260fe8NBwvrcBi8bTiaaPv8IcxCUAkJPJ73NJlQiD4TU++2HmUsGrFyjZbyKtQs8Dk5uS0uSwKyEcAIiGRT/lewo0bN4RFJSUl4ieHEpHIPnyEfL3NtDdrj0R0YIpSAhAJpeQ8vFxxcbFikeBIzL7eFjqXl+fhVqJ7riAAkXAFZTe0oVQkeM2OLp91ph5dg6i6utoNPUeTnkYAIuFpHnFSf5SKBEfO9jNb6fcDB53UE1SjdwIQCb178AP9VyISvNgLPzblhXmQQMBGACJhIyHZZ1tFYtOGjWIEMS4yEgFpJDsX1JoDkVBL0EPLt0UkdiQlkZ/ZQmMiRlO1g0V8PNREdMtFBCASLgLt6mZaKxI2gYiMiKCXL166uptoTwcEIBI6cJKSLrZGJFggeNLUxHHj6S1iXirBbIgyEAlJ3WwTiZWJKxxamJ6WRj7eZho6KJTu3rlLlZWVVF5e3ig/ffqUeEFhJGMTgEhI6v+ioiIxLTshLt6hheEjR4pRBI8kOvj6kY/Z0ij7WqzULfBL4nkTSMYmAJGQ1P+1tbVUcLmAHjx44NDCkuJiKigooIv/ukgX8vMd5suXLlFdXZ3D8thpHAIQCeP4GpaCgCICEAlF2FAIBIxDACJhHF/DUhBQRAAioQgbCoGAcQhAJIzja1gKAooI/A+xRWAm7BvpbwAAAABJRU5ErkJggg==[/img]
Here is a tape diagram. Which equations match this diagram?[br][br][img]data:image/png;base64,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[/img]
Draw a diagram that represents the equation 18 = 3 + x.
Find the value of the unknown that makes the equation [math]18=3+x[/math] true.
Draw a diagram that represents the equation 18 = 3 ∙ y.
Find the value of the unknown that makes the equation [math]18=3\cdot y[/math] true.
You are walking down a road, seeking treasure. The road branches off into three paths. A guard stands in each path. You know that only one of the guards is telling the truth, and the other two are lying. Here is what they say:[br][br][list][*]Guard 1: The treasure lies down this path.[/*][*]Guard 2: No treasure lies down this path; seek elsewhere.[/*][*]Guard 3: The first guard is lying.[/*][/list][br]Which path leads to the treasure?
关闭

信息: IM 6.6.1 Lesson: Tape Diagrams and Equations