You are viewing this question as it will appear in the manual grading interface. Return to the normal view when you are done.

Element pl-order-blocks-optional: Dragging blocks to form one of the solutions to a problem

Drag and drop SOME of the following blocks to prove the statement:

Construct a python function that computes the sum of two numbers.

Drag from here:
  • 1
    def my_sum(first, second):
    
  • 1
    return sum
    
  • 1
    sum += first + second
    
  • 1
    sum += first
    
  • 1
    sum += second
    
  • 1
    sum = 0
    
Construct your solution here:
Drag and drop SOME of the following blocks to prove the statement:

If $n$ is an even integer, then $n + 10$ is also an even integer.

Drag from here:
  • Since $m$ is integer, $m-5$ is integer
  • Since $n$ can be written as 2 times and integer plus 1, then $n$ must be odd, which is a contradition.
  • Since $m$ is an integer, $m+5$ is an integer.
  • Suppose by way of contradiction that $n + 10$ is odd.
  • We can rewrite this as $n = 2m - 9 = 2(m - 5) + 1.$
  • By the definition of even, there exists some integer $m$ such that $n = 2m$.
  • Then $n + 10 = 2m + 1$ for some integer $m$
  • Let $n$ be an arbitrary even integer.
  • Therefore, $n + 10$ is an even integer.
  • So $n + 10$ can be rewritten as $2$ times some integer
  • Then we know that $n + 10 = 2m + 10 = 2(m + 5)$
Construct your solution here:

Correct answer

Correct answer (there may be other answers, correct indentation required):
  • 1
    def my_sum(first, second):
    
  • 1
    sum = 0
    
  • 1
    sum += second
    
  • 1
    sum += first
    
  • 1
    return sum
    
Correct answer (there may be other answers):
  • Let $n$ be an arbitrary even integer.
  • By the definition of even, there exists some integer $m$ such that $n = 2m$.
  • Since $m$ is an integer, $m+5$ is an integer.
  • Then we know that $n + 10 = 2m + 10 = 2(m + 5)$
  • So $n + 10$ can be rewritten as $2$ times some integer
  • Therefore, $n + 10$ is an even integer.

Student view placeholder

In student views this area is used for assessment and score info.
Tools

Staff information

Question

Title:
Element pl-order-blocks-optional: Dragging blocks to form one of the solutions to a problem

Variant

Started at:
2026-08-04 22:42:41 (CDT)
Duration:
0s
Show/Hide answer
{
  "even-implies-even": [
    {
      "tag": "1",
      "uuid": "d55d4d73-29c1-45a4-8590-6178ea892354",
      "final": false,
      "index": 0,
      "indent": null,
      "depends": [],
      "ranking": -1,
      "group_info": {
        "tag": null,
        "depends": null
      },
      "inner_html": "Let $n$ be an arbitrary even integer.",
      "distractor_for": null,
      "initially_placed": false,
      "ordering_feedback": null,
      "distractor_feedback": null
    },
    {
      "tag": "2",
      "uuid": "afc0dbc0-643f-4776-8d3b-4873081f7678",
      "final": false,
      "index": 1,
      "indent": null,
      "depends": [
        "1"
      ],
      "ranking": -1,
      "group_info": {
        "tag": null,
        "depends": null
      },
      "inner_html": "By the definition of even, there exists some integer $m$ such that $n =\n    2m$.",
      "distractor_for": null,
      "initially_placed": false,
      "ordering_feedback": null,
      "distractor_feedback": null
    },
    {
      "tag": "3",
      "uuid": "b493167e-080e-4912-b024-ef7b4c7bcbeb",
      "final": false,
      "index": 2,
      "indent": null,
      "depends": [
        "2"
      ],
      "ranking": -1,
      "group_info": {
        "tag": null,
        "depends": null
      },
      "inner_html": "Then we know that $n + 10 = 2m + 10 = 2(m + 5)$",
      "distractor_for": null,
      "initially_placed": false,
      "ordering_feedback": null,
      "distractor_feedback": null
    },
    {
      "tag": "4",
      "uuid": "e4386fe4-19b0-4b4c-b780-7f6d06854495",
      "final": false,
      "index": 3,
      "indent": null,
      "depends": [
        "2"
      ],
      "ranking": -1,
      "group_info": {
        "tag": null,
        "depends": null
      },
      "inner_html": "Since $m$ is an integer, $m+5$ is an integer.",
      "distractor_for": null,
      "initially_placed": false,
      "ordering_feedback": null,
      "distractor_feedback": null
    },
    {
      "tag": "5",
      "uuid": "c16afc5c-2888-40c7-89c1-30bddeda2f21",
      "final": false,
      "index": 4,
      "indent": null,
      "depends": [
        "3",
        "4"
      ],
      "ranking": -1,
      "group_info": {
        "tag": null,
        "depends": null
      },
      "inner_html": "So $n + 10$ can be rewritten as $2$ times some integer",
      "distractor_for": null,
      "initially_placed": false,
      "ordering_feedback": null,
      "distractor_feedback": null
    },
    {
      "tag": "7",
      "uuid": "ffc9b6dc-e8ba-4f9b-8523-c9fb27505b3f",
      "final": false,
      "index": 5,
      "indent": null,
      "depends": [],
      "ranking": -1,
      "group_info": {
        "tag": null,
        "depends": null
      },
      "inner_html": "Suppose by way of contradiction that $n + 10$ is odd.",
      "distractor_for": null,
      "initially_placed": false,
      "ordering_feedback": null,
      "distractor_feedback": null
    },
    {
      "tag": "8",
      "uuid": "c8f77961-63fc-4f65-bed2-d7734775f026",
      "final": false,
      "index": 6,
      "indent": null,
      "depends": [
        "7"
      ],
      "ranking": -1,
      "group_info": {
        "tag": null,
        "depends": null
      },
      "inner_html": "Then $n + 10 = 2m + 1$ for some integer $m$",
      "distractor_for": null,
      "initially_placed": false,
      "ordering_feedback": null,
      "distractor_feedback": null
    },
    {
      "tag": "9",
      "uuid": "cefbe3ab-4a18-41f9-a4a4-75be489add88",
      "final": false,
      "index": 7,
      "indent": null,
      "depends": [
        "8"
      ],
      "ranking": -1,
      "group_info": {
        "tag": null,
        "depends": null
      },
      "inner_html": "We can rewrite this as $n = 2m - 9 = 2(m - 5) + 1.$ ",
      "distractor_for": null,
      "initially_placed": false,
      "ordering_feedback": null,
      "distractor_feedback": null
    },
    {
      "tag": "10",
      "uuid": "eb5756d8-973a-4231-a575-e86c3d294efa",
      "final": false,
      "index": 8,
      "indent": null,
      "depends": [
        "8"
      ],
      "ranking": -1,
      "group_info": {
        "tag": null,
        "depends": null
      },
      "inner_html": "Since $m$ is integer, $m-5$ is integer ",
      "distractor_for": null,
      "initially_placed": false,
      "ordering_feedback": null,
      "distractor_feedback": null
    },
    {
      "tag": "11",
      "uuid": "b568d36f-a541-4690-836e-4657a85ae845",
      "final": false,
      "index": 9,
      "indent": null,
      "depends": [
        "9",
        "10"
      ],
      "ranking": -1,
      "group_info": {
        "tag": null,
        "depends": null
      },
      "inner_html": "Since $n$ can be written as 2 times and integer plus 1, then $n$\n    must be odd, which is a contradition.",
      "distractor_for": null,
      "initially_placed": false,
      "ordering_feedback": null,
      "distractor_feedback": null
    },
    {
      "tag": "6",
      "uuid": "e9c75bff-af80-4eeb-a54d-59d4105b0efd",
      "final": true,
      "index": 10,
      "indent": null,
      "depends": [
        [
          "5"
        ],
        [
          "11"
        ]
      ],
      "ranking": -1,
      "group_info": {
        "tag": null,
        "depends": null
      },
      "inner_html": "Therefore, $n + 10$ is an even integer.",
      "distractor_for": null,
      "initially_placed": false,
      "ordering_feedback": null,
      "distractor_feedback": null
    }
  ],
  "python-plus-equals": [
    {
      "tag": "1",
      "uuid": "f52caf87-b69a-4054-98af-f5d45ec1f66b",
      "final": false,
      "index": 0,
      "indent": 0,
      "depends": [],
      "ranking": -1,
      "group_info": {
        "tag": null,
        "depends": null
      },
      "inner_html": "<pl-code language=\"python\">def my_sum(first, second):</pl-code>",
      "distractor_for": null,
      "initially_placed": false,
      "ordering_feedback": null,
      "distractor_feedback": null
    },
    {
      "tag": "2",
      "uuid": "ab90a844-fb51-47f0-9fe3-1e8c14867da7",
      "final": false,
      "index": 1,
      "indent": 1,
      "depends": [
        "1"
      ],
      "ranking": -1,
      "group_info": {
        "tag": null,
        "depends": null
      },
      "inner_html": "<pl-code language=\"python\">sum = 0</pl-code>",
      "distractor_for": null,
      "initially_placed": false,
      "ordering_feedback": null,
      "distractor_feedback": null
    },
    {
      "tag": "3",
      "uuid": "accea588-5937-4d75-a589-4672ddf9bbf0",
      "final": false,
      "index": 2,
      "indent": 1,
      "depends": [
        "2"
      ],
      "ranking": -1,
      "group_info": {
        "tag": null,
        "depends": null
      },
      "inner_html": "<pl-code language=\"python\">sum += first</pl-code>",
      "distractor_for": null,
      "initially_placed": false,
      "ordering_feedback": null,
      "distractor_feedback": null
    },
    {
      "tag": "4",
      "uuid": "a087d871-9765-47a3-b490-56ad7ff041c8",
      "final": false,
      "index": 3,
      "indent": 1,
      "depends": [
        "2"
      ],
      "ranking": -1,
      "group_info": {
        "tag": null,
        "depends": null
      },
      "inner_html": "<pl-code language=\"python\">sum += second</pl-code>",
      "distractor_for": null,
      "initially_placed": false,
      "ordering_feedback": null,
      "distractor_feedback": null
    },
    {
      "tag": "5",
      "uuid": "cb6724c5-ae9c-4088-a82d-dda968cd6ace",
      "final": false,
      "index": 4,
      "indent": 1,
      "depends": [
        "2"
      ],
      "ranking": -1,
      "group_info": {
        "tag": null,
        "depends": null
      },
      "inner_html": "<pl-code language=\"python\">sum += first + second</pl-code>",
      "distractor_for": null,
      "initially_placed": false,
      "ordering_feedback": null,
      "distractor_feedback": null
    },
    {
      "tag": "6",
      "uuid": "f34c035c-58e9-44f9-bc61-b43e99003eae",
      "final": true,
      "index": 5,
      "indent": 1,
      "depends": [
        [
          "3",
          "4"
        ],
        [
          "5"
        ]
      ],
      "ranking": -1,
      "group_info": {
        "tag": null,
        "depends": null
      },
      "inner_html": "<pl-code language=\"python\">return sum</pl-code>",
      "distractor_for": null,
      "initially_placed": false,
      "ordering_feedback": null,
      "distractor_feedback": null
    }
  ]
}
History
dec frac
rad deg