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

Correct answer

Student view placeholder

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

Staff information

Question

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

Variant

Started at:
2026-08-04 22:49:06 (CDT)
Duration:
0s
Show/Hide answer 
{
  "even-implies-even": [
    {
      "tag": "1",
      "uuid": "f9fe495c-d685-4187-895a-fb6293a5dc7b",
      "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": "d96b50f6-aeb6-44dc-964a-c7cf96614428",
      "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": "c5258826-4173-4110-9de6-f43b89203923",
      "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": "c41005bb-f9db-4f9b-baef-1ca85d943c24",
      "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": "e1c31b15-93ee-4dca-9cb3-654478a9fe9e",
      "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": "d5de4305-8380-4294-9615-c51fb0634d04",
      "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": "c48449c9-33c8-410e-9ca5-dab9c5244e1d",
      "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": "a2e292a7-6a37-402a-ae94-3820d4da79a7",
      "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": "d47140a6-ca28-4aa8-bcd8-0cc11559ae1b",
      "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": "a99e3166-4a9f-4679-b74e-26508c6700b4",
      "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": "f398916f-fa30-4455-bac9-a945977c0bc0",
      "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": "cec6c3ba-1f7a-4285-8ff2-c513563b6ae2",
      "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": "a0991a8e-e289-461e-8dca-1200c420e9fd",
      "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": "b164f178-69f5-43c0-ab7b-8575f9f5f09e",
      "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": "ede96e4f-ba4f-4a2d-b172-3dcb8f3f6404",
      "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": "b605467b-1589-4dc5-bb93-21f42fb79970",
      "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": "dd34b956-c50c-4d3b-98c0-e8e1e6fbf38c",
      "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
    }
  ]
}
This box is not visible to students.
History
dec frac
rad deg