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 $m$ is an integer, $m+5$ is an integer.
  • We can rewrite this as $n = 2m - 9 = 2(m - 5) + 1.$
  • Therefore, $n + 10$ is an even integer.
  • So $n + 10$ can be rewritten as $2$ times some integer
  • Then we know that $n + 10 = 2m + 10 = 2(m + 5)$
  • Suppose by way of contradiction that $n + 10$ is odd.
  • Let $n$ be an arbitrary even integer.
  • 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 $n = 2m$.
  • Then $n + 10 = 2m + 1$ for some integer $m$
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:
2026-09-19 10:08:47 (CDT)
Duration:
0s
Show/Hide answer 
{
  "even-implies-even": [
    {
      "tag": "1",
      "uuid": "b64d89a5-5e82-4b2b-8396-88f998cab347",
      "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": "a172fe6b-77db-462b-bc53-b434d79d8d41",
      "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": "dd129b32-754f-47ee-97cb-ce18aedfef68",
      "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": "dff8ebf8-20df-4802-a766-655c7152b1c6",
      "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": "ee7dadad-d9fe-4fc3-bfd0-c75a3fd70d9a",
      "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": "bec0421f-436f-4323-80b6-b2c2a64a7a55",
      "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": "d20d050d-291b-4d69-9d39-445ff9fabaae",
      "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": "e16f480e-3a8f-46ff-a4ec-1902defcb385",
      "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": "bc89b8e1-ed95-4168-80e7-ab0dd19795f5",
      "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": "f77e8e3e-a5bb-4194-960a-2c5fb451d360",
      "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": "f2e41301-6ce2-4eba-abea-2c6dd50bbbd8",
      "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": "fbcf1c43-b38d-4a42-bb29-1600c0feca60",
      "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": "fb709bad-0d0e-4b7e-99d7-d672d8b1fa78",
      "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": "cd0cf70d-7e77-4095-ac75-e20786233a6f",
      "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": "d1d472aa-a184-4b43-8551-d4a7ffdcbc75",
      "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": "a1df9bd1-2407-4933-9237-32868cbbd0ef",
      "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": "a92ea94b-7ca3-4bc8-a18c-3afae308c3e1",
      "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