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.
  • Therefore, $n + 10$ is an even integer.
  • Suppose by way of contradiction that $n + 10$ is odd.
  • Then $n + 10 = 2m + 1$ for some integer $m$
  • Since $n$ can be written as 2 times and integer plus 1, then $n$ must be odd, which is a contradition.
  • We can rewrite this as $n = 2m - 9 = 2(m - 5) + 1.$
  • Then we know that $n + 10 = 2m + 10 = 2(m + 5)$
  • By the definition of even, there exists some integer $m$ such that $n = 2m$.
  • Let $n$ be an arbitrary even integer.
  • So $n + 10$ can be rewritten as $2$ times some 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:
2026-09-19 07:03:06 (CDT)
Duration:
0s
Show/Hide answer 
{
  "even-implies-even": [
    {
      "tag": "1",
      "uuid": "b359d4b6-a4af-480f-8b16-beeebcacb11a",
      "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": "eb696bfd-819a-4be9-b8c4-98373fe0d9c2",
      "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": "bba7d094-25c8-431a-bfde-7939e802c723",
      "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": "f3b459a7-1747-4b42-91f1-088d14448a39",
      "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": "ccc13abe-6f8a-495d-bee4-90020434cc1b",
      "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": "c1845241-a313-4d5d-bef5-bcd4274b650c",
      "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": "e4214458-a7b1-4596-8b45-3ecb192f2970",
      "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": "fb04d43b-b7e4-4b33-875c-1184a9f79e17",
      "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": "dace8165-acb7-49f7-b082-ef3c875d3853",
      "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": "d461852a-c165-4c1a-88db-bee82d19cda2",
      "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": "b9350920-466d-4392-b4d6-72406e084838",
      "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": "da0f31d5-235e-4eb9-b122-854f2f822650",
      "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": "c6a762c9-398c-462f-abb0-747559bc558e",
      "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": "a5647403-6ea2-4d6b-84b5-fecc9e006396",
      "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": "bdf21bfb-3a34-4d87-af41-3465d3ebe62e",
      "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": "b751c1f1-0e54-45d1-9ceb-58b3a5e8920c",
      "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": "b5e75390-eba5-43b3-aea6-b139fcc0ad5b",
      "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