Mystery number challenges build number sense and place value concepts.

Students are successful in math when they can think mathematically, not just when they find the right answer. To build students' flexibility in thinking, a great strategy to use is sharing mystery number challenges with them. These are great for several reasons.

First, there is more than one correct answer to these challenges. Rather than trying to guess the number in the teacher's head, students have to decide on their own whether or not an answer will meet all the criteria of the challenge. Instead of asking, "Am I right?", students will have to evaluate their solution themselves.

Second, multiple correct answers requires students to justify their answers. When more than answer is available, it allows the teacher to hold a class discussion examining the virtues of each possible solution put forth. Maybe a proposed solution meets all of the clues except for the final one. This is a perfect opportunity to model how to think mathematically using all available information.

Third, when more then one answer is possible, it allows slower thinking students to fully participate. Sometimes math can seem like a race, with the quickest students being rewarded while those who think more methodically are left behind. With mystery number challenges, racing to find the answer doesn't reap the same reward because multiple correct answers are possible.

Finally, the hints included in the mystery number challenges provide an opportunity to model strategic thinking. The teacher (and ultimately the students) can use each clue to eliminate possible answers. Instead of simply guessing and checking, these challenges are a perfect venue to help students develop their logical skills.

Click the button below to go to the FREE challenges or keep reading for more detailed information.

### Implementation

Mystery number challenges are designed to be done either as a whole class or in groups, not individually. Their true power lies in discussion and justification, not as worksheets. To get the most out of mystery number challenges, I recommend starting as a whole group.

Display the mystery number challenge for all students to see.

Let students know there is more than one correct answer.

Give students a few minutes to discuss with their group.

Let each group call out one possible answer.

Work through the challenge, verbally justifying or rejecting the answer based on each clue.

Ask if any groups had an additional answer they would like to submit.

After students are used to mystery number challenges, release the burden of justification to them.

Display the mystery number challenge for all students to see.

Let students know there is more than one correct answer.

Give students a few minutes to discuss with their group.

Pair groups together.

Let each group give one possible answer.

The partner group works through the challenge, verbally justifying or rejecting the answer based on each clue.

Bring the class back together and allow each group to submit their answer, giving feedback as needed.

### TEKS Alignment

The mystery number challenges are each aligned to grade level TEKS.

Grade level | TEKS |

1st | 2(B) use concrete and pictorial models to compose and decompose numbers up to 120 in more than one way as so many hundreds, so many tens, and so many ones; 2(C) use objects, pictures, and expanded and standard forms to represent numbers up to 120; 2(D) generate a number that is greater than or less than a given whole number up to 120; 2(E) use place value to compare whole numbers up to 120 using comparative language; 5(B) skip count by twos, fives, and tens to determine the total number of objects up to 120 in a set; |

2nd | 2(A) use concrete and pictorial models to compose and decompose numbers up to 1,200 in more than one way as a sum of so many thousands, hundreds, tens, and ones; 2(B) use standard, word, and expanded forms to represent numbers up to 1,200; 2(C) generate a number that is greater than or less than a given whole number up to 1,200; 2(D) use place value to compare and order whole numbers up to 1,200 using comparative language, numbers, and symbols (>, <, or =); 7(A) determine whether a number up to 40 is even or odd using pairings of objects to represent the number; |

3rd | 2(A) compose and decompose numbers up to 100,000 as a sum of so many ten thousands, so many thousands, so many hundreds, so many tens, and so many ones using objects, pictorial models, and numbers, including expanded notation as appropriate; 2(B) describe the mathematical relationships found in the base-10 place value system through the hundred thousands place; 2(C) represent a number on a number line as being between two consecutive multiples of 10; 100; 1,000; or 10,000 and use words to describe relative size of numbers in order to round whole numbers; and 2(D) compare and order whole numbers up to 100,000 and represent comparisons using the symbols >, <, or =. 4(I) determine if a number is even or odd using divisibility rules; |

4th | 2(A) interpret the value of each place-value position as 10 times the position to the right and as one-tenth of the value of the place to its left; 2(B) represent the value of the digit in whole numbers through 1,000,000,000 and decimals to the hundredths using expanded notation and numerals; 2(C) compare and order whole numbers to 1,000,000,000 and represent comparisons using the symbols >, <, or =; 2(D) round whole numbers to a given place value through the hundred thousands place; |

5th | 2(A) represent the value of the digit in decimals through the thousandths using expanded notation and numerals; 2(B) compare and order two decimals to thousandths and represent comparisons using the symbols >, <, or =; and 2(C) round decimals to tenths or hundredths. |

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