Summative Assessment Task: Grade 2
Routes to the City
Brandon is finding the shortest route to the city. One route goes from Brandon's town through two towns. The miles between the towns are 131 miles, 37 miles, and 63 miles. Another route goes from Brandon's town through one town. The miles between the towns are 70 miles and 159 miles. Brandon writes 131 + 37 + 63 < 70 + 159 to show which route is the shortest. Is Brandon correct? Show all your mathematical thinking.
The Comparing Numbers Unit involves understanding the relative position and magnitude of whole numbers, and their relationships within the numeration system. Students will answer questions such as –
- Which number is greatest? Least? How do you know? How can you use symbols to show these relationships?
- How can you order these numbers from least to greatest? How can you prove you are correct?
- How can you use a number line to show the relationships between these numbers?
Math Concepts and Skills Covered
The student compares whole numbers and understands place value relationships. The student:
Exemplars Task-Specific Evidence
The student is expected to combine numbers and then use the symbols >, =, and < to compare the totals to find the shortest distance.
Underlying Mathematical Concepts
- Positional Property of Base-10 Number System
- Part/Whole reasoning
- Number sense to 200
Possible Problem-Solving Strategies
- Model (manipulatives)
- Number line
Formal Mathematical Language and Symbolic Notation
- Number line
- More than (>)/Greater than (>)/Less than (<)
- Equivalent/Equal to
- Place value
- Hundreds, tens, ones
- Standard notation/Expanded notation
No, Brandon should write 131 + 37 + 63 > 70 + 159 or 231 > 229.
The shortest way is 229 miles.
Scoring Rationales and Corresponding Anchor Papers
Below are some examples of mathematical connections. Your students may discover some that are not on this list.
- Repeat the activity with other rolls of the number cubes.
- 6 is a half dozen.
- 6 threes is 1 1/2 dozen.
- Patterns: Stars +3 or +6, Circles +1.
- When you add equal groups on a number line, you jump over the same number of spaces each time moving to the right, away from zero.
- Extend the number of equal sets of 3 beyond 6.
- Solve more than one way to verify answer.
- Relate to a similar task and state a math link.
- Rewrite the story with a new expression.
- Explain how 6 x 3 and 3 x 6 are both 18 but are used differently to represent the situation in the game.
- 6 x 3 is an even number times an odd number which gives you an even product.
- Generalize and prove the rules 3 · c = s and 6 · c = s (key: c is circles, s is stars).