Within 20 (make ten, doubles, fact families) Transitional Reasoning Download PDF

Questions

1. 1.

   In a classroom math station, Leo is sorting equation cards into fact family sets. He finds a card with the equation $14 - \square = 7$ and realizes that the missing number forms a doubles fact with the given number. Which statement correctly identifies the missing number, the complete set of unique equations in this fact family, and the reason it has fewer than four equations?

   • A) The missing number is 8; the family has only two unique equations, $6 + 8 = 14$ and $14 - 8 = 6$, because near-doubles facts always combine to form just two equations.
   • B) The missing number is 7; the family has four unique equations, $7 + 7 = 14$, $7 + 7 = 14$, $14 - 7 = 7$, and $14 - 7 = 7$, because every addition-subtraction fact family must contain four separate cards.
   • C) The missing number is 7; the family has only two unique equations, $7 + 7 = 14$ and $14 - 7 = 7$, because the two addends are identical and do not produce new equations when their order is reversed.
   • D) The missing number is 6; the family has four unique equations, $8 + 6 = 14$, $6 + 8 = 14$, $14 - 6 = 8$, and $14 - 8 = 6$, because 14 can only be split into different numbers to make a complete family.
2. 2.

   In a math station activity, Liam needs to find the missing number in the equation $9 + \square = 16$. He uses a make-ten strategy by adding 1 to reach 10 and then adding 6 more to reach 16, determining that the unknown number is 7. Which group of equations represents the complete fact family for the three numbers in Liam's problem?

   • A) $10 + 6 = 16$, $6 + 10 = 16$, $16 - 6 = 10$, and $16 - 10 = 6$
   • B) $9 + 7 = 16$, $16 + 7 = 23$, $16 - 9 = 7$, and $23 - 7 = 16$
   • C) $9 + 7 = 16$, $7 + 9 = 16$, $16 - 7 = 9$, and $16 - 9 = 7$
   • D) $9 + 7 = 16$, $7 + 9 = 16$, $9 - 7 = 2$, and $16 - 7 = 9$
3. 3.

   Maya has a strip of 13 tokens and needs to remove 6 tokens to complete a challenge. To solve $13 - 6$, she first subtracts to reach 10 and then checks her result using a related addition fact from the same fact family. Which explanation correctly shows Maya's strategy and her verification fact?

   • A) She decomposes 6 into 4 and 2, calculates $13 - 4 = 9$ and $9 - 2 = 7$, and verifies her answer using $6 + 6 + 1 = 13$.
   • B) She decomposes 6 into 3 and 3, calculates $13 - 3 = 10$ and $10 - 3 = 7$, and verifies her answer using $8 + 5 = 13$.
   • C) She decomposes 6 into 3 and 3, calculates $13 - 3 = 10$ and $10 - 3 = 7$, and verifies her answer using $7 + 6 = 13$.
   • D) She decomposes 13 into 10 and 3, calculates $10 - 6 = 4$ and $4 - 3 = 1$, and verifies her answer using $1 + 6 = 7$.
4. 4.

   Elena is organizing craft paint jars on two shelves, placing 7 jars on the top shelf and 8 jars on the bottom shelf. She uses a doubles-plus-one strategy to find the total number of jars and then records a related subtraction equation from the same fact family. Which statement correctly describes Elena's calculation and provides a valid related subtraction fact?

   • A) Decompose 8 into 7 and 1, add the doubles $7 + 7 = 14$, subtract 1 to get 13 jars, and use the related fact $13 - 8 = 5$.
   • B) Decompose 7 into 8 and $-1$, add the doubles $8 + 8 = 16$, add 1 more to get 17 jars, and use the related fact $17 - 8 = 9$.
   • C) Decompose 8 into 7 and 1, add the doubles $7 + 7 = 14$, add 1 more to get 15 jars, and use the related fact $14 - 7 = 7$.
   • D) Decompose 8 into 7 and 1, add the doubles $7 + 7 = 14$, add 1 more to get 15 jars, and use the related fact $15 - 8 = 7$.
5. 5.

   Ken is packing 8 red apples and 5 green apples into a carton that holds 10 apples when completely full. To find the total number of apples quickly, Ken decides to use the make-ten strategy by breaking apart the green apples. How does Ken decompose the 5 green apples to make a ten, and what is the final step to find the total?

   • A) He splits 5 into 2 and 3, adds 8 + 2 to make 10, and then adds 10 + 3 to get 13 apples.
   • B) He splits 5 into 1 and 4, adds 8 + 1 to make 9, and then adds 9 + 4 to get 13 apples.
   • C) He splits 5 into 3 and 2, adds 8 + 3 to make 11, and then adds 11 + 2 to get 13 apples.
   • D) He splits 5 into 2 and 3, adds 10 + 2 to make 12, and then adds 12 + 3 to get 15 apples.