Halves, quarters, thirds, fourths (partitioning) Transitional Reasoning Download PDF

Questions

1. 1.

   A gardener divides a rectangular plot of land into two equal halves and reserves one half for growing tomatoes. He then partitions the remaining half into two equal sections, planting peppers in one section and herbs in the other. Which statement correctly describes the size of the herb section and the total portion of the plot planted with tomatoes and herbs together?

   • A) The herb section is one third of the entire plot, and the total portion planted with tomatoes and herbs is two thirds of the plot.
   • B) The herb section is one fourth of the entire plot, and the total portion planted with tomatoes and herbs is three fourths of the plot.
   • C) The herb section is one half of the entire plot, and the total portion planted with tomatoes and herbs is the entire plot.
   • D) The herb section is one fourth of the entire plot, and the total portion planted with tomatoes and herbs is two fourths of the plot.
2. 2.

   Liam has two identical rectangular sheets of craft paper. He partitions the first sheet into 3 equal parts and keeps 2 of those parts, while he partitions the second sheet into 4 equal parts and keeps 2 of those parts. Which statement correctly compares the total amount of craft paper Liam keeps from each sheet?

   • A) He keeps more paper from the second sheet because four equal parts is more parts than three equal parts.
   • B) He keeps the same amount of paper from both sheets because he keeps exactly two parts from each sheet.
   • C) He keeps more paper from the first sheet because each third is larger than each fourth, so two thirds is greater than two fourths.
   • D) He keeps less paper from the first sheet because dividing a whole into fewer shares always results in smaller individual pieces.
3. 3.

   Three students each receive an identical rectangular strip of paper for an art project. Mateo partitions his strip into equal halves, Nora partitions hers into equal thirds, and Oliver partitions his into equal fourths. If each student cuts out and takes exactly one piece from their own strip, which of the following statements correctly compares the sizes of these single pieces?

   • A) Nora's piece is larger than Mateo's piece because dividing a strip into three parts creates larger sections than dividing it into two parts.
   • B) Oliver's piece is the largest of all three because a whole divided into fourths has the greatest number of pieces.
   • C) Mateo's piece is smaller than Oliver's piece because two parts are fewer than four parts.
   • D) Mateo's piece is the largest and Oliver's piece is the smallest because partitioning an identical whole into more equal parts makes each part smaller.
4. 4.

   Chef Elena bakes three identical round pies for a family gathering and partitions each pie into equal-sized slices. She cuts the apple pie into halves, the pumpkin pie into thirds, and the berry pie into fourths. If a guest takes one slice of the apple pie, which of the following represents an amount of pie that is exactly equal in size to that slice?

   • A) Two slices of the berry pie
   • B) Two slices of the pumpkin pie
   • C) Three slices of the berry pie
   • D) One slice of the berry pie
5. 5.

   Four classmates each received an identical rectangular strip of craft paper to make bookmarks. Ayla folded her strip into 2 equal parts, Bora folded his strip into 3 equal parts, and Can folded his strip into 4 equal parts. Deniz also cut his strip into 4 pieces, but two pieces were noticeably wider than the other two. Based on this information, which of the following statements is correct?

   • A) Deniz can describe each of his pieces as one fourth because his strip was cut into four separate pieces.
   • B) Ayla's single piece is longer than Bora's single piece because dividing the same whole into fewer equal parts creates larger individual parts.
   • C) Can's single piece is longer than Bora's single piece because dividing a whole into four parts gives bigger sections than dividing it into three parts.
   • D) Bora can describe each of his pieces as one quarter because any equal partitioning produces quarters.