Cogito
Grade 5 Math · Chapter 5 · Lesson 4
Judging an Answer with Benchmarks
Is it near 0, near a half, or near 1?
10 problems · about 14 minutes · 5.NF.A.2
What this lesson teaches
The child uses benchmark fractions to judge whether an answer is reasonable.
- Every fraction sits near 0, near a half, or near 1.
- Estimate a sum from the benchmarks first.
- It catches the answer that came from adding the bottoms.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
2 problemsReview — Mixed Numbers with Regrouping: 4 1/3 − 2 2/3. How many whole ones in the answer?
Answer 1
Why 1 2/3.
Review — Adding Unlike Fractions: 2/3 + 1/4, in twelfths. What is the top number?
Answer 11
Why 11/12.
Warm Up
Straightforward practice. Get the method working first.
4 problemsAbout how much is 8/9 + 1/10? Nearest whole number.
Answer 1
Why About 1.
What are the three useful benchmarks?
Answer 0, a half, and 1.
Why 0, 1/2, and 1.
Is 1/12 nearest 0 or 1?
Answer Near 0.
Why A tiny piece.
Is 5/9 nearest 0, a half, or 1?
Answer Near a half.
Why Half of 9 is 4.5.
Build It Up
The same ideas with more to keep track of.
2 problemsAbout how much is 7/8 + 6/7? Nearest whole number.
Answer 2
Why Both near 1.
Could 1/2 + 1/3 be 2/5?
Answer No. It must be more than a half.
Why A sum cannot be smaller than a part.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsNear What?: Is 9/10 nearest to 0, 1/2, or 1?
Answer Near 1.
Why 9/10 is nearly a whole one.
The Estimate: About how much is 4/9 + 5/11? Nearest whole number.
Answer 1
Why About a half plus a half, so about 1.