Product Predictors

Fact: Exact product is greater than 1,200!

Question: What if one factor rounds UP and one rounds DOWN? The effects balance each other out!

Guided Challenge

Magnitude Face-Off: Which is Greater?

Slide 5 of 6

Expression A

\(78 \times 42\)

Estimate: \(80 \times 40 = \mathbf{3,200}\)

>

GREATER

Expression B

\(89 \times 28\)

Estimate: \(90 \times 30 = \mathbf{2,700}\)

How we know without calculating:

\(3,200\) is significantly larger than \(2,700\) (a difference of \(500\)). Even with rounding shifts, Expression A is clearly greater than Expression B!

Compare products in seconds using leading digits and zeros. Face-Off Ready

Next Step

Your Mission: Practice Pages

Slide 6 of 6

1. Round First

Round each factor to its highest place value before doing any multiplication.

2. Check Over/Under

State whether your estimate is an overestimate or underestimate based on rounding arrows.

3. Fast Compare

Insert >, <, or = symbols between expressions by comparing their rounded estimates!

Grab your pencil and your Practice Pages. Work independently or with a partner! Start Estimating!

Est. A:

Est. B:

13. \(612 \times 49\)

\(295 \times 98\)

Est. A:

Est. B:

4 Level 4: Real-World Grant Scenario

Budget analysis using estimation

Scenario: The 5th Grade STEM Club received a $2,000 science grant. They plan to buy 38 sensor robotics kits priced at $49 each.

a. Round each factor to its greatest place value to estimate the total cost.

Rounded Expression:

Estimated Total: $

b. Is this estimate an overestimate or an underestimate? Explain how you know from the factors.

c. Will the $2,000 grant be enough to purchase all 38 kits? Explain using your answer from part b.

Product Predictors • Student Worksheet Page 2 of 2

1 pt each (symbol + estimates)

8. \(68 \times 31\) < \(42 \times 59\)

Est A: \(70 \times 30 = 2,100\)

Est B: \(40 \times 60 = 2,400\)

Exact: \(2,108 < 2,478\)

9. \(89 \times 48\) < \(61 \times 82\)

Est A: \(90 \times 50 = 4,500\)

Est B: \(60 \times 80 = 4,800\)

Exact: \(4,272 < 5,002\)

10. \(308 \times 21\) > \(492 \times 12\)

Est A: \(300 \times 20 = 6,000\)

Est B: \(500 \times 10 = 5,000\)

Exact: \(6,468 > 5,904\)

11. \(514 \times 39\) > \(788 \times 19\)

Est A: \(500 \times 40 = 20,000\)

Est B: \(800 \times 20 = 16,000\)

Exact: \(20,046 > 14,972\)

12. \(47 \times 82\) < \(52 \times 78\)

Est A: \(50 \times 80 = 4,000\)

Est B: \(50 \times 80 = 4,000\)

Ests equal (4,000); exact is \(3,854 < 4,056\). (= also accepted)

13. \(612 \times 49\) > \(295 \times 98\)

Est A: \(600 \times 50 = 30,000\)

Est B: \(300 \times 100 = 30,000\)

Ests equal (30,000); exact is \(29,988 > 28,910\). (= also accepted)

4 Level 4 Solutions: Grant Scenario (4 Points total)

Comprehensive Rubric

Part a (1 pt): Round factors to greatest place value to estimate total cost.

Rounded Expression: \(40 \times 50\)  |  Estimated Total: \$2,000

Part b (1 pt): Overestimate or underestimate? Explain.

Overestimate. Both factors were rounded UP (\(38 \rightarrow 40\) and \(\$49 \rightarrow \$50\)). Because both numbers were made larger, the resulting product of $2,000 is guaranteed to be greater than the exact cost.

Part c (2 pts): Will the $2,000 grant be enough to cover the purchase? Explain.

Yes! The grant will definitely cover the cost. Because $2,000 is an overestimate, the true cost must be less than $2,000. (The exact cost is \(38 \times \$49 = \$1,862\), which leaves the club with $138 remaining). Students earn full credit for concluding "Yes" based on the overestimate property without needing exact multiplication.

Product Predictors • Teacher Answer Key Page 2 of 2