Math English Language Arts Science & Engineering Social Studies Global Languages Health & Physical Education Special Education Counseling & Life Skills Arts & Creativity ESL

Number Trek

A targeted 5th-grade math lesson focusing on multi-digit and decimal addition and subtraction, place-value alignment, and multi-step real-world problem solving.

Ddanaorr

Number Trek Worksheet

NUMBER TREK

Grade 5 • Decimals & Multi-Digit Operations

Name:

Date:

Score: ___ / 25

Directions: Align decimal points carefully. Annex placeholder zeros when subtracting, and show all regrouping marks. Standards: 5.NBT.7 • 5.OA.1

PART A

Decimal Mental Sprint

Fluency with tenths and hundredths (10 pts)

0.6 + 0.8 =

1.5 − 0.7 =

0.25 + 0.75 =

2.0 − 0.45 =

3.7 + 4.3 =

5.1 − 2.8 =

0.85 + 0.15 =

7.0 − 3.25 =

12.4 + 6.8 =

10.0 − 4.65 =

PART B

Standard Algorithm with Decimals

Align by place value and record trades (6 pts)

4 8 . 6 5

3 7 . 9 0

8 2 . 4 0

− 3 6 . 7 5

2 4 5 . 8 0

1 7 8 . 6 5

4 0 0 . 5 0

− 1 8 6 . 7 2

6 1 9 . 0 8

2 8 4 . 9 5

7 0 0 . 0 0

− 3 4 5 . 8 5

PART C

Multi-Step Real-World Problems

Write an equation, show work, and include units (6 pts)

7

Track Relay Split Times

In a 400-meter relay, Runner 1 clocked 52.48 seconds and Runner 2 clocked 49.75 seconds. The coach set a target combined time of 105.00 seconds. By how many seconds did the two runners beat the target time?

Equation:

Workspace

Final Answer:

seconds

8

Science Lab Soil Sample

An empty beaker weighs 145.60 g. A researcher adds 78.45 g of moist soil. After baking to dry the soil, the beaker and dry sample have a total mass of 209.15 g. How many grams of water evaporated?

Equation:

Workspace

Final Answer:

grams

BONUS

Brain Buster: Decimal Mystery Number (3 pts)

Extra Challenge

"I am a secret decimal number with two decimal places. If you add 14.85 to me, and then subtract 9.4 from the sum, the result is 32.75. What was my starting number?"

Scratch Line:

Secret Number

Number Trek Answer Key

NUMBER TREK

Answer Key

Grade 5 • Decimals & Multi-Digit Operations

Total Points 25 Points

Mastery Target 21+ / 25 (84%)

Scoring Guide: Part A = 1 pt each (10 pts) • Part B = 1 pt each (6 pts) • Part C = 3 pts each (6 pts) • Part D = 3 pts bonus. Standards: 5.NBT.7 • 5.OA.1

PART A

Decimal Mental Sprint (10 Points)

1 point per correct answer

0.6 + 0.8 =

1.4

1.5 − 0.7 =

0.8

0.25 + 0.75 =

1.00

2.0 − 0.45 =

1.55

3.7 + 4.3 =

8.0

5.1 − 2.8 =

2.3

0.85 + 0.15 =

1.00

7.0 − 3.25 =

3.75

12.4 + 6.8 =

19.2

10.0 − 4.65 =

5.35

PART B

Standard Algorithm with Decimals (6 Points)

Verify decimal point alignment & trades (1 pt each)

1

4 8 . 6 5

3 7 . 9 0

86.55

7

11

13

8 2 . 4 0

− 3 6 . 7 5

45.65

1

2 4 5 . 8 0

1 7 8 . 6 5

424.45

3

9

14

4 0 0 . 5 0

− 1 8 6 . 7 2

213.78

1

6 1 9 . 0 8

2 8 4 . 9 5

904.03

6

9

7 0 0 . 0 0

− 3 4 5 . 8 5

354.15

PART C

Word Problem Solutions (6 Points)

3 pts each (1 pt eq, 1 pt work, 1 pt answer + unit)

7

Track Relay Split Times

2-Step Problem

Step 1: Add split times • Step 2: Subtract from target time.

Equation: 105.00 − (52.48 + 49.75) = 2.77

Model / Computation

¹ ¹

5 2 . 4 8

+ 4 9 . 7 5

1 0 2 . 2 3 s

1 0 5 . 0 0

− 1 0 2 . 2 3

2 . 7 7 s

Final Answer:

2.77

seconds

8

Science Lab Soil Sample

2-Step Problem

Step 1: Total wet mass • Step 2: Subtract dry mass to find water.

Equation: (145.60 + 78.45) − 209.15 = 14.90

Model / Computation

¹ ¹

1 4 5 . 6 0

+ 7 8 . 4 5

2 2 4 . 0 5 g

2 2 4 . 0 5

− 2 0 9 . 1 5

1 4 . 9 0 g

Final Answer:

14.90

grams

BONUS SOLUTION

Brain Buster: Inverse Operations with Decimals (3 Points)

Algebraic Thinking

Step 1 (Inverse of subtract 9.4): \( 32.75 + 9.40 = 42.15 \)

Step 2 (Inverse of add 14.85): \( 42.15 - 14.85 = 27.30 \)

Check: 27.30 + 14.85 = 42.15, and 42.15 − 9.40 = 32.75. Verified!

Equation n + 14.85 − 9.4 = 32.75

Secret Number

27.30

You might also like

Visual Math Bridges

A comprehensive visual reference toolkit providing tiered mathematical supports for Grade 5 division situations and Grade 6 ratio concepts, crafted with specialized instructional scaffolds for diverse learners.

DB

Danny Brooks

6

Food Truck Rally

Fifth-grade mathematicians take charge of their own food truck businesses, managing wholesale inventory expenses, order receipts, and cash flow. Through place-value modeling and real-world budgeting, students master estimating, adding, and subtracting decimals to hundredths.

CM

Carol M Reyes

5

Model Architects Answer Key

A comprehensive 3-page teacher answer key containing complete visual solutions for all 10 practice packet problems, the exit ticket, and the homework sheet, with highlighted values and grading criteria.

TG

Tyonna Gunter

Kindergarten Foundations

A foundational kindergarten sequence bridging early literacy and numeracy, featuring active phonemic awareness hunts and hands-on conservation of number explorations.

NS

Neelab Sayah

8

Operations Jumpstart

A foundational mathematics lesson for 7th grade intervention students bridging 1st and 2nd grade arithmetic. Features scaffolded addition, subtraction, and concrete multiplication models including open number lines, place-value decomposition, equal groups, and rectangular arrays.

MJ

Meg Jones

4

Array Power Answer Key

A two-page educator answer key, diagnostic misconception reference, and pedagogical coaching guide for Array Power Math Worksheet. Features complete worked solutions, skip-jump analysis, array dimension breakdowns, and secondary intervention scripts.

MJ

Meg Jones

Area Adventures

A foundational two-lesson 3rd-grade math sequence introducing area through unit square tiling and multiplication of side lengths, structured with explicit whiteboard scripts and guided notes for substitute teachers.

SM

Samantha McBath

6

Divide and Conquer

A multi-phase diagnostic, progress monitoring, and mastery assessment sequence for fraction division. Targets conceptual visual models, procedural inversion strategies, and mixed number operations.

N

ntobin

6

Chunking Champions

A comprehensive multi-day division unit introducing students to the partial quotients method with one-digit divisors. The sequence moves from conceptual area models and friendly multiplication chunks to the standard Big Seven algorithm, remainder problem solving, and error analysis.

DM

Deborah Marshall

9