Ready-to-teach lesson
MATH UNIT | GRADE 1
Two Groups Side by Side How many more? How many fewer?
4 LESSONS 4 x 30 MINUTES 3 SOURCE
BOOKS
120 MINUTES
The question this unit follows
How much bigger, and how do you know?
About this unit A child may know which group has more and still not know how many more. This unit makes the difference visible. Students align two rows, match objects one to one, and read the unmatched part as the gap.
The same arrangement then answers three connected questions: How many more? How many fewer? How many must be added to make the groups equal? Students finish by saying one difference in both directions without rebuilding or recounting.
UNIT PROMISE
Every answer is tied to an arrangement students can point to. No comparison floats free of the matched rows.
UNIT DESIGN
A short, deliberate progression
Mathematical arc
- 1.Match two aligned rows and read the unmatched objects as the difference.
- 2.Read that same gap as the amount needed to make the groups equal.
- 3.Use a zero gap to prove that two groups have the same number.
- 4.State one difference both ways: more than and fewer than.
Source books Henry Keeps Score - Lessons 1 and 2 Open book Sir Cumference and the Off-the-Charts Dessert - Lesson 3 Open book The Yum-Yum House - Lesson 4 Open book
ADAPTATION NOTE
This guide keeps each source lesson's book connection and mathematical structure, but brings every working number within
- 20.Use the sequence and student pages here when teaching the unit.
GRADE 1 CURRICULUM PLACEMENT
Where This Fits in Your Year
Pennsylvania edition
This sequence fits naturally within Pennsylvania Grade 1 algebraic-concepts work as students build the concrete meaning of comparison and missing-part situations.
Lessons 1 and 2 establish the central model. Students align two rows at the same starting line, match objects one to one and count only the objects without partners. They then read that visible gap in three connected ways: how many more, how many fewer and how many must be added to make the rows equal. The checkpoint requires the same number to answer all three questions.
Lesson 3 gives the zero case an important place in the progression. Students use a complete match to prove that two groups have the same number, rather than relying on appearance or recounting.
page 1
Lesson 4 reverses the language while holding the model still: one group is more than the other, and the other is fewer by exactly the same amount.
The unit is strongest as concrete preparation and reinforcement for comparison problem solving. It does not present story problems or require students to write equations. Add those representations later if the local expectation requires them; the four lessons here secure the quantitative relationship that those forms must express.
Strongest curriculum relationship
REINFORCES / PREPARES FOR
Represent and solve problems involving addition and subtraction within 20 (CC.2.2.1.A.1). This unit reinforces only the concrete comparison structure. To complete the coded expectation, add contextual comparison problems, vary the unknown position, and introduce any other problem types or representations required by the jurisdiction.
OFFICIAL CURRICULUM SOURCE
https:/ / www.pa.gov/ agencies/ education/ programs -and -services/ instruction/ elementary -and -secondary -education/ curriculum/ mathematics TumbleTA | Grade 1 Mathematics | Pennsylvania
TEACHER MAP
Unit at a glance
1 | READ THE LEFTOVER
Source: Henry Keeps Score - How Many More, How Many Fewer Collect: Matched rows plus both comparison sentences.
2 | CLOSE THE GAP
Source: Henry Keeps Score - One More Makes It Match Collect: Four trials recording how many were added.
3 | PROVE A TIE
Source: Sir Cumference - The Same Number Collect: A match proof and one equality sentence.
4 | SAY IT BOTH WAYS
Source: The Yum-Yum House - Eight Fewer, Eight More Collect: Two sentences about one unmoved model.
Vocabulary - more / fewer - said as a pair about the same unmoved arrangement.
- match - place one object beside one object in the other group.
- left over - objects with no partner after matching.
page 2
- equal - the groups have the same number; nothing is left over.
EVIDENCE PLAN
Assessment that follows the model
Daily evidence Listen for complete comparison sentences while the child points to the unmatched objects. Keep one model or quick photograph from Lessons 1 and 2; collect the printed checkpoints after Lessons 2 and 4.
CHECKPOINT 1 - FIND AND CLOSE THE GAP Rows of 7 and 4. The child identifies 3 more, 3 fewer and 3 to add. The same three must answer all three questions.
CHECKPOINT 2 - SAY IT THE OTHER WAY Rows of 12 and 5. Without moving anything, the child states: 12 is 7 more than 5; 5 is 7 fewer than 12.
CULMINATING TASK - ONE MODEL, THREE STATEMENTS
Rows of 13 and 8. The child matches, identifies the 5 unmatched objects, states the difference both ways and records how many must be added to make the rows equal.
DECISION RULE
Secure means the child uses one aligned model for every statement. A correct number produced without matching is not yet the evidence this unit is designed to collect.
LESSON 1 | 30 MINUTES
Read the Leftover
Henry Keeps Score
Lesson 1 - How Many More, How Many Fewer
I CAN
I can match two groups and find how many more or fewer.
BIG IDEA
After one-to-one matching, the objects without partners are the difference.
SUCCESS EVIDENCE
The child points to the same leftover objects while stating both comparison sentences.
CONNECT |
5 MIN
Build rows of 5 and 3. Ask which has more, then ask how many more. Leave the second question open until students match.
SOURCE CORE |
20 MIN
Pairs build each score as a row, align both rows at the same start line, match one to one and count only the unmatched objects. For every card, students say both complete sentences.
CLOSE |
5 MIN
Use 4 flower cards and 3 flower cards. Students match, point to the one leftover flower and tell both comparisons.
COLLECT
One aligned score mat with the leftover visible and both sentences recorded or heard.
page 3
MATERIALS
Two-colour counters; aligned score mat; four score-pair cards within 5; flower cards; word cards:
more, fewer, match.
WATCH FOR
Rows that begin at different places. Draw a start line and require both first counters to touch it.
LESSON 2 | 30 MINUTES
Close the Gap
Henry Keeps Score
Lesson 2 - One More Makes It Match
I CAN
I can add just enough to make two groups equal.
BIG IDEA
The difference and the amount needed to close the gap are the same quantity.
SUCCESS EVIDENCE
The child adds one counter for each empty partner position, stops exactly at equality and records the number added.
CONNECT |
5 MIN
Return to yesterday's leftover. Ask: If the shorter row grew, how many counters would fill those unmatched positions?
SOURCE CORE |
20 MIN
Pairs build 4 and 3, match the rows, and add into the empty partner positions one at a time. Repeat with three additional cards, including an equal pair that requires 0.
CLOSE |
5 MIN
Give rows of 7 and 4. Students find the gap, state both comparisons and add exactly enough to make the rows equal. Complete Checkpoint 1.
COLLECT
Four trials showing the starting pair and number added, including the zero case.
MATERIALS
Two aligned row mats; counters; four number-pair cards within 10, including one equal pair;
Checkpoint 1.
WATCH FOR
Adding until the rows merely look level. Have the child touch each pair and each empty partner position.
LESSON 3 | 30 MINUTES
Prove the Tie
Sir Cumference and the Off-the-Charts Dessert
Lesson 3 - The Same Number
I CAN
I can prove two groups have the same number by matching.
page 4
BIG IDEA
A complete one-to-one match leaves a gap of zero; no recount is needed.
SUCCESS EVIDENCE
The child matches every object, identifies zero leftover and states that both groups have the same number.
CONNECT |
5 MIN
So far a gap has been visible. Ask what the model will look like when the difference is zero.
SOURCE CORE |
20 MIN
Pairs work with two prebuilt groups of 10. They align or pair the objects one to one without recounting, verify that nothing is left over, and state an equality sentence. Add one object to one side and test again.
CLOSE |
5 MIN
Show matched rows of 8 and 8, then add one counter to the second row. Students state what changed and identify the new gap.
COLLECT
The matched groups, a recorded gap of 0 and one sentence explaining why the groups are equal.
MATERIALS
Two groups of 10 counters in different colours per pair; two cups; aligned mats; word cards: equal, same number, zero.
WATCH FOR
Recounting instead of using the match. Cover any written totals and ask what the complete pairing proves.
LESSON 4 | 30 MINUTES
Say It Both Ways
The Yum-Yum House
Lesson 8 - Eight Fewer, Eight More, Same Eight
I CAN
I can state the same difference in two directions.
BIG IDEA
The comparison words reverse, but the difference does not change because the model does not move.
SUCCESS EVIDENCE
Both sentences name both groups, use the same difference and are spoken over one untouched arrangement.
CONNECT |
5 MIN
Display rows of 11 and 3. Ask for one comparison sentence, then challenge students to begin the next sentence with the other group.
SOURCE CORE |
20 MIN
Pairs build 15 and 7, align and match the rows, then count the 8 unmatched objects. They say: 15 is 8 more than 7; 7 is 8 fewer than 15. Repeat with two additional pairs within 20.
page 5
CLOSE |
5 MIN
Complete Checkpoint 2 with rows of 12 and 5. Students explain why nothing moved between the two sentences.
COLLECT
Two complete sentences for each number pair, with the same difference used in both directions.
MATERIALS
Counters; aligned mats; three number-pair cards within 20; sentence frames; Checkpoint 2.
WATCH FOR
Searching for a new fact or moving counters before the reverse sentence. Cover the model and ask the child to reverse only the words and group order.
CULMINATING ASSESSMENT
Teacher key and compact rubric
Answer key - Checkpoint 1: 7 is 3 more than 4; 4 is 3 fewer than 7; add 3 to 4 to make 7.
- Checkpoint 2: 12 is 7 more than 5; 5 is 7 fewer than 12.
- Culminating task: 13 is 5 more than 8; 8 is 5 fewer than 13; add 5 to 8 to make 13.
Rubric
MODEL
Both rows share a start line and each object is matched one to one.
DIFFERENCE
The child counts only unmatched objects and uses that number as the gap.
LANGUAGE
Both complete sentences name both groups and reverse more/fewer correctly.
EQUALITY
The child identifies the same gap as the amount to add and stops at equality.
DEVELOPING / NOT YET
Developing: completes the reasoning with the model and a prompt. Not yet: gives an unsupported number, misaligns the rows, or changes the model between directions.
STUDENT RECORD | GRADE 1
Checkpoint 1: Find and Close the Gap
Name ______________________________________ Date __________________ Match the rows from the start line. Point to the objects with no partner before answering.
ROW A
ROW B
7 is ______ more than 4.
4 is ______ fewer than 7.
Add ______ to 4 to make 7.
EXPLAIN
Why does the same number answer all three questions?
________________________________________________________________________________
page 6
STUDENT RECORD | GRADE 1
Checkpoint 2: Say It the Other Way
Name ______________________________________ Date __________________ The rows are already aligned. Do not move anything. Use the same gap in both sentences.
ROW A
ROW B
12 is ______ more than 5.
5 is ______ fewer than 12.
EXPLAIN
Why did the number stay the same when more changed to fewer?
________________________________________________________________________________
STUDENT RECORD | GRADE 1
Performance Task: One Model, Three
Statements
Name ______________________________________ Date __________________ Match the rows.
Circle the objects with no partner. Complete every statement from this one model.
ROW A
ROW B
13 is ______ more than 8.
8 is ______ fewer than 13.
Add ______ to 8 to make 13.
EXPLAIN
The difference is ______ because ________________________________________________ ________________________________________________________________________________
page 7