Number Concepts to 100
Warm-up
Show 47 with base-ten blocks. How many tens? How many ones? What is the number? Then reverse: I say 63, you show it with blocks. What does the 6 mean? What does the 3 mean? The 6 means 60, not 6. The position changes its value.
Explore
Place value decomposition challenge: each student receives a two-digit number card and must show it three ways: base-ten blocks, place value mat (tens + ones), and a number sentence (67 = 60 + 7). Then decompose in a non-standard way: 67 = 50 + 17 = 40 + 27. Both are still 67. Why?
Formalize
Even and odd investigation: students build numbers 1-20 with linking cubes, pairing the cubes. Which numbers pair perfectly? (Even.) Which leave one over? (Odd.) Record and look for the pattern in the ones digit. Does this rule work for numbers bigger than 20? Test 34, 47, 58.
Number Concepts to 100
Benchmark estimation: mark 0, 25, 50, 75, 100 on a number line. Place numbers (37, 62, 84, 19) near their closest benchmark. This is not about precise placement but about benchmark reasoning: 37 is closer to 25 than to 50.
Practice
Students decompose 8 two-digit numbers into tens and ones, classify 10 numbers as even or odd, and place 5 numbers on a benchmark number line. Exit ticket: show me 73 in two different ways using tens and ones.
Exit ticket
Students decompose 8 two-digit numbers into tens and ones, classify 10 numbers as even or odd, and place 5 numbers on a benchmark number line. Exit ticket: show me 73 in two different ways using tens and ones.
Step 1: Build 47 with base-ten materials: 4 ten-rods and 7 unit cubes. Count the rods by tens (10, 20, 30, 40), then the units on (41, 42 … 47).
Step 2: Read it three ways and record all three side by side: forty-seven; 4 tens and 7 ones; 40 + 7.
Step 3: The check question: "Which digit is worth more — the 4 or the 7?" Students must justify with the materials: the 4 stands for four whole RODS (40 cubes), the 7 for seven single cubes. The smaller-looking digit is worth more.
Why it matters: a student who says "the 4 means four" without the tens attached is reading digits, not place value. Every later algorithm leans on this.
Step 1: Build 63 (6 rods, 3 units). Ask for TEN MORE: add one rod — 73. No counting by ones happened; only the tens digit moved.
Step 2: Ten less: remove a rod — 53. One more: add a unit — 64. One less: 62. Each answer is one physical move.
Step 3: Now on the hundred chart: ten more = one step DOWN, ten less = one step UP, one more/less = one step right/left. The chart's geometry encodes place value.
Step 4: Fluency check without materials: "ten more than 89?" (99) "ten more than 95?" — 105 crosses the hundred and is EXPECTED to cause hesitation. Let students build 95 + 10 with materials to see the ten rods becoming ten-and-a-bit-of-a-hundred.
Exit skill: answering ±10 questions instantly, because only one digit changes.
What happened: the student transcribed the words literally — "sixty" → 60, "three" → 3 — and glued them together: 603. Same root cause as writing fifteen as 105 in Grade 1, now at the tens level.
Step 1: Confirm the understanding underneath is right: ask them to BUILD sixty-three. Most will correctly grab 6 rods and 3 units. The math is fine; the notation is the problem.
Step 2: Show the compression with arrow cards: the 60 card and the 3 card slide together so the 3 sits ON TOP of the 60's zero → 63. The zero didn't vanish — the 3 is standing in its place (that's why it's called PLACE value).
Step 3: Contrast: build 603 with materials (6 flats, 0 rods, 3 units) and compare it to their 6 rods + 3 units. The sizes are wildly different — 603 is a much bigger number than what they built.
Check: dictate "eighty-one" and "forty". Watch for 801 and 400.