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Override for the tutor's lesson content generation calls. Auto uses the system default (Claude Sonnet 5 for lesson text, Opus 5 for diagrams).

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System default

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Tutoring abilities

Imagine you have 38 shiny stickers and a friend asks how many you have. It is much faster to say, "I have about 40!"

Finding a friendly number that is close to your exact number is called **rounding**.

A **number line** places numbers in order like steps on a path. To round to the nearest ten, we look at the friendly 'tens' benchmarks on either side.

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <title>Rounding on a Number Line</title>
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
      font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      user-select: none;
    }

    body {
      background: transparent;
      color: #1e2945;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      min-height: 100%;
      padding: 12px 16px;
      gap: 12px;
    }

    .controls-row {
      display: flex;
      flex-wrap: wrap;
      justify-content: center;
      gap: 8px;
      width: 100%;
      max-width: 500px;
    }

    .btn-group {
      display: flex;
      background: #eef2f6;
      border-radius: 20px;
      padding: 3px;
    }

    .btn {
      border: none;
      background: transparent;
      padding: 6px 14px;
      font-size: 14px;
      font-weight: 600;
      color: #6b7280;
      border-radius: 16px;
      cursor: pointer;
      transition: all 0.2s ease;
    }

    .btn.active {
      background: #ffffff;
      color: #0284c7;
      box-shadow: 0 2px 6px rgba(0,0,0,0.08);
    }

    .diagram-area {
      width: 100%;
      max-width: 520px;
      position: relative;
    }

    svg {
      width: 100%;
      height: auto;
      display: block;
      overflow: visible;
    }

    .slider-container {
      width: 100%;
      max-width: 440px;
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 6px;
    }

    .range-slider {
      width: 100%;
      accent-color: #0284c7;
      cursor: pointer;
      height: 6px;
    }

    .result-badge {
      display: inline-flex;
      align-items: center;
      gap: 8px;
      padding: 8px 18px;
      border-radius: 24px;
      background: #f0f9ff;
      border: 1px solid #bae6fd;
      color: #0369a1;
      font-size: 16px;
      font-weight: 700;
    }

    .result-badge .target {
      color: #0284c7;
      font-size: 18px;
    }
  </style>
</head>
<body>

  
  <div class="controls-row">
    <div class="btn-group" role="tablist">
      <button class="btn active" id="btn10" onclick="setMode(10)">Nearest 10</button>
      <button class="btn" id="btn100" onclick="setMode(100)">Nearest 100</button>
    </div>
  </div>

  
  <div class="diagram-area">
    <svg id="svgLine" viewBox="0 0 500 200">
      
      <defs>
        <filter id="shadow" x="-20%" y="-20%" width="140%" height="140%">
          <feDropShadow dx="0" dy="2" stdDeviation="3" flood-opacity="0.15" />
        </filter>
      </defs>

      
      <path id="leftArc" fill="none" stroke="#94a3b8" stroke-width="2.5" stroke-dasharray="5,5" />
      <path id="rightArc" fill="none" stroke="#94a3b8" stroke-width="2.5" stroke-dasharray="5,5" />

      
      <g id="leftLabelGroup" filter="url(#shadow)">
        <rect id="leftLabelBg" rx="10" height="24" fill="#ffffff" stroke="#cbd5e1" stroke-width="1.5"/>
        <text id="leftLabelText" y="0" text-anchor="middle" dominant-baseline="central" font-size="13" font-weight="700" fill="#64748b"></text>
      </g>

      <g id="rightLabelGroup" filter="url(#shadow)">
        <rect id="rightLabelBg" rx="10" height="24" fill="#ffffff" stroke="#cbd5e1" stroke-width="1.5"/>
        <text id="rightLabelText" y="0" text-anchor="middle" dominant-baseline="central" font-size="13" font-weight="700" fill="#64748b"></text>
      </g>

      
      <line x1="40" y1="140" x2="460" y2="140" stroke="#cbd5e1" stroke-width="4" stroke-linecap="round" />

      
      <g id="ticksGroup"></g>

      
      <g id="leftBenchmark" transform="translate(50, 140)">
        <circle id="leftBenchDot" r="14" fill="#ffffff" stroke="#cbd5e1" stroke-width="3" filter="url(#shadow)"/>
        <text id="leftBenchText" y="32" text-anchor="middle" font-size="16" font-weight="800" fill="#64748b">30</text>
      </g>

      
      <g id="rightBenchmark" transform="translate(450, 140)">
        <circle id="rightBenchDot" r="14" fill="#ffffff" stroke="#cbd5e1" stroke-width="3" filter="url(#shadow)"/>
        <text id="rightBenchText" y="32" text-anchor="middle" font-size="16" font-weight="800" fill="#64748b">40</text>
      </g>

      
      <g id="midGroup" transform="translate(250, 140)">
        <line y1="-8" y2="8" stroke="#94a3b8" stroke-width="2" />
        <text id="midText" y="26" text-anchor="middle" font-size="12" font-weight="600" fill="#94a3b8">35</text>
      </g>

      
      <g id="currentPin" transform="translate(370, 140)">
        <circle r="9" fill="#0284c7" filter="url(#shadow)"/>
        <circle r="4" fill="#ffffff"/>
        
        <g transform="translate(0, -22)" filter="url(#shadow)">
          <rect x="-18" y="-12" width="36" height="24" rx="12" fill="#0284c7"/>
          <text id="currentValText" y="0" text-anchor="middle" dominant-baseline="central" font-size="13" font-weight="800" fill="#ffffff">38</text>
        </g>
      </g>
    </svg>
  </div>

  
  <div class="slider-container">
    <input type="range" class="range-slider" id="numSlider" min="30" max="40" value="38" step="1" oninput="onSliderChange(this.value)">
  </div>

  
  <div class="result-badge" id="resultBadge">
    <span id="resFrom">38</span>
    <span>→</span>
    <span class="target" id="resTo">40</span>
  </div>

  <script>
    let mode = 10;
    let minVal = 30;
    let maxVal = 40;
    let currentVal = 38;

    const leftX = 50;
    const rightX = 450;
    const axisY = 140;

    function setMode(newMode) {
      mode = newMode;
      document.getElementById('btn10').classList.toggle('active', mode === 10);
      document.getElementById('btn100').classList.toggle('active', mode === 100);

      const slider = document.getElementById('numSlider');
      if (mode === 10) {
        minVal = 30;
        maxVal = 40;
        slider.min = 30;
        slider.max = 40;
        slider.step = 1;
        currentVal = 38;
      } else {
        minVal = 300;
        maxVal = 400;
        slider.min = 300;
        slider.max = 400;
        slider.step = 10;
        currentVal = 380;
      }
      slider.value = currentVal;
      renderTicks();
      update();
    }

    function onSliderChange(val) {
      currentVal = parseInt(val, 10);
      update();
    }

    function renderTicks() {
      const g = document.getElementById('ticksGroup');
      g.innerHTML = '';
      const steps = 10;
      for (let i = 1; i < steps; i++) {
        if (i === 5) continue; // midpoint handled separately
        const x = leftX + (i / steps) * (rightX - leftX);
        const line = document.createElementNS('http://www.w3.org/2000/svg', 'line');
        line.setAttribute('x1', x);
        line.setAttribute('x2', x);
        line.setAttribute('y1', axisY - 4);
        line.setAttribute('y2', axisY + 4);
        line.setAttribute('stroke', '#e2e8f0');
        line.setAttribute('stroke-width', '2');
        g.appendChild(line);
      }
    }

    function update() {
      const midVal = (minVal + maxVal) / 2;
      const ratio = (currentVal - minVal) / (maxVal - minVal);
      const currX = leftX + ratio * (rightX - leftX);

      // Benchmark texts
      document.getElementById('leftBenchText').textContent = minVal;
      document.getElementById('rightBenchText').textContent = maxVal;
      document.getElementById('midText').textContent = midVal;
      document.getElementById('currentValText').textContent = currentVal;

      // Pin position
      document.getElementById('currentPin').setAttribute('transform', `translate(${currX}, ${axisY})`);

      // Distances
      const leftDist = currentVal - minVal;
      const rightDist = maxVal - currentVal;
      const unitLabel = mode === 10 ? 'steps' : '';

      // Determine rounding target
      const roundsUp = currentVal >= midVal;
      const roundedTo = roundsUp ? maxVal : minVal;

      // Update Result text
      document.getElementById('resFrom').textContent = currentVal;
      document.getElementById('resTo').textContent = roundedTo;

      // Update Benchmark Highlights
      const leftDot = document.getElementById('leftBenchDot');
      const rightDot = document.getElementById('rightBenchDot');
      const leftText = document.getElementById('leftBenchText');
      const rightText = document.getElementById('rightBenchText');

      if (!roundsUp) {
        leftDot.setAttribute('stroke', '#0284c7');
        leftDot.setAttribute('stroke-width', '4');
        leftDot.setAttribute('fill', '#e0f2fe');
        leftText.setAttribute('fill', '#0284c7');

        rightDot.setAttribute('stroke', '#cbd5e1');
        rightDot.setAttribute('stroke-width', '3');
        rightDot.setAttribute('fill', '#ffffff');
        rightText.setAttribute('fill', '#64748b');
      } else {
        rightDot.setAttribute('stroke', '#0284c7');
        rightDot.setAttribute('stroke-width', '4');
        rightDot.setAttribute('fill', '#e0f2fe');
        rightText.setAttribute('fill', '#0284c7');

        leftDot.setAttribute('stroke', '#cbd5e1');
        leftDot.setAttribute('stroke-width', '3');
        leftDot.setAttribute('fill', '#ffffff');
        leftText.setAttribute('fill', '#64748b');
      }

      // Draw Arcs
      const leftArc = document.getElementById('leftArc');
      const rightArc = document.getElementById('rightArc');

      // Left Arc
      if (leftDist > 0) {
        const hLeft = Math.min(65, Math.max(25, (currX - leftX) * 0.35));
        const midLX = (leftX + currX) / 2;
        const peakLY = axisY - hLeft;
        leftArc.setAttribute('d', `M ${leftX} ${axisY - 14} Q ${midLX} ${peakLY - 20} ${currX} ${axisY - 14}`);
        leftArc.style.display = 'block';

        const isWinner = !roundsUp;
        leftArc.setAttribute('stroke', isWinner ? '#0284c7' : '#cbd5e1');
        leftArc.setAttribute('stroke-width', isWinner ? '3' : '2');
        leftArc.setAttribute('stroke-dasharray', isWinner ? 'none' : '5,5');

        // Position Left Label
        const lg = document.getElementById('leftLabelGroup');
        lg.style.display = 'block';
        const txt = document.getElementById('leftLabelText');
        const bg = document.getElementById('leftLabelBg');
        txt.textContent = `${leftDist} ${unitLabel}`.trim();
        txt.setAttribute('fill', isWinner ? '#0284c7' : '#64748b');

        const width = txt.textContent.length * 8 + 16;
        bg.setAttribute('width', width);
        bg.setAttribute('x', -width / 2);
        bg.setAttribute('y', -12);
        bg.setAttribute('stroke', isWinner ? '#bae6fd' : '#cbd5e1');
        lg.setAttribute('transform', `translate(${midLX}, ${peakLY - 10})`);
      } else {
        leftArc.style.display = 'none';
        document.getElementById('leftLabelGroup').style.display = 'none';
      }

      // Right Arc
      if (rightDist > 0) {
        const hRight = Math.min(65, Math.max(25, (rightX - currX) * 0.35));
        const midRX = (currX + rightX) / 2;
        const peakRY = axisY - hRight;
        rightArc.setAttribute('d', `M ${currX} ${axisY - 14} Q ${midRX} ${peakRY - 20} ${rightX} ${axisY - 14}`);
        rightArc.style.display = 'block';

        const isWinner = roundsUp;
        rightArc.setAttribute('stroke', isWinner ? '#0284c7' : '#cbd5e1');
        rightArc.setAttribute('stroke-width', isWinner ? '3' : '2');
        rightArc.setAttribute('stroke-dasharray', isWinner ? 'none' : '5,5');

        // Position Right Label
        const rg = document.getElementById('rightLabelGroup');
        rg.style.display = 'block';
        const txt = document.getElementById('rightLabelText');
        const bg = document.getElementById('rightLabelBg');
        txt.textContent = `${rightDist} ${unitLabel}`.trim();
        txt.setAttribute('fill', isWinner ? '#0284c7' : '#64748b');

        const width = txt.textContent.length * 8 + 16;
        bg.setAttribute('width', width);
        bg.setAttribute('x', -width / 2);
        bg.setAttribute('y', -12);
        bg.setAttribute('stroke', isWinner ? '#bae6fd' : '#cbd5e1');
        rg.setAttribute('transform', `translate(${midRX}, ${peakRY - 10})`);
      } else {
        rightArc.style.display = 'none';
        document.getElementById('rightLabelGroup').style.display = 'none';
      }
    }

    // Initialize
    renderTicks();
    update();
  </script>
</body>
</html>

Since 38 is only 2 steps away from 40, but 8 steps away from 30, we **round up** to 40.

What happens if a number lands right in the middle, like 35? In math, when a number is exactly halfway, the rule is to **round up** to the larger ten.

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <title>Rounding Explorer</title>
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
      font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif;
      user-select: none;
      -webkit-user-select: none;
    }

    body {
      background: #f8f9fa;
      color: #1e2945;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      min-height: 100%;
      padding: 16px;
    }

    .main-wrap {
      width: 100%;
      max-width: 520px;
      display: flex;
      flex-direction: column;
      gap: 16px;
    }

    /* Mode selector */
    .tabs {
      display: flex;
      background: #e2e8f0;
      padding: 4px;
      border-radius: 10px;
      gap: 4px;
    }

    .tab-btn {
      flex: 1;
      border: none;
      background: transparent;
      padding: 8px 12px;
      border-radius: 7px;
      font-size: 14px;
      font-weight: 600;
      color: #64748b;
      cursor: pointer;
      transition: all 0.2s ease;
    }

    .tab-btn.active {
      background: #ffffff;
      color: #0f172a;
      box-shadow: 0 1px 3px rgba(0,0,0,0.1);
    }

    /* Display Board */
    .display-card {
      background: #ffffff;
      border: 1px solid #e2e8f0;
      border-radius: 14px;
      padding: 20px 16px;
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 16px;
      box-shadow: 0 4px 6px -1px rgba(0,0,0,0.05);
    }

    .result-badge {
      display: inline-flex;
      align-items: center;
      gap: 8px;
      font-size: 22px;
      font-weight: 700;
      color: #1e2945;
    }

    .arrow-icon {
      color: #22b7ff;
      font-weight: 800;
    }

    .target-val {
      color: #0284c7;
      background: #e0f2fe;
      padding: 2px 10px;
      border-radius: 8px;
      border: 1px solid #bae6fd;
    }

    .rule-tag {
      font-size: 12px;
      font-weight: 600;
      text-transform: uppercase;
      letter-spacing: 0.5px;
      padding: 3px 8px;
      border-radius: 6px;
      background: #f1f5f9;
      color: #475569;
    }

    .rule-tag.halfway {
      background: #fef3c7;
      color: #b45309;
      border: 1px solid #fde68a;
    }

    /* Visual Track */
    .track-container {
      position: relative;
      width: 100%;
      height: 80px;
      margin-top: 10px;
      display: flex;
      align-items: center;
    }

    .track-line {
      position: absolute;
      left: 20px;
      right: 20px;
      height: 8px;
      background: #e2e8f0;
      border-radius: 4px;
    }

    .track-fill {
      position: absolute;
      left: 20px;
      height: 8px;
      background: #38bdf8;
      border-radius: 4px;
      width: 50%;
      transition: width 0.15s ease-out;
    }

    .benchmark {
      position: absolute;
      top: 50%;
      transform: translate(-50%, -50%);
      display: flex;
      flex-direction: column;
      align-items: center;
      pointer-events: none;
    }

    .benchmark-tick {
      width: 2px;
      height: 18px;
      background: #94a3b8;
      border-radius: 1px;
    }

    .benchmark.mid .benchmark-tick {
      height: 24px;
      width: 3px;
      background: #f59e0b;
    }

    .benchmark-label {
      margin-top: 8px;
      font-size: 13px;
      font-weight: 600;
      color: #64748b;
    }

    .benchmark.mid .benchmark-label {
      color: #d97706;
      font-weight: 700;
    }

    /* Active Marker Ball */
    .marker {
      position: absolute;
      top: 50%;
      transform: translate(-50%, -50%);
      width: 38px;
      height: 38px;
      background: #0284c7;
      color: #ffffff;
      border-radius: 50%;
      display: flex;
      align-items: center;
      justify-content: center;
      font-size: 14px;
      font-weight: 700;
      box-shadow: 0 3px 8px rgba(2, 132, 199, 0.4);
      z-index: 5;
      transition: left 0.15s ease-out, background-color 0.2s;
    }

    .marker.mid {
      background: #d97706;
      box-shadow: 0 3px 8px rgba(217, 119, 6, 0.4);
    }

    /* Slider Input */
    .slider-wrap {
      width: 100%;
      position: relative;
    }

    input[type=range] {
      -webkit-appearance: none;
      width: 100%;
      background: transparent;
      outline: none;
      cursor: pointer;
      margin: 0;
    }

    input[type=range]::-webkit-slider-runnable-track {
      width: 100%;
      height: 38px;
      background: transparent;
    }

    input[type=range]::-webkit-slider-thumb {
      -webkit-appearance: none;
      height: 38px;
      width: 38px;
      border-radius: 50%;
      background: transparent;
      cursor: pointer;
    }

    /* Presets */
    .presets {
      display: flex;
      justify-content: center;
      gap: 8px;
      width: 100%;
    }

    .preset-btn {
      border: 1px solid #cbd5e1;
      background: #ffffff;
      padding: 6px 14px;
      border-radius: 6px;
      font-size: 13px;
      font-weight: 600;
      color: #334155;
      cursor: pointer;
      transition: all 0.15s ease;
    }

    .preset-btn:active {
      background: #f1f5f9;
      transform: translateY(1px);
    }
  </style>
</head>
<body>

  <div class="main-wrap">
    
    <div class="tabs">
      <button class="tab-btn active" id="tabTen" onclick="setMode('ten')">Nearest 10</button>
      <button class="tab-btn" id="tabHundred" onclick="setMode('hundred')">Nearest 100</button>
    </div>

    
    <div class="display-card">
      <div class="result-badge">
        <span id="currentVal">35</span>
        <span class="arrow-icon">→</span>
        <span class="target-val" id="roundedVal">40</span>
      </div>

      <div class="rule-tag halfway" id="ruleTag">Halfway: Round Up</div>

      
      <div class="track-container" id="trackBox">
        <div class="track-line"></div>
        <div class="track-fill" id="trackFill"></div>

        
        <div class="benchmark" style="left: 20px;">
          <div class="benchmark-tick"></div>
          <div class="benchmark-label" id="minLabel">30</div>
        </div>

        
        <div class="benchmark mid" style="left: 50%;">
          <div class="benchmark-tick"></div>
          <div class="benchmark-label" id="midLabel">35</div>
        </div>

        
        <div class="benchmark" style="right: 20px; left: auto; transform: translate(50%, -50%);">
          <div class="benchmark-tick"></div>
          <div class="benchmark-label" id="maxLabel">40</div>
        </div>

        
        <div class="marker mid" id="marker">35</div>
      </div>

      
      <div class="slider-wrap">
        <input type="range" id="slider" min="30" max="40" value="35" step="1" oninput="updateValue(this.value)">
      </div>

      
      <div class="presets" id="presetRow">
        
      </div>
    </div>
  </div>

  <script>
    const modes = {
      ten: {
        min: 30,
        max: 40,
        mid: 35,
        step: 1,
        presets: [32, 35, 38]
      },
      hundred: {
        min: 200,
        max: 300,
        mid: 250,
        step: 5,
        presets: [230, 250, 280]
      }
    };

    let currentMode = 'ten';

    function setMode(mode) {
      currentMode = mode;
      document.getElementById('tabTen').classList.toggle('active', mode === 'ten');
      document.getElementById('tabHundred').classList.toggle('active', mode === 'hundred');

      const config = modes[mode];
      const slider = document.getElementById('slider');
      slider.min = config.min;
      slider.max = config.max;
      slider.step = config.step;
      slider.value = config.mid;

      document.getElementById('minLabel').textContent = config.min;
      document.getElementById('midLabel').textContent = config.mid;
      document.getElementById('maxLabel').textContent = config.max;

      // Render preset buttons
      const presetRow = document.getElementById('presetRow');
      presetRow.innerHTML = '';
      config.presets.forEach(val => {
        const btn = document.createElement('button');
        btn.className = 'preset-btn';
        btn.textContent = val;
        btn.onclick = () => {
          slider.value = val;
          updateValue(val);
        };
        presetRow.appendChild(btn);
      });

      updateValue(config.mid);
    }

    function updateValue(val) {
      val = parseInt(val, 10);
      const config = modes[currentMode];
      const percent = (val - config.min) / (config.max - config.min);

      // Math rounding logic
      let rounded;
      let tagText;
      let isHalfway = (val === config.mid);

      if (val < config.mid) {
        rounded = config.min;
        tagText = `Closer to ${config.min}`;
      } else if (val === config.mid) {
        rounded = config.max;
        tagText = 'Halfway: Round Up';
      } else {
        rounded = config.max;
        tagText = `Closer to ${config.max}`;
      }

      // Update text
      document.getElementById('currentVal').textContent = val;
      document.getElementById('roundedVal').textContent = rounded;
      
      const ruleTag = document.getElementById('ruleTag');
      ruleTag.textContent = tagText;
      ruleTag.className = isHalfway ? 'rule-tag halfway' : 'rule-tag';

      // Update marker and fill
      const marker = document.getElementById('marker');
      marker.textContent = val;
      marker.className = isHalfway ? 'marker mid' : 'marker';

      // Track inset padding is 20px each side
      const trackBox = document.getElementById('trackBox');
      const trackWidth = trackBox.clientWidth - 40;
      const leftPx = 20 + (percent * trackWidth);

      marker.style.left = `${leftPx}px`;
      
      const trackFill = document.getElementById('trackFill');
      trackFill.style.width = `${percent * trackWidth}px`;
    }

    // Initialize
    window.addEventListener('resize', () => {
      const slider = document.getElementById('slider');
      updateValue(slider.value);
    });

    setMode('ten');
  </script>
</body>
</html>

What if you are counting much bigger piles of items, like 230 buttons? Can we use the same idea with hundreds?

To round to the **nearest hundred**, find which two hundreds your number sits between. For 230, the two benchmarks are 200 and 300.

<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<meta name="aspect-ratio" content="4:3">
<style>
  * { box-sizing: border-box; margin: 0; padding: 0; }
  body {
    font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
    background: #f8f9fa;
    color: #1e2945;
    display: flex;
    flex-direction: column;
    align-items: center;
    justify-content: space-between;
    padding: 16px 12px;
    min-height: 100%;
    user-select: none;
    -webkit-user-select: none;
  }

  .preset-row {
    display: flex;
    gap: 8px;
    width: 100%;
    max-width: 440px;
    justify-content: center;
  }

  .preset-btn {
    flex: 1;
    padding: 8px 0;
    font-size: 15px;
    font-weight: 600;
    background: #ffffff;
    border: 1px solid #e2e8f0;
    border-radius: 8px;
    color: #475569;
    cursor: pointer;
    transition: background 0.2s, color 0.2s, box-shadow 0.2s;
    text-align: center;
  }

  .preset-btn.active {
    background: #22b7ff;
    color: #ffffff;
    border-color: #22b7ff;
    box-shadow: 0 2px 6px rgba(34, 183, 255, 0.35);
  }

  .line-wrapper {
    position: relative;
    width: 100%;
    max-width: 460px;
    height: 180px;
    margin: 10px 0;
    display: flex;
    align-items: center;
  }

  svg {
    width: 100%;
    height: 100%;
    overflow: visible;
  }

  .slider-box {
    width: 100%;
    max-width: 440px;
    display: flex;
    flex-direction: column;
    align-items: center;
    gap: 6px;
  }

  .slider {
    width: 100%;
    height: 6px;
    border-radius: 3px;
    background: #cbd5e1;
    outline: none;
    appearance: none;
    -webkit-appearance: none;
    cursor: pointer;
  }

  .slider::-webkit-slider-thumb {
    -webkit-appearance: none;
    width: 24px;
    height: 24px;
    border-radius: 50%;
    background: #22b7ff;
    border: 3px solid #ffffff;
    box-shadow: 0 2px 5px rgba(0, 0, 0, 0.2);
    cursor: grab;
  }

  .slider::-moz-range-thumb {
    width: 24px;
    height: 24px;
    border-radius: 50%;
    background: #22b7ff;
    border: 3px solid #ffffff;
    box-shadow: 0 2px 5px rgba(0, 0, 0, 0.2);
    cursor: grab;
  }

  .result-banner {
    background: #ffffff;
    padding: 8px 16px;
    border-radius: 20px;
    font-size: 16px;
    font-weight: 700;
    display: flex;
    align-items: center;
    gap: 8px;
    box-shadow: 0 1px 4px rgba(0,0,0,0.06);
    border: 1px solid #e2e8f0;
  }

  .result-banner .tag {
    font-size: 12px;
    font-weight: 700;
    padding: 3px 8px;
    border-radius: 12px;
    text-transform: uppercase;
    letter-spacing: 0.5px;
  }

  .tag-down {
    background: #e0f2fe;
    color: #0284c7;
  }

  .tag-up {
    background: #dcfce7;
    color: #16a34a;
  }
</style>
</head>
<body>

  <div class="preset-row">
    <button class="preset-btn active" data-val="230">230</button>
    <button class="preset-btn" data-val="250">250</button>
    <button class="preset-btn" data-val="280">280</button>
  </div>

  <div class="line-wrapper">
    <svg viewBox="0 0 400 160">
      
      <rect x="40" y="70" width="160" height="20" fill="#e0f2fe" opacity="0.6" rx="4" />
      <rect x="200" y="70" width="160" height="20" fill="#dcfce7" opacity="0.6" rx="4" />

      
      <line x1="40" y1="80" x2="360" y2="80" stroke="#94a3b8" stroke-width="4" stroke-linecap="round" />

      
      <path id="roundArc" d="M 136 64 Q 88 20 40 68" fill="none" stroke="#22b7ff" stroke-width="3" stroke-dasharray="5 5" />
      <polygon id="arcArrow" points="40,72 35,60 45,60" fill="#22b7ff" />

      
      <line x1="40" y1="68" x2="40" y2="92" stroke="#64748b" stroke-width="3" />
      <circle id="node200" cx="40" cy="80" r="7" fill="#0284c7" />
      <text x="40" y="112" font-size="15" font-weight="700" text-anchor="middle" fill="#1e2945">200</text>
      <text x="40" y="128" font-size="11" font-weight="600" text-anchor="middle" fill="#64748b">Benchmark</text>

      
      <line x1="200" y1="62" x2="200" y2="98" stroke="#f59e0b" stroke-width="2" stroke-dasharray="3 3" />
      <circle cx="200" cy="80" r="4" fill="#f59e0b" />
      <text x="200" y="112" font-size="14" font-weight="700" text-anchor="middle" fill="#d97706">250</text>
      <text x="200" y="128" font-size="11" font-weight="600" text-anchor="middle" fill="#d97706">Halfway</text>

      
      <line x1="360" y1="68" x2="360" y2="92" stroke="#64748b" stroke-width="3" />
      <circle id="node300" cx="360" cy="80" r="7" fill="#cbd5e1" />
      <text x="360" y="112" font-size="15" font-weight="700" text-anchor="middle" fill="#1e2945">300</text>
      <text x="360" y="128" font-size="11" font-weight="600" text-anchor="middle" fill="#64748b">Benchmark</text>

      
      <g id="targetGroup" transform="translate(136, 0)">
        <line x1="0" y1="52" x2="0" y2="80" stroke="#1e2945" stroke-width="2" />
        <circle cx="0" cy="80" r="6" fill="#1e2945" />
        <rect x="-24" y="24" width="48" height="24" rx="6" fill="#1e2945" />
        <text id="targetText" x="0" y="40" font-size="13" font-weight="700" fill="#ffffff" text-anchor="middle">230</text>
      </g>
    </svg>
  </div>

  <div class="slider-box">
    <input type="range" class="slider" id="valSlider" min="200" max="300" value="230" step="5">
  </div>

  <div class="result-banner">
    <span id="equationText">230 ≈ 200</span>
    <span id="roundTag" class="tag tag-down">Round Down</span>
  </div>

<script>
  const slider = document.getElementById('valSlider');
  const targetGroup = document.getElementById('targetGroup');
  const targetText = document.getElementById('targetText');
  const equationText = document.getElementById('equationText');
  const roundTag = document.getElementById('roundTag');
  const node200 = document.getElementById('node200');
  const node300 = document.getElementById('node300');
  const roundArc = document.getElementById('roundArc');
  const arcArrow = document.getElementById('arcArrow');
  const presetBtns = document.querySelectorAll('.preset-btn');

  function update(val) {
    val = parseInt(val, 10);
    slider.value = val;

    // Position mapping: 200 -> x=40, 300 -> x=360
    const x = 40 + ((val - 200) / 100) * 320;
    targetGroup.setAttribute('transform', `translate(${x}, 0)`);
    targetText.textContent = val;

    const roundsUp = val >= 250;
    const rounded = roundsUp ? 300 : 200;

    equationText.textContent = `${val} ≈ ${rounded}`;

    if (roundsUp) {
      roundTag.textContent = 'Round Up';
      roundTag.className = 'tag tag-up';
      node300.setAttribute('fill', '#16a34a');
      node200.setAttribute('fill', '#cbd5e1');

      // Arc towards 300
      const midX = (x + 360) / 2;
      const heightY = Math.max(10, 60 - (360 - x) * 0.25);
      roundArc.setAttribute('d', `M ${x} 64 Q ${midX} ${heightY} 360 68`);
      roundArc.setAttribute('stroke', '#16a34a');
      arcArrow.setAttribute('points', '360,72 355,60 365,60');
      arcArrow.setAttribute('fill', '#16a34a');
    } else {
      roundTag.textContent = 'Round Down';
      roundTag.className = 'tag tag-down';
      node200.setAttribute('fill', '#0284c7');
      node300.setAttribute('fill', '#cbd5e1');

      // Arc towards 200
      const midX = (x + 40) / 2;
      const heightY = Math.max(10, 60 - (x - 40) * 0.25);
      roundArc.setAttribute('d', `M ${x} 64 Q ${midX} ${heightY} 40 68`);
      roundArc.setAttribute('stroke', '#0284c7');
      arcArrow.setAttribute('points', '40,72 35,60 45,60');
      arcArrow.setAttribute('fill', '#0284c7');
    }

    // Update preset active class
    presetBtns.forEach(btn => {
      btn.classList.toggle('active', parseInt(btn.dataset.val, 10) === val);
    });
  }

  slider.addEventListener('input', (e) => update(e.target.value));

  presetBtns.forEach(btn => {
    btn.addEventListener('click', () => update(btn.dataset.val));
  });

  update(230);
</script>
</body>
</html>

The halfway mark between 200 and 300 is 250. Because 230 is before the halfway mark, we **round down** to 200.

Whenever you round, find your two benchmarks and check the halfway point to see which way to jump!

math

Rounding Whole Numbers to the Nearest 10 and 100. Round multi-digit numbers to the nearest ten and hundred using number line benchmarks.

Rounding to the Nearest 10 and 100 on the Number Line

How to Round Numbers to the Nearest 10, 100 and 1000 (CfE Second Level Maths)

Reasoned Rounding: Games and Visual Tasks for Primary Mathematics

Pedagogical strategy focuses on concrete-pictorial-abstract (CPA) scaffolding: begin with physical and vertical number lines to anchor spatial distance and boundary multiples before introducing rhyme-based or purely symbolic rules ('$5$ or more raise the score'). Emphasize real-world estimation contexts to fulfill CfE MNU 2-01a, guiding learners to consistently reflect on whether their rounded estimate makes sense in context.

Rounding Whole Numbers to the Nearest 10 and 100

Rounding to the Nearest Ten

The Halfway Rule

Rounding to the Nearest Hundred